PAT328, Section 3, March 2001 S7-1MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

SECTION 7

CHOICE OF ELEMENTS:TOPOLOGY AND RESTARTING

PAT328, Section 3, March 2001 S7-2MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

TABLE OF CONTENTS

Section Page

7.0 Choice of Elements: Topology and Restarting GeometricOverview……………………………………………………………………………………………………………..

7-3Element Topology…………………………………………………………………………………………………..7-4Structural Element Types In MSC.Marc………………………………………………………………………….7-51d (Bar) Elements…………………………………………………………………………………………………..7-6Beam Section Orientation Vector………………………………………………………………………………… 7-72d Solid (Continuum) Elements…………………………………………………………………………………...

7-8 2d Shell Elements (Thin Shell: 5 DOF @ Nodes)……………………………………………………………….

7-102d Shell Elements (Thick Shell: 6 DOF @ Nodes)……………………………………………………………...

7-113d Shell Elements (3 DOF @ Nodes)…………………………………………………………………………….

7-121st And 2nd Order Elements………………………………………………………………………………………...

7-13 Choice Of Elements………………………………………………………………………………………………...

7-15 Connecting Elements Of Different Types………………………………………………………………………...

7-17Choice Of Integration Method……………………………………………………………………………………..7-18

PAT328, Section 3, March 2001 S7-3MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

OVERVIEW

Selecting and Using Finite Elements

Element Topology Versus Element Property

Dimensions of Structural Space versus Dimensions of Finite Element

Connecting Elements of Different Topology

Methods of Numerical Integration

Plane Elements Plane Strain Plane Stress Axisymmetry

Orientation of Beam Cross Sections in Space

Thin Shells Versus Thick Shells

PAT328, Section 3, March 2001 S7-4MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

0-D Elements

1-D Elements

Element Types in MSC.MARC

2-D Elements

3-D Elements

ELEMENT TOPOLOGY

PAT328, Section 3, March 2001 S7-5MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

Example: First modal shape of beam model combining element types

STRUCTURAL ELEMENT TYPES IN MSC.MARC

0-D Point Masses 1D (Bar) Elements 2D Solid (Continuum)

Elements 2D Shell Elements 3D Solid (Continuum)

Elements

PAT328, Section 3, March 2001 S7-6MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

1D (BAR) ELEMENTS Beam Elements (Standard, Euler-

Bernoulli) Truss (Spar) Elements Axisymmetric Shell Elements Springs Dashpots (Use Springs Options

These elements may have nonlinear properties

Example : Snap-through of Bottom of a Soft-Drink Can

Simulated with quadratic (3-node) 1D Axisymmetric elements

Aluminum can –plasticity included When pressure increases the bottom

of the can “snaps” thus increasing the volume inside the can –relieving the pressure- and preventing the rupture and spilling of contents.

Because of plasticity the bottom cannot return back to the original shape thus protecting the consumer from spoilage.

PAT328, Section 3, March 2001 S7-7MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

XZ Plane

Node 1

Node 2

Y

X

Z

1”

2”

J

Izz

Ixx

Z

Global CS

X

Y

BEAM SECTION ORIENTATION VECTOR

PAT328, Section 3, March 2001 S7-8MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

Plane Stress

Plane Strain

2D SOLID (CONTINUUM) ELEMENTS

Plane Stress Elements (2 DOF @ nodes: Ux, Uy)

Planar structures, All out-of-plane stresses zero

Typical: Flat panels subject to inplane loads

Plane Strain Elements (2 DOF @ nodes: Ux, Uy)

Planar model, All out-of-plane strains constant or zero

Typical: Slice of car’s door rubber seal

Membrane Elements (3 DOF @ nodes: Ux, Uy, Uz)

Curved, very thin structures unable to sustain bending

PAT328, Section 3, March 2001 S7-9MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

Axisymmetric Elements (2 DOF @ nodes: Ux, Uy)

Axisymmetric structures with axisymmetric loadings

2D SOLID (CONTINUUM) ELEMENTS (CONT.)

X = Axial Y = Radial !

PAT328, Section 3, March 2001 S7-10MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

1

Z

Y

X

n4 3

2n 3

2

1

Top

Bottom

2D SHELL ELEMENTS (THIN SHELL: 5 DOF @ NODES)

In-plane/out-of-plane loadings in planar and curved surfaces

Ignores out-of-plane normal stress Ignores out-of-plane transverse

shear stresses (Normals remain normals)

Thickness very small (<5%) compared to typical surface

PAT328, Section 3, March 2001 S7-11MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

2D SHELL ELEMENTS (THICK SHELL: 6 DOF @ NODES)

In-plane/out-of-plane loadings in planar and curved surfaces

Ignores out-of-plane normal stress Considers out-of-plane transverse

shear stresses (Plane Sections remain Plane)

Thickness small (>5%, but <10%, ) compared to typical surface dimensions

PAT328, Section 3, March 2001 S7-12MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

3D SHELL ELEMENTS (3 DOF @ NODES)

Considers all 6 components of stresses and strains

Suitable for 3D solid bodies

Although valid, 3D Solid Elements are neither efficient, nor very accurate for thin surfaces, or long and slender parts.

PAT328, Section 3, March 2001 S7-13MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

Linear

Quadratic

Herrmann - extra node carries compressibility degree of

freedom typically GUI handles this in an automated fashion.

1ST AND 2ND ORDER ELEMENTS

PAT328, Section 3, March 2001 S7-14MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

Truss/SparBeam (2D)

Beam (3D)

Axysym. Shell

9,51 5,1613,14,25,31,52,78,

79,981,15

Elem 31 is a curved pipe (Elbow)/Straight Beam ElementElem 98 is a Thick (Timoshenko) Beam Element

1D (2-Node Line) Structural Elements:

Shape/Type Shell

ShellPlane Stress

Plane Strain Azysym. SolidMembrane Shear

Tri3 8, 138 6 2 2Quad4 75, 139, 4, 24 3 11 11 10 18Quad4 (RI) 140 114 115 116 116 68Tri6 49 124 125 126 126Quad8 22, 72 26 27 28 28 30Quad8 (RI) 53 54 54 55

2D (Surface) Structural Elements:

Elem 3, 11 can be used with/without assumed strainElem 22, 75, 140 are Thick shell Elements

ShapeElement Number

Tet4 134Hex8 7Hex8 (RI) 117Tet10 127Hwx20 21Hex20 (RI) 57

3D (Solid) Structural Elements:

HEX8 (Elem 7) can be used with/without assumed strain

Springs, Dashpots: SPRINGS for both springs and dashpots

Point MASS: MASSES for concentrated (point) Masses

1ST AND 2ND ORDER ELEMENTS (Cont.)

PAT328, Section 3, March 2001 S7-15MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

CHOICE OF ELEMENTS

Use beam elements to model beam-like structures, if possible and appropriate.

They are economical and give very good answers within the assumptions of beam theory.

Also very useful to represent stiffeners on shells

Example:Pantograph

Including beam-to-beam contact

PAT328, Section 3, March 2001 S7-16MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

CHOICE OF ELEMENTS (Cont.)

For bending problems with solid elements (2D or 3D), element type and meshing can greatly affect the results.

Solid elements may be necessary in bending problems where beam theory is not sufficient if thickness is too large or stresses in the thickness direction are important.

How shall we choose the element type?

How fine a mesh do we need?

PAT328, Section 3, March 2001 S7-17MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

CONNECTING ELEMENTS OF DIFFERENT TYPES

Part of the structure may be represented by shell elements and part by solid elements

The number of degrees of freedom is different for solid elements than for shell element

How to prevent the free rotation of the shell at the interface with the solid

PAT328, Section 3, March 2001 S7-18MAR120, Lecture 4, March 2001MAR120, Section 7, December 2001

CHOICE OF INTEGRATION METHOD

Different methods of integration are available. Their performance is discussed in further detail in the next chapter

Standard Elements provide full integration

Materials with incompressible behavior (such as rubber) require special options such as Reduced Integration or Herrmann formulation. The reason for this is that a Poisson’s ratio of 0.5 will have an indeterminate stiffness coefficient Integration Points for Standard

8-Node Membrane Element