fea in practice_2011 (presentation slideshow)

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Finite Element Analysis in Practice


Introduction



Overview

• This course is taught with a mixture of theoretical information and applied finite element analysis (FEA) using the

software. Concepts are illustrated with simple, hands-on exercises.

• Models are created that illustrate a broad range of topics including theory, element types, analysis types, meshing techniques, results evaluation, and more.

Autodesk® Algor® Simulation Professional


What is FEA?

• FEA is a mathematical solution to engineering problems where a physical model is divided into discrete components.

• FEA models are defined by nodes and elements (commonly called a mesh).


• Basic engineering equations, such as Hooke’s law, are solved at the nodes and elements.

• A matrix equation, including terms from each element, is solved.

What is FEA?


What is FEA?

• Predicts changes within the element (for example, deformation and stress).

• The results are plotted on the model using colors to show the lowest and highest values.


• Provides a non-destructive means of testing products.

• Faster prototyping for “what if” scenarios.

• Design optimization.

• Speed up time to market by shortening the design cycle.

Why Use FEA?


Best Practices

• FEA requires engineering judgment. In the best case, you should know the approximate answer before you begin.

• Proper selection of elements, materials, loads, constraints, and analysis parameters comes from experience.


• Understand that the computer model never exactly matches reality (it’s only an approximation).

• The surest route to failure in FEA is to underestimate the complexity of the technology.

Best Practices


• The link below may be used to access examples of various types of FEA models from different industries: Algor® Simulation Software in Action

FEA in Different Industries

http://www.algor.com/products/analysis_replays/default.asp


FEA Overview and Examples using

Autodesk® Algor® Simulation



The Basic Steps of FEA

Define FEA Model –

Element and Analysis Details

Define Loads and Constraints

Review Results and Create Presentations

Build/Mesh a Model

Analyze Model (Solve)


Example Using Algor® Simulation

Set up Analysis Type, Element Type/Data, Materials, and Analysis Parameters within the FEA Editor Environment

Apply Loads and Constraints within the FEA Editor Environment

Review Results within the Results Environment and Create an HTML Report within the Report Environment

Create the Mesh within the FEA Editor Environment

Analyze the Model (Solve)


Algor® Simulation User Interface• A. Title bar

• B. Menu bar

• C. Toolbars

• D. Tree view

• E.ViewCube

& View Controls

• F. DisplayArea

• G. Miniaxis & Scale Ruler

• H. Status bar


Create Mesh

• Open and mesh models from CAD solid modelers or universal files.

• Generate 2-D and 3-D meshes from sketches.

• Add lines to existing meshes.


Assign FEA Parameters

• Assign element types and parameters.

• Assign material properties.

• Apply loads and constraints.

• Assign analysis parameters.

• Analyze the model.


Review Results

• Results Environment

– Review the model setup.

– Review the analysis results.

– Create images or animations of results.


Present Results

• Report Environment

– Generate a report of the analysis for presentation purposes.

– Add images or animations.

– View summary and log files from the analysis.


Introductory Example



• Select “File: Open...”

• Change the file type to “STEP (*.ste, *.stp, *.step)”

• Select “MotorMount.stp”

• Choose model’s existing units when prompted.

(Note: The CAD model’s length unit is inches. STEP files may be rescaled on import if desired.)

• Choose “Linear: Static Stress with Linear Material Models” when prompted.

Opening the Model


• Go to the model mesh settings dialog (“Mesh: Model Mesh Settings…”).

• Move the Mesh Size slider to 75% of the default mesh size.

• Create a mesh by pressing the “Mesh model” button.

• As desired, choose “Yes” or “No” when asked if you wish to view the meshing results.

Creating a Mesh


• Select the Material headings in the model tree view for all three parts by clicking on the first one and holding down the <Ctrl> key while clicking on the second and third ones.

• Right-click on any of the selected headings and choose “Modify: Materials...”.

• Select “Steel (ASTM-A36)”, which is near the bottom of the listed materials in the “Steel” folder, and click the “OK” button.

Applying the Materials


• Rotate the view as required to see the top surfaces of the brackets.

• Use the surface selection option.

• Select the two top surfaces of the brackets.

• After the surfaces are selected, right-click and select “Add: Surface Forces...”

• Specify a magnitude of 75 lbf (this is the force per surface). Keep the default “Normal” direction.

Applying the Loads


• Rotate the model as required to see the surfaces of both holes running through the shaft.

• Select the inside surfaces of both holes. (Note: There are two surfaces per hole.)

• After the surfaces are selected, right-click and select “Add: Surface Boundary Conditions...”.

• Press the “Fixed” button and then the “OK” button.

Applying the Constraints


• Run the analysis by selecting “Analysis: Perform Analysis...”.

• Once the analysis is complete, the von Mises stress results will appear.

Reviewing the Results


Creating a Report• Select the “Report” tab at the bottom of the screen or go to the “Tools:

Report” menu command.

• Select the “HTMLReport” heading.

• Right-click and selectthe “Configure Report”command.

• The configure reportscreen may be used toreorder the contents ofthe report and to customize user-definedcontent. (Image shownwith optional Autodesk®

logo activated.


Additional Examples

Refer to the “Tutorials” command within the software’s “Help” menu for

additional analysis examples.


FEA Concepts



What is a DOF?

• The unknowns in a finite element problem are referred to as degrees of freedom (DOF).

• Degrees of freedom vary by element and analysis type.

DOF Type Action Application

Displacement Force Structural

Temperature Heat Flow Rate Thermal

Velocity Fluid Flow Rate Fluid

Voltage Electromotive Force (EMF) Electrostatic


What is a DOF?

Node

Uy

Rot x

Rot y

UzRot z

Ux


Node

• A node is a coordinate location in space where the DOF are defined. The DOF of this point represent the possible response at this point due to the loading of the structure.


Element

• An element is a mathematical relation that defines how the DOF of a node relate to the next. These elements can be lines (beams), areas (2-D or 3-D plates) or solids (bricks and tetrahedra).


Nodes and Elements

• A node has a given set of DOF, which characterizes the response. For structural analyses, these DOF include translations and rotations in the three global directions.

• The type of element being used will also characterize which type of DOF a node will have.

• Some analysis types have only one DOF at a node. An example is the temperature in a heat transfer analysis. Heat flow rates are calculated from the nodal temperatures and the material thermal conductivity (no flow DOF).


Element Connectivity(Conventional Bonding)

• Elements can only transfer loads to one another via common nodes.

No CommunicationBetween the Elements

CommunicationBetween the Elements


Element Connectivity(“Smart Bonding”)

With "Smart Bonding" it is possible to connect adjacent parts to each other without having to match the meshes (i.e., common nodes at part boundaries are no longer mandatory). This feature is available for both CAD and hand-built models and is applicable to the following analysis types:

• Static Stress with Linear Material Models• Natural Frequency (Modal)• Transient Stress (Direct Integration)


Element Connectivity(“Smart Bonding” – continued)

Smart bonding is disabled by default for new models and for legacy models. The option may be changed within the "Contact" tab of the Analysis Parameters dialog. Note that where nodal coordinates do not fall within the default or user-specified tolerance for matching, the nodes will be bonded by means of multipoint constraint equations (MPCs). This is indicated below by the white nodes…


Stress and Strain Review

• The basic stress and strain equations:


Stress

• Basic equations do not require the use of a computer to solve.

• Computer-based analysis is needed when complexity is added as follows:

–Geometric complexity makes the elasticity equation difficult or impossible to solve.

–Variations in material properties exist throughout the part.

–Multiple load cases and complex or combined loading exists.

–Dynamics are of interest.


General Case

• The DOF components of each element combine to form a matrix equation:

[K] {d} = {A}

– [K] = element stiffness components

– {d} = DOF results (unknown)

– {A} = action value (e.g., force, temperature)


Structural FEA Equation

• To determine the displacement of a simple linear spring under load, the relevant equation is:

{f} = [K] {d}

Known Unknown

where {f} = force vector[K] = stiffness matrix{d} = displacement vector


FEA Equation Solution

• This can be solved with matrix algebra by rearranging the equation as follows:

{d} = [K] {f}-1


Calculation of s and e

• Strains are computed based on the classical differential equations previously discussed.

• Stress can then be obtained from the strains using Hooke’s law (F = kx).


Dynamic Equation

• For a more complex analysis, more terms are needed. This is true in a dynamic analysis, which is defined by the following equation:

{f} = [K] {d} + [c] {v} + [m] {a}

where... {f} = force vector[K] = stiffness matrix{d} = displacement vector[c] = damping matrix{v} = velocity vector[m] = mass matrix{a} = acceleration vector


Other Applications

• FEA can be applied to a wide variety of applications such as:

–Dynamics

–Nonlinear Materials

–Heat Transfer

–Fluid Flow

–Electrostatics


Exercise A – FEA Example by Hand

• Draw trusses in the XY plane

• No TZ DOF (2-D)

• F = 10,000 lb

• A = 2 in2

• E = 30 x 106 psi

• L = 120 in

• = 45°

L

FL

Node1

Node 2

Node3

Node 4

y

x


Element Stiffness Matrix Formulation(General Case)

ntdisplacemeDsc

where

D

D

D

D

scsscs

csccsc

scsscs

csccsc

L

EAk

DDDD

ii

y

x

y

x

i

iiiElement

yxyx

),sin(),cos(

...

2

2

1

1

22

22

22

22

2211

(All Z-translation is constrained and, therefore, not considered for this example.)

Li

Node 1

Node 2

i

y

x


Element 1

y2

x2

y1

x1

6

1

y2x2y1x1

D

D

D

D

1010

0000

1010

0000

120

10x302k

DDDD

L

= 90º

F

Node1

Node 2

y

x


Element 2

y3

x3

y1

x1

6

2

y3x3y1x1

D

D

D

D

½½½½

½½½½

½½½½

½½½½

2120

210x30k

DDDD

y

xF

Node1

Node3

= 45º


Element 3

y4

x4

y1

x1

6

3

y4x4y1x1

D

D

D

D

0000

0101

0000

0101

120

10x302k

DDDD

y

x

FL

= 0ºNode1

Node 4


Global Stiffness Matrix Assembly

y4

x4

y3

x3

y2

x2

y1

x1

6

y4x4y3x3y2x2y1x1

D

D

D

D

D

D

D

D

000000000000000000000000

000100000000000000000100

00000004

200

4

200000000

4

200

4

20

00000004

200

4

200000000

4

200

4

20

000000000000100000001000

000000000000000000000000

00000004

200

4

200010000

4

210

4

20

00010004

200

4

200000000

4

201

4

20

120

10x302K

DDDDDDDD

Each entry in the global stiffness matrix is the sum of the cell values for the three individual element matrices (in order of ascending element number).


Global Stiffness Matrix

Struck out values are where there is no DOF, due to nodal constraints. This simplifies the solution to a 2x2 matrix for this example.

00000000

01000001

00354.0354.000354.0354.0

00354.0354.000354.0354.0

00001010

00000000

00354.0354.010354.1354.0

01354.0354.000354.0354.1

)000,500(K


Force and Displacement Vectors

y4

x4

y3

x3

y2

x2

y1

x1

F

F

F

F

F

F

000,10F

0F

F

0D

0D

0D

0D

0D

0D

D

D

D

x4

x4

y3

x3

y2

x2

y1

x1


Displacement and Stress Results

in0158579.0D

in00414214.0D

y1

x1

psi3.035,1

psi6.464,1

psi5.964,3

3

2

1

Displacements are found by solving the equation… {F} [K]-1 = {D}This is simply Hooke’s law, in matrix notation, with the terms arranged as required.

Once displacements are known, element strains can be determined.Finally, the stress can be determined via the equation…


Algor® Simulation Model


Algor® Simulation Results

in0159.0D

in00414.0D

y1

x1

psi036,1

psi464,1

psi964,3

3

2

1


Analysis Options



Choosing an Analysis Type

• The first decision in the FEA process is to decide what type of analysis you need to run.

• The analysis type will dictate what type of results you will obtain.

• For example, if you need the displacement of your part, then you will need to run a structural analysis.


Analysis Options• Linear

– Linear static– Linear dynamics (incl. eight

analysis types + DDAM)

• Nonlinear

– Nonlinear static– MES – Modal w/ nonlinear materials– Riks (post buckling & collapse)

• Thermal

– Steady-state heat transfer– Transient heat transfer

• Fluid Flow

– Steady fluid flow– Unsteady fluid flow– Flow through porous media– Open channel flow

• Electrostatic

– Current and voltage– Field strength and voltage

• Mass Transfer

– Transient mass transfer

• Multiphysics

– Steady coupled fluid flow and thermal

– Transient coupled fluid flow and thermal


Structural

• Linear static

–Small changes in stiffness.

–No changes in loading direction.

–Material remains in the linear elastic range.

–Small deformation and strain.


Structural (continued)

• Linear dynamics

–Natural frequency (modal)

–Natural frequency (modal) with load stiffening

–Response spectrum

–Random vibration

–Frequency response

–Transient stress (direct integration)

–Transient stress (modal superposition)

–Critical buckling load

–Dynamic Design Analysis Method (DDAM)



• Nonlinear/MES

–Linear and nonlinear material models.

–Large deformation and strain.

–Failure due to:• Material yielding.

• Local and structural buckling.

–Permanent deformation – residual stress.

–Large-scale motion.



• Nonlinear/MES

–Surface-to-surface contact

– Impact

–Creep


Thermal

• Steady-state heat transfer

–Steady-state conditions

• Transient heat transfer

–Time-varying conditions


Fluid Flow

• Steady fluid flow

• Unsteady fluid flow

• Flow through porous media

• Open channel flow


Electrostatic

• Electrostatic current and voltage

• Electrostatic field strength and voltage


Mass Transfer

• Transient mass transfer

–Mass transfer refers to mass in transit due to gradients in the concentration of species within a mixture, and the transfer is due to random molecular motion. A typical application example is chemical species migrating through a membrane.


Element Options



Choosing an Element Type

• Selecting the type of element will depend on the following:

–Analysis type selected.

–How you create your mesh.

–Assumptions you can make about geometric properties.


Element Categories• Line Elements: A line connecting 2 nodes (representing

beams, trusses, springs, actuators, pipes, and so on).

• Area (2-D) Elements: YZ-planar elements that are each triangular or quadrilateral (3 or 4 lines enclosing an area). These elements can represent thin parts, cross-sections of a specified thickness, or radial cross-sections of axisymmetric parts.

• Area (3-D Planar) Elements: Planar or nearly planar elements in 3-D space. Each must be triangular or quadrilateral and represents a thin part with a specified thickness. The plane of the element is at the midplane of the part it represents.

• 3-D Solid Elements: Must be enclosed volumes with 4, 5, or 6 triangular and/or quadrilateral faces and with 4, 5, 6, or 8 corner nodes.


Meshing and Modeling



Proper Modeling Techniques

• For any region (3, 4, 5, 6 or 8-nodes), to be a valid element, it:–Must consist of either three or four undivided line

segments (forming triangular or quadrilateral faces). If an element edge consists of multiple line segments, the region is invalid.

–Must not have curved or arched sides. The exception to this is second order elements, where midside nodes are located on the original surface for curved, CAD-based geometry.


• Certain shapes can create elements which are not recommended for FEA analysis. The following regions will be eliminated, requiring adjustment of the geometry or meshing parameters:o Regions with any collinear or concave sides.

o Regions with excessive curvature relative to the element size (causing non-flat, excessively warped element faces).

Proper Modeling Techniques (continued)


Valid and Invalid Regions

Proper Modeling Techniques (continued)


Meshing Guidelines

• Meshing can be completed either by using automatic mesh engines, semiautomatic structured meshing tools, or by creating a mesh completely “by hand”.

• Automatic mesh generation is usually completed on CAD solid models or within outline sketches (for 2D models).

• Semiautomatic meshing tools and “hand” meshing techniques are generally used for simple models where a structured mesh is desirable.


Structured Meshing Tools• Regions can be meshed based on user-

specified coordinates and edge divisions using the following commands:

– “Mesh: Structured Mesh: 3 Point Triangular…”– “Mesh: Structured Mesh: 4 Point Rectangular…”– “Mesh: Structured Mesh: 8 Point 3-D…”

• Meshes can be generated from bounding edges represented by construction lines and arcs using the following commands:

– “Mesh: Structured Mesh: Divide 1 Object…”– “Mesh: Structured Mesh: Between 2 Objects…”– “Mesh: Structured Mesh: 4 Object 3-D…”


“Hand” Meshing• There are two types of “hand” meshing—

building from scratch and building from a sketch or wireframe.

• Building from scratch:

–Draw the elements by hand one at a time, line-by-line, to create a structured mesh.

• Building from a sketch or wireframe:

–Build a 2-D sketch or 3-D wireframe of the model using construction objects and apply a watertight surface mesh using the 2-D mesh engine and/or structured meshing tools. Use an automatic solid mesh engine to generate internal elements for3-D parts, or extrude planar meshes into solids.


Extruding Lines and Planar Meshes

• Selected lines or 1 object meshes may be extruded into surfaces. Planar meshes (hand drawn or from structured meshing tools) may be extruded into solids. Use one of the following three commands with the “Copy” and “Join” options enabled to do so:

–Move or Copy…–Rotate or Copy…–Scale or Copy…

(These three operations may be combined to simultaneously move, rotate, and scale the selected lines or mesh into a surface or solid structure.)


Loads and Constraints



Introduction to Loads & Constraints

• You will have to decide what type of loads and constraints will properly define the engineering criteria for the model.

• In FEA, there are different types of loads and constraints for each analysis type.

• Applying the proper loads and constraints is one of the most important factors in getting the correct answer.

• Always double-check your model.


• There are multiple ways to apply different loads and constraints to a model:

–Nodal Loads and Constraints

–Edge Loads and Constraints

–Surface Loads and Constraints

–Element Loads (this includes part-based or global loads). An example is gravity or acceleration. Other examples are axial preloads, end releases, and neutral axis offsets applied to beam elements.

Introduction to Loads & Constraints (continued)


Structural Nodal Loads

• Displacements

• Forces

• Lumped Masses

• Moments

• Temperatures (thermal stress)

• Voltages (piezoelectric materials)


Structural Nodal Constraints

• Boundary Conditions: Prevent specified DOF from undergoing translation or rotation in a specified direction.

• Boundary Elements: Act like a spring with a specified stiffness along a specified direction.


Structural Nodal Constraints(continued)

• Using Boundary Conditions to Model Symmetry

–Along the line or plane of symmetry, boundary conditions must be applied to represent the symmetrical part, as follows:

• Out-of-plane displacement = 0

• Two in-plane rotations = 0


Structural Nodal Constraints (continued)

Plane of Symmetry

P P

Line of Symmetry

P


Structural Nodal Constraints(continued)

• Using Boundary Conditions to Model Antisymmetry (where the part is symmetrical but the loads act in opposite directions)

–Along the line or plane of antisymmetry, boundary conditions must be applied to represent the part, as follows:

• Out-of-plane rotation = 0

• Two in-plane displacements = 0


Structural Nodal Constraints (continued)

Plane of Antisymmetry

P P

Line of Antisymmetry

P


Boundary Conditions

• Proper boundary conditions are necessary for an accurate analysis.

• The global stiffness of the system must be modeled correctly for any local behavior to be captured correctly.


Boundary Conditions (continued)

• Two of the most unwanted FEA effects to watch out for are:

–Overstiffening

–Understiffening

• Unlike the real-world equivalent, constraints in FEA are perfect.


Linear Surface Loads

• Uniform or Hydrostatic Pressure and Traction

– Applied to the faces of plate, composite, brick, shell, and nonlinear membrane elements.

– Applied to the edges of 2-D elements (though selected as surfaces because the edges represent surfaces).

• Surface Force

– Can specify magnitude and direction of a force that will be evenly distributed over a given surface.


Linear Surface Loads (continued)

• Variable Pressure or Traction

–Define a function of the position (i.e., the X-, Y- and/or Z-coordinates along the surface) that controls the varying magnitude of the load acting on the surface.


Surface and Edge Constraints

Note: The same boundary constraints, including symmetry/antisymmetry, described previously under “Structural Nodal Constraints” are also available and applicable to surfaces and edges.


Linear Element Loads

• Gravity/Acceleration

–Can specify gravitational or general acceleration value and direction. You must have a mass density defined for each part.

• Centrifugal Loads

–Specify center of rotation, angular velocity and angular acceleration values.

• Distributed Loads

–Specify the magnitude and direction at each end of beam elements.


Truss Elements



Truss Elements

• Truss elements are two-node members, which allow arbitrary orientation in the X, Y, Z system.

• The truss transmits axial force only and, in general, is a three DOF element (i.e., three global translation components at each end of the member). Trusses are used to model structures such as towers, bridges, and building framework (skeletons).


Truss Elements (continued)

• Guidelines for using truss elements:

–The length of the element is much greater than the width or depth (approximately 8-10 times or more).

–The connections to the rest of the model are as ball joints that do not transfer moments.

–The external forces are applied only at joints.


Exercise B – Truss Frame Model

• Material: Aluminum (6061-T6).

• Loads: Nodal forces as shown in the image to the right.

• Constraints: – Fully fixed at Point A.

– Ty and Tz constrained at Point G.

– The rest of the model will have Tzconstrained.

• Objective: Construct and analyze a frame of truss elements loaded with 2 nodal forces.

• Geometry: Cross-sectional area = 1 in2.


Beam Elements



Beam Elements

• Beam elements are slender structural members that offer resistance to axial forces, bending, and torsion under applied loads.

• Beams are found in building frames, transmission towers, and bridges.

• A beam differs from a truss in that a beam resists moments (twisting and bending) at the connections.


Beam Elements (continued)

• In addition to the two nodes defining the location and length of the element, beams use a third node (auxiliary vertex) to define the orientation of the cross-section. The location of the auxiliary vertex is controlled by the surface number of the beam element lines or may be manually specified at a custom coordinate location for selected lines.

• Cross-sectional properties are defined for bending about both the strong and weak axes and for torsional resistance.


NOTE: For details concerning beam element orientation, access the “Contents” tab of the Help files, go to “Autodesk Algor Simulation: Setting Up and Performing the Analysis: Setting Up Part 1: Linear: Element Types and Parameters: Beam Elements.” Scroll down the resultant page, and click on the “Beam Element Orientation” heading.



• Guidelines for using beam elements:

– The length of the element is much greater than the width or depth.

– The cross-section of the element is constant. (Note: A variable cross-section wizard is available for approximating tapered beam spans via a series of multiple elements, each having a constant cross-section that differs from the adjacent beam elements.)

– The element is able to transfer moments, though end releases are available to simulate pinned or slotted connections.

– The element is able to handle a load distributed along its length.



Exercise C – Support Beam Under Gravity

• Objective: Determine the maximum deflection of thebeam due to its own weight.

• Geometry: W10 x 100 cross-section.

• Material: Steel (AISI 4130).

• Loads: Gravity in the -Y direction.

• Constraints: – Far end has constraints against all DOF except Rz.

– Near end has constraints against all DOF except Tx and Rz.


2-DElements



2-D Elements

• Two-dimensional elements, with three or four corner nodes, that are formulated in the Y-Z plane. They are used to model any part or assembly that can be accurately represented using a 2-D outline or cross-section and for which 2-D loading and constraint assumptions are valid (examples to follow).


2-D Elements (continued)

• 2-D Geometry Types

–Axisymmetric: For parts that are represented by cross-sections revolved about an axis (such as a bearing, shaft seal, or hydraulic cylinder).

–Plane strain: A cross-section of an object of semi-infinite length, having no deflection normal to the cross-section (such as a large dam).

–Plane stress: Objects of finite thickness with no stress normal to the cross-section (such as a plate under in-plane loads).


• Within the FEA Editor environment, create wireframe sketches for each part.

• Use the 2-D mesh engine to generate the 2-D elements within the sketch outlines.

2-D Elements (continued)


Exercise D - Axisymmetric Thick-walled Cylinder

• Objective: Determine the hoop stress at the inner radius of the cylinder from the applied pressure load.


• Loads: Uniform internal pressure of 10,000 psi.

• Constraints: The bottom surface will have Tz constrainted.


Plate/ShellElements



Plate/Shell Elements

• Plate/shell elements have three or four corner nodes are planar (or nearly planar), and are formulated in 3-D space. These elements are used to model and analyze thin objects such as pressure vessels and automotive body parts.

• A numerical thickness is assigned to the elements but the model geometry itself has no thickness.

• Stresses are assumed to vary linearly through the thickness.


Plate/Shell Elements (continued)

• Guidelines for using plate/shell elements:

–The thickness is small in relation to the length and width (about 1/10).

–Good for small displacements and rotations.

–Elements remain planar (i.e., no warpage).

–No rotation about the direction normal to the element.


Membrane Elements

• Planar (or nearly planar) elements, with three or four corner nodes, formulated in three-dimensional space.

• Used to model "fabric-like" objects such as tents or cots, or structures such as the roof of a sports stadium.

• Represent thin solids of a specified thickness that exhibit no stress normal to the thickness.


Composite Elements• There are two types of composite

elements—thin and thick. Thick composites have a core layer that is typically much thicker than the other laminae.

• Each element can have multiple laminae, each with different material properties and fiber orientations.

• Multiple failure criteria are available.

• As with plates and membranes, the thickness, in this case for each lamina, is defined numerically (not graphically).


Exercise E - Plate Under Uniform Pressure

• Objective: Determine the maximum stress in the plate from the applied pressure load. Use the 4 Point structured meshing tool to make the plate.

• Geometry: The plate is 10” x 5” x 0.25”.


• Loads: Uniform pressureof 50 psi.

• Constraints: – The two long edges will have

Ty and Tz constraints.

– One short edge will have Txand Tz constraints.


Brick Elements



Brick Elements

• Brick elements are four-, five-, six- or eight-node elements formulated in three-dimensional space.

• Brick elements should be used for solids with irregular shapes and when the stress through the thickness of a part is important.


Exercise F – Cantilever Beam Model• Objective: Using brick

elements, determine themaximum bending stressin the beam from theapplied load.

• Material: Steel (4130).

• Loads: 10,000 pounds distributedacross the free end.

• Constraints: – The center horizontal row of nodes (running in the Y-direction)

at the fixed end will be fully constrained.

– The remaining nodes at the fixed end will have only the Tx constraint applied.


Comparing Element Types



Exercise G - Comparing Element Types

• Objective: Analyze a beam model using different element types and compare the results.


• Loads: 100 psi in the -Z direction on the top of the beam.

• Constraints: Fixed at the left end and simply supported at the right.

• Elements:

– 2-D: Apply a 100 psi pressure to thetop edge.

– Beam: Convert the 100 psi load over the 0.25” width to a 25 lb/in distributed load.

– Plate: Model the 10” x 0.5” dimensions with a thickness of 0.25”. Apply nodal forces equivalent to the pressure load. The forces at the end nodes should be half the magnitude of the forces at the interior nodes.

– Plate: Model the 10” x 0.25” dimensions with a thickness of 0.5”. Apply a 100 psi pressure load in the –Z direction to the surface of the plate elements.

– Brick: Apply a 100 psi pressure to the top surface.


Comparison of Results

Element TypeDisplacement Magnitude (inch)

X-Reaction Moment * (in-lb)

Shear Force *(lb)

y *

Max.(psi)

y *

at mid-span

(psi)

yz

Max.(psi)

2-D 0.01751 ** ** 28,349 14, 976 1,625

First Plate Model(0.25" Thick)

0.01751 ** ** 28,349 14,976 1,625

Beam 0.01761 311.9 156.2 29,933 15,024 **

Second Plate Model (0.5" Thick)

0.01722 313.5 *** ** 30,413 14,929 **** **

Brick 0.01741 ** ** 29,331 14,912 **** 1,814Values above are magnitudes. Actual results may be positive or negative.

Notes: * For the beam element part, the “Local 3 Moment” corresponds to the X-Reaction Moment; the "Local 2 Force" corresponds to the Shear Force; and the "Bending Stress in Local 3 Direction" corresponds to the bending stress ( y).

** This result type is not calculated for this element type.

*** The X-Reaction moment for the 0.5” thick plate is the sum the reactions for all fixed nodes.

**** This stress was determined at the node in the middle of the 0.25” thickness.


Mesh Convergence



Mesh Convergence

• For mesh convergence testing, it is suggested that you run at least three analyses at different mesh sizes:

–Coarse

–Fine

–Somewhere in between coarse and fine


Mesh Convergence (continued)

• Usually, you will not see much change in the direct equation solutions (such as displacements) for the differing mesh sizes.

• You will see the numerical method answers (such as stresses) converge to an answer as the mesh gets finer.


• Geometry: Thickness = 1.0”.

• Material: Stainless steel (AISI 302) cold-rolled.

• Loads: 1000 psi on one edge as shown in the image.

• Constraints: Fixed at opposite end as shown in the image.

Exercise H – Mesh Convergence

• Objective: To perform a 2-D analysis using plane stress elements, utilizing different mesh density settings of 200, 400, 800, 1600, 3200, and 6400. Use an angle setting of 30 degrees for all cases. Compare the y values.


Mesh

Density y max (psi) Reference

(psi) % difference

200 3,460.5 3,560 -2.80 400 3,448.1 3,560 -3.14 800 3,494.6 3,560 -1.84

1,600 3,544.3 3,560 -0.44 3,200 3,552.9 3,560 -0.20

6,400 3,563.4 3,560 +0.10

Mesh Convergence Example

maxy maxy


Mesh Study Wizard

• Automates the process of checking multiple mesh sizes to achieve good convergence of the stress results.

• May be performed only for CAD-based models and for the analysis type "Static Stress with Linear Material Models.“

• To access this feature, go to the command "Mesh Study Wizard," found in the Start menu within the folder "All Programs: Autodesk: Autodesk Algor Simulation: Tools."

For more information regarding how to set up and run a mesh study, go to the "Contents" tab of the help files, accessible from the “Help” pull-down menu in the user interface. Then, go to “Autodesk Algor Simulation: Meshing Overview: Mesh Overview: Meshing CAD Solid Models: Performing a Mesh Study."


Meshing CAD Solid Models



Meshing CAD Models

• Build a solid model in any CAD solid modeler.

• Using direct CAD/CAE data exchange or a universal file (IGES, STEP, ACIS), open the model in Autodesk® Algor® Simulation.

• Create a mesh on the model.


Mesh Refinement

• To optimize solution time, it is useful to create a fine mesh in areas where the results are critical and a coarser mesh in areas where the results will not be as high or as important.

• You can add refinement points to achieve localized refinement.


Exercise I - Bracket Model

• Objective: Determine the maximum stress in the bracket from a load applied at the hole.

• Material: Steel (ASTM - A514).

• Loads: 40 pounds in the -Y direction at the hole.

• Constraints: The back surface (-X end of bracket) is fully constrained.


Midplane Meshing

Refer to the software’s “Help: Tutorials” menu command. The “Computer Case CAD Model” tutorial listed under “Meshing and Modeling Tutorials” demonstrates midplane meshing.


Assembly Meshing

• When working with multiple parts in an assembly, it is critical that the meshes match between the parts if they are to interact with each other (via conventional bonded, welded, surface, or edge contact).

• If the parts that come together should be free to slide along each other or separate but not penetrate each other, then surface or edge contact should be used to produce the desired interaction.


Assembly Meshing (continued)

• Alternately, the optional feature, “Smart Bonding” may be enabled (as previously discussed under the “Element Connectivity” topic). When enabled, meshes that are not perfectly matched will be connected automatically using multipoint constraint equations (MPCs) between the mismatched nodes. The Smart Bonding settings are found within the “Contact” tab of the Analysis Parameters dialog.


Exercise J – Hanger Assembly Model

• Objective: Determine the maximum stress in the hanger assembly from a load applied at the center of the shaft.

• Mesh the model at 90% of thedefault mesh size.

• Material: Brackets: Iron, Fe Shaft: Steel (4130)

• Loads: 100 pounds in the -Y direction. Distribute over a full ring on nodes at the center of the shaft.

• Constraints: The bottom surfaces of both brackets are fully constrained.


Combining Element Types



Combining Element Types

• Any combination of element types is possible in an assembly.

• Nodes must be matched where the parts meet in order for loads to be transferred.

• The available DOF of the element types that are connected must be considered to avoid unstable geometry.


Combining Element Types (continued)

• Non-brick elements may be created using the plate/shell or midplane mesh settings; by using structured meshing tools; via tools such as “Create bolt,” “Create Joint” and “Create Remote Load” (all of which generate line elements); or they may be manually drawn.

Refer to the software’s “Help: Tutorials” menu command. The “Crank CAD Model” tutoriallisted under “Meshing and Modeling Tutorials” demonstrates the combination of brick andbeam elements.


Contact



Contact

• Select pairs of parts or surfaces in the FEA Editor environment and specify edge or surface contact.

• The nodes on the surfaces will be able to move apart from each other with no restrictions.

• The nodes will translate loads when they move together.

• An iterative solution method is used to determine which nodes are in contact.


Contact (continued)

• Contact is not considered during the first iteration. Therefore, it may be necessary to apply weak elastic boundary elements to ensure stability.

• When specifying linear contact, only the first load case is considered. Any other load case(s) defined within the Analysis Parameters dialog will be ignored.


Exercise K – Linear Contact Model• Objective: Determine the stress in the assembly

for a maximum load of 1,000 pounds appliedto the bottom of the latch. Use a meshsize of 0.15” (absolute).

• Material: Latch: Iron, FeHandle: Brass, Red

Housing & Base Plate:Steel (ASTM - A36)

• Constraints: – Four bolt holes are fully constrained.

– Weak (100 lb./in.) “rigid” boundary elements in the X, Y, and Z directions at the back face (+Y end) of the latch.

• Load: 1,000 pounds will be applied in the Z direction at the underside of the latch extension.

• Default contact should be Bonded. Surface contact should be defined between the latch and the housing, and between the latch and the base plate.


Solving Options



Introduction to Solvers

• There are many different ways to solve the matrices that were discussed earlier.

• As computers get faster, new technologies are used that create faster processing of the equations.

• You should usually accept the default settings, which are optimized for the fastest processing.


Solver Options

• Sparse

–Solves only non-zero equations

• Skyline

–Variable bandwidth

• Banded

–Fixed bandwidth

• Iterative

–Requires a tolerance and initial conditions


Results Evaluation



Result Options

• The types of results depend on the type of analysis that is performed.

• For example, a structural analysis will give you displacement and stress results while a thermal analysis will give you temperature and heat flux results.


How Results are Calculated

• The results are either calculated directly through linear equations or calculated through numerical integration methods.

• For example, displacements are calculated directly from Hooke’s law, but strains are calculated through numerical methods.


How to Justify Your Results

• The best method for justification is to run the model with different mesh sizes.

• Remember, you are approximating an area or volume with the elements.

• The better the quality of the elements, the better the results.

• Usually a fine mesh will give more accurate answers than a coarse mesh.

• Verify that reaction forces are as expected.


Structural Results

• Displacement (unit: length)

• Stress (units: force / length2)

• Strain (units: dimensionless, length/length)

• Reaction Forces (internal nodal forces)Note: Equivalent forces applied to elements to produce expansion or contraction associated with thermal effects will be included in this result.

• Residual Forces (support reactions)


Presentation of Results



Presentation Guidelines

• Use colors that will stand out from each other.

• Make presentations that everyone can understand.

• Remember that many people looking at engineering reports are not engineers.

• Have a standard report template.

• Include 3-D representations with charts and graphs.


Presentation Options

• Contour images

• Animations

• Time-dependent plots

• Report generation


Contour Images


Animations


Time-Dependent Plots


Report Generation


Other Analysis Types



Thermal Analyses



Thermal Analyses

• Steady-State Heat Transfer

• Transient Heat Transfer

The following two types of thermal analysis are available:


Thermal Elements

• Thermal elements are geometrically identical to the corresponding structural elements. The available types are:

– Rod (this is a line element)

– 2-D

– Plate

– Brick


Thermal Nodal Loads

• Initial Temperature

– Specify the temperature of a node(s) at the beginning of the analysis (transient analysis).

• Applied Temperature

– Specify a temperature at which a node(s) will be held during the analysis. A stiffness value specifies the amount of thermal energy (heat source or heat sink) available for maintaining the temperature.


Thermal Surface Loads

• Convection

–Assign a convection coefficient and the ambient temperature.

• Radiation

–Assign the radiation function and the ambient temperature.

• Heat Flux

–Assign the amount of heat added or removed per unit area.


Thermal Element Loads

• Heat Generation

–Enter the amount of volumetric heat generated in a given part.


Body-to-Body Radiation

• Define the surfaces that will exchange heat through radiation and assign emissivity values.

• Define body-to-body radiation enclosures (i.e., groups of surfaces that will radiate to/from each other).

• The processor will automatically calculate the view factors between elements.


Thermal Contact

• Used to simulate imperfect thermal conduction between two parts or the resistance of a substance that is not modeled (such as epoxy) between two parts.

• Define contact pairs in the FEA Editor environment.

• Define the resistance value between the surfaces.

• Applicable to 3D CAD, hand-built, and 2-D models.


Thermal Results

• Temperature

• Heat flux (energy / time / length2)

• Heat rate of face (energy / time)


Exercise L - Thermal Model

• Objective: Analyzethe thermal effects ofa material containing hot and cold waterpassages. Use a meshsize of 80% of default.

• Material: Steel (ASTM - A514)

• Loads:

– Largest Hole: Convection coefficient = 1.4Ambient temperature= 65°F

– Second Largest Hole: Convection coefficient = 2.8Ambient temperature = 180°F

F sec in

lbsin 2

F sec in

lbsin 2


Electrostatic Analyses



Electrostatic Analyses

• Electrostatic Field Strength and Voltage

• Electrostatic Current and Coltage

The following two types of electrostatic analysis are available:


Electrostatic Elements

• Electrostatic 2-D and brick elements are geometrically identical to the analogous structural elements.


Electrostatic Nodal Loads

• Applied Voltages

–Specify a certain voltage at which a node(s) will be held, due to a voltage source.

• Temperatures

–Specify the temperature of a node(s) to influence the electrostatic results when temperature-dependent material properties are being used.


Electrostatic Results

• Voltage (Volts or mV)

• Current (Amps or mA / length2)

• Current Rate of Face (Amps or mA)

• Electric field (voltage/length)

• Displacement field (force/voltage * length)

• Electrostatic force

• Electrostatic charge (current * time)


Electrostatic Analysis Exercise

Refer to the software’s “Help: Tutorials” menu command. Follow the “Radial Comb Motor Electrostatic Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing an electrostatic analysis.


Fluid Flow Analyses



Fluid Flow Analyses

• Steady Fluid Flow

• Unsteady Fluid Flow

• Flow Through Porous Media

• Open Channel Flow

The following four types of fluid flow analysis are available:


Fluid Flow Elements

• The fluid flow 2-D and brick elements are geometrically identical to the analogous structural elements.


Fluid Flow Loads

• Prescribed Velocity

–Can be used to specify an inlet velocity or zero velocity along a wall.

• Surface Prescribed Inlet/Outlet

• Fan Curves

–Can be used to model flow generated by intake, exhaust or internal fans.

• Rotating Frames of Reference

–Can be used to model flow in rotating machinery.

• Gravity


Fluid Flow Loads (continued)• Pressure/Traction

–Applied normal to the edge of 2-D elements (selected as surfaces since the edges represent surfaces).

–Applied normal to the face of 3-D elements.

–Applied in a specified vector direction to the edge surface of 2-D elements or the face of 3-D elements.

• Buoyancy Force

–Apply thermal results from a steady-state heat transfer analysis to a steady fluid flow analysis.

• Surface Prescribed Turbulence Condition

• Surface Prescribed Wall Roughness


Fluid Flow Results

• Velocity (length/time)

• Pressure (force/length2)

• Stress tensors (force/length2)

• Reaction forces


Fluid Flow Analysis

Refer to the software’s “Help: Tutorials” menu command. Follow the “Ball Valve Fluid Flow Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing a fluid flow analysis.


Mechanical Event

Simulation (MES)



Mechanical Event Simulation (MES)

MES overcomes many limitations of static stress analysis by accounting for…

• Geometric nonlinearity (large deformations that change the load and/or constraint positions and directions)

• Acceleration/inertia

• Damping

• Motion-enabled contact or impact (that is, surface-to-surface contact that changes over time due to motion or component deformation)

• Nonlinear material behavior (such as plastic deformation due to exceeding the material yield strength).


Mechanical Event Simulation (MES)(continued)

Other MES characteristics:

• Loads and results are time-dependent, providing many instantaneous results “snapshots” over a user-defined period of time.

• Load curves are used to define how the given loads vary over time.

• Multiple results time steps are provided for post-processing.

• Results may be graphed versus time. The integral and first or second derivative of the results may also be graphed.


Comparison of Linear Static Stress and MES

{f} = [K] {d}Where: {f} = force vector, [K] = stiffness matrix, {d} = displacement vector

Previously, we introduced the following governing equation for static stress analysis:

For MES, additional terms are included, resulting in the following equation:

}]{[ dmdcdKf

Where: [c] = damping matrix, [m] = mass matrix, = velocity vector (first derivative of displacement), = acceleration vector (second derivative of displacement)

d

d


MES – Shell Elements

• MES shell elements are similar to linear plate elements. They are triangular or quadrilateral, are planar (or nearly planar), and have three or four corner nodes.

• There are several available formulations (consult the Help files for more information).

• Composites are a subset of shell elements in MES, rather than a separate element type.


MES – Kinematic Elements

• Kinematic elements can be either 2-D or 3-D elements.

• Kinematic elements do not experience strains and do not report stresses. Otherwise, these elements behave just like flexible brick elements.

• They have an advantage over conventional brick elements because of their small contribution to the size of the global stiffness matrix. This results in faster run times.


MES – Contact Elements

• Contact elements can have different stiffness values in compression and tension.

• These elements can also have a breaking stress at which point the stiffness will be zero.

• These elements can be used to simulate cables.


MES – Coupling Elements

• Coupling elements aid in the simulation of parts that "couple" at a known length.

• This coupling is modeled by introducing a stiffness when it reaches this length. This stiffness is calculated using the modulus of elasticity, a coupling area, and the length of the element.


MES – Dashpot Elements

• Dashpot elements can be used to apply local damping to a model.

• You can specify a damping coefficient that will control how much these elements affect motion.


MES – Actuator Elements

• Actuator elements are line elements whose lengths can change over time.

• They are used to simulate defined movement of a part (such as hydraulic cylinders or solenoids).


MES – Slider Elements

• A slider element consists of two collinear lines connected at one node.

• The node in the middle will be allowed to move along the line defined by the other two points, letting the node “slide” such as if it were in a guide or slot.


MES – Pulley Elements

• Pulley elements consist of three nodes: driver, pivot, and slack.

• As the driver node moves toward or away from the pivot, the slack node will move in the opposite direction by a set relationship.


MES – Pipe Elements

• Pipe elements allow you to model piping systems under internal pressure loads.

• The pipe elements can be either straight sections or bends.


MES – Hydrodynamic Elements

• Hydrodynamic elements can be either 2-D or 3-D elements.

• These elements allow for the simulation of the interaction of fluids with solids without considering the details of the flow.


MES – Impact Planes

• Specify a wall, floor, or ceiling parallel to the global X, Y and Z axes.

• Objects will not be able to pass through this plane.


MES – Surface-to-Surface Contact

• Specify two or more surfaces that may come into contact during the event duration.

• Can include static and dynamic friction effects.

• A “slide, no bounce” option is available to prevent objects from separating once they’ve come into contact.

• Consult the Help files for more information concerning the various surface contact options and parameters.


Mechanical Event Simulation Example

For an introductory level mechanical event simulation (MES) example, refer to the software’s “Help: Tutorials” menu command. Follow the “Piston Mechanical Event Simulation” tutorial listed under “Analyzing and Evaluating Results Tutorials.”

Also, refer to “Example M” (next slide) for a more complex and challenging MES example involving surface number reassignment and surface-to-surface contact.


• Center of Joint 1 (0, 0, -0.125) & Joint 2 (1.414214, 0, -0.125): Fixed except for Rz• Center of Joint 3 (0, 0, 0.875) & Joint 4 (1.414214, 0, 0.875): Tx, Ty, Rx & Ry

constrained

Exercise M – MES, Geneva Mechanism

Slide 1 of 4


1. Before meshing, set the default contact = “Free/No Contact” and define a surface contact pair between Part 1 and Part 2, which will prevent mesh matching between the parts (this is desirable for MES contact surfaces).

2. Mesh the model at an absolute mesh size of 0.0625” (1/16th of an inch).

3. Modify line attributes to consolidate the contact surfaces. Use surface 100 for the 1st contact pair, 101 for the 2nd, and 102 for the 3rd – include chamfers. For the drive wheel, surfaces 100 and 101 will each encompass about one-third of the perimeter of the wheel’s C-shaped cylindrical contact surface.

4. From the “General Surface-to-Surface Contact” screen, redefine the first pair to be Part 1/Surface 100 to Part 2/Surface 100. Create two more pair—Part 1/ Surface 101 to Part 2/Surface 101 and Part 1/Surface 102 to Part 2/Surface 102. Set the contact element “Updating” to “Automatic.” Set the contact parameters for all three pair as follows…

• Contact problem type = “High Speed Contact (Impact)”• Contact type = “Surface to Surface”• User specified contact stiffness = 1000 lbf/in• User specified contact tolerance = 0.0011” (eliminates the effects of 0.001” part clearances

and prevents chatter, resulting in a quicker and more stable solution).

Exercise M (continued)

Slide 2 of 4


5. Create four universal joints, one at each end face of the four stub shafts, entering the specified vertex coordinates from the preceding diagram.

6. In the element definition screen for parts 1 and 2, set the analysis type to “Large Displacement.” Set the material for the drive wheel to “Brass, Red” and for the driven wheel to “Plastic – Nylon Type 6/6.” For all four joints… Change the element type to “Pipe” – In the element definition screen, set the OD to 0.1” and the wall thickness to 0.03” – The material is to be custom defined, E=100e6; all other values remain at zero.

7. Apply the nodal boundary conditions and loads specified on the preceding diagram to the center points of the four joints. For Joint 4’s lumped mass, specify a uniform mass of 0.00088 lbf·s2/in and a mass moment of inertia in the Z-direction of 0.00135 lbf·s2·in. These values simulate a steel disk 1/8” thick with a diameter of 3.5”.

Use load curve 1 for the prescribed displacement (rotation) and loadcurve 2 for the nodal moment. Load curve 1 ramps linearly from 0 to 1 in 1 second. Load curve 2 is constant at 1. Set a death time of 1 second in the active range data dialog for the prescribed displacement.


Slide 3 of 4


8. In the analysis parameters screen, set the event duration to 1 second and the capture rate to 90. This will produce a time step for every two degrees of drive wheel rotation.

9. Under the equilibrium tab of the advanced analysis parameters, uncheck the “Automatic” box for the displacement tolerance and set the value to 0.02.

10. Run the Analysis and review the results. Generate a von Mises stress animation and a plot of displacement magnitude vs. time for two nodes – one on the drive wheel’s indexing pin and one on the perimeter of the driven wheel.

* * *

NOTE: Depending upon the computer hardware, this analysis may take several hours to run. You may wish to allow several steps to converge, stop the analysis, and then load the already completed model from the provided archive file, “Exercise M\Results Archive\Exercise M.ach”.


Slide 4 of 4


Combining Analysis Types

(Multiphysics)



Multiphysics

• A multiphysics analysis combines the effects of multiple analysis types.

• The initial analysis is performed.

• Another analysis is set up using the results from the initial analysis as the loading in the subsequent analysis.

• For some analyses, iterations are required to reach a converged solution.

• Steady or unsteady coupled fluid flow and thermal analyses solve for fluid and thermal results simultaneously.


Examples of Combining Analysis Types

• Apply temperature results from a heat transfer analysis to a stress analysis to analyze thermal stress.

• Apply boundary forces from a fluid flow analysis to a stress analysis (fluid/structural interaction).

• Apply velocity results from a fluid flow analysis to a heat transfer analysis to analyze the effect of forced convection on the temperature distribution (where the temperature does not significantly influence the flow pattern).

• Apply temperature results from a heat transfer analysis to a fluid flow analysis to drive natural convection (where the flow does not significantly influence the temperature distribution).


Examples of Combining Analysis Types (continued)

• Apply current results from an electrostatic analysis to a heat transfer analysis to analyze Joule heating.

• Apply electrostatic attraction/repulsion forces from an electrostatic analysis to a stress analysis to determine displacements and stresses (commonly used in the analysis of micro electromechanical systems – MEMS).


Multiphysics Example:

Analysis of Stresses due to Electrostatic Forces

Refer to the software’s “Help: Tutorials” menu command. Follow the “Radial Comb Motor Static Stress Analysis” tutorial listed under “Analyzing and Evaluating Results Tutorials” for further information on performing a multiphysics analysis of structural stress and displacement due to electrostatic forces.


Material Models



Background on Material Models

• Material models are subsets of the element types.

• These models allow you to make decisions on what type of material properties will be used for each part in the model.

• For example, if a part will see the plastic region of a stress versus strain curve, you should select one of the von Mises material models for an elastic/plastic analysis.


Isotropic

• This is the standard material model. The material properties are independent of direction.


Orthotropic

• This material model can have different properties in the three orthogonal directions.

• The required properties are identical to the isotropic material model. However, you enter separate values for the three directions.


Temperature-Dependent

• For some elements, the properties for both isotropic and orthotropic materials can be defined on a temperature-dependent basis.

• The values are linearly interpolated between the specified temperature points.


Elastic-Plastic (von Mises)• von Mises: This material models is based on a bilinear

simplification of the stress-strain curve. The modulus for the elastic region, the yield point, and the modulus for the plastic region must be defined. If the material library includes the elastic modulus, yield point, ultimate strength, and elongation; the program will automatically calculate the plastic modulus for you.

• von Mises Curve: This material model uses either an approximated stress-strain curve or actual stress-strain data. As above, if the material library includes the elastic modulus, yield point, ultimate strength, and elongation; the approximated stress-strain curve will be generated automatically. Alternately, you may define a table of true stress-strain data (either within the material library manager or the material application screen).


Elastic-Plastic (von Mises)(continued)

• Isotropic hardening and kinematic hardening variants of the von Mises material models are available.

– Use the “von Mises with Isotropic Hardening” model for non-reversing load conditions.

– The “von Mises with Kinematic Hardening” model is recommended for greater accuracy when reversing strain cycles will occur.


Hyperelastic and Foam Material Models

• The following rubber-like (hyperelastic) material models are available:–Mooney-Rivlin – Yeoh–Arruda-Boyce – Neo-Hookean–Ogden – Van der Waals

• The following foam-like material models are available:

–Blatz-Ko

–Hyperfoam (accounts for compressibility)


Drucker-Prager

• This material model is used to model rock and concrete.


Viscoelastic and Viscoplastic

• These material models are used to account for rate-dependent material behavior due to dissipative losses from viscous effects. The viscoelastic material models are variants of the previously listed hyperelastic material models.

• A material model that can be used to model thermal creep is also available (“Thermal Creep Viscoelastic”).


Thermoelastic and Thermoplastic

• These material models are used for thermal stress analyses. The Thermoplastic model is used when stresses beyond the yield point occur.


Piezoelectric

• This material model is for parts that experience stress due to a voltage distribution.


Curve

• This material model allows you to input a bulk modulus versus strain curve to control the behavior of the part.


Reinforced Concrete

• This material model allows different tensile and compressive behaviors. It can simulate cracking and crushing failure of concrete under relatively monotonic loading. A maximum of three independent directions of rebar are allowed for the concrete material. The rebar locations (in height or depth) are not considered; they are treated as "smeared" throughout the part.


Exercise N - Nonlinear Material Model• Objective: Analyze a cantilever beam

using beam elements and an elastic material model. Determine if yielding occurs. If it does, reanalyze the beam using a plastic material model.

• Geometry: The beam is 10’ longand is 5” x 5” square.

• Material: Steel (ASTM - A36)

• Loads: 56,000 pounds in the -Y direction at the free end.

• Constraints: The fixed end is fully constrained.

• Duration: 10 seconds.

• Capture rate: 2 steps per second.

Load curve:

Time (s)

Multiplier

0 0

10 1

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