Introduction to virtual engineering

László Horváth www.nik.hu

Budapest TechJohn von Neumann Faculty of Informatics

Institute of Intelligent Engineering Systems

Lecture 6.

Modeling by finite elements for analysis of engineering objects

Finite Element Modeling (FEM). Finite Element Analysis (FEA). Shape Optimalization

CONTENTS

Definition

Short story

The FEM/FEA process

Finite elements mesh

Finite elements

Optimizing shapes

Loads and boundary conditions

Main features

Analysis in model space

Parameters to be calculated

Examples for analysis and visualization of results

Definition

Edge

Node

Reveals the impact of design variables on the design performance

Calculation of location dependent parameters for rods, shells and volumes

Analysis is done on a finite number of finite elements

Finite Element Modeling (FEM) creates special model for Finite Element Analysis (FEA)

Main features

The FE analysis is a numerical method for the approximation by finite elements placed in mesh.

The values of the analyzed parameters are calculated using mathematical equations built into FEA programs of defined by the users for FEA programs.

The FE analysis is a simulation of behaviors of engineering objects.

FE analysis is a general purpose problem solving method for arbitrarily complex shape.

Any location dependent parameter can be calculated and any load or boundary condition can be considered.

An example for FEM/FEA

Source: www.catia.com

Analysis in model space

Source: www.catia.com

Short story

First application: analysis of structural eleents of airplanes.

First application of the phrase ”finite element analysis”: Clough, 1960.

First book: Zienkiwiecz and Chung, 1967

End of the 60s: Nonlinear problem solving.

Oden, 1972: First book about nonlinear problem solving.

70s: The mathematical basics were established.

Recently: product modeling systems include or interfaced to FEM/FEA.

FEM/FEA has become a fundamental method for analysis.

The FEM/FEA process

FEM

Postprocessing

Processing of resultsfor engineers

Color coding of intervals for parameter values

Construction of data sets and tables

Visualization of variation in time

Simplified regions

Preparation of geometric

Convert model fromoutside source

New geometric model

New entities

model

Hálógenerálás

Definition of loads andBoundary conditions

Checking for consistency and correctness

Optimizing the FEM

Preparation of FEM

Selection of materialproperties

Creating model for analysis (preprocessing)

Mesh generation

Controlled by engineer

Automatic correction

Automatic

Refining mesh

Graphical visualization of 2D és 3D functions

Finite element mesh

Finite element entities

They describe finite elements connected by common edges and parameters that are calculated by FEA. Libraries are established for finite elements.

Nodes

Calculation of the analyzed parameters is done at nodes.

Degree of edges

Straight line edges, or approximation by straight lines (linearization).

Quadratic edge is defined by three, cubic edge is defined by four nodes.

Exact edge is described as curve of the degree same as of the geometry

Mesh, meshing

Fixed of varying density. Density varies according to the load on each region.

Two-way associatívity between shape model and mesh for automatic change of the mesh in case of changed geometry.

Adaptive meshing is an automatic modification of mesh density, element order, and element shape according to accuracy and other specifications.

Parameters to be calculated

Stress

Deformation, gradient

Pressure

Internal force

Reaction force

Torque

Deformation energy

Natural frequency

Temperature, gradient

Heat flow

Magnetic field

By layers at composites

Finite elements

Solid

Planar

One-dimensional

Mesh Elements

Shell

Loads and boundary conditions

Simulation of real operating conditions. Associativity with the shape model.

Load model: placing loads and restraints on mesh (at nodes) and shape model (along lines and on surfaces).

LoadsConcentrated and distributed force.

Torque and acceleration ( (gravity, translation, rotation).

Inertia and centrifugal forces.

Contact load Pressure

Temperature on surface

Concentrated or distributed heat source.

Magnetic

Functional variations of loads are handled by mathematical expressions.

Constraints and restraintsMechanical restraints restrict movements in specified directions and result reaction forces.

Definition of degrees of freedom. Non-restrained nodes have six degrees of freedom.

Automatic contact recognition.

Analysis of stress on connecting bodies

Source: www.catia.com

Analysis of displacement

Source: www.catia.com

Analysis of temperature

Source: www.catia.com

Dynamic analysis

Source: www.catia.com

Application of color code

Source: www.catia.com

Design optimization

Active application of FEA.

Instead of analysis of a proposed shape, design parameters are proposed by analysis.

Specification by the engineer (conditions for design optimization):Design parameters to be optimized

Design limits (allowable values):

Allowable ranges of design parameters,

Stress, deformation, natural frequency.

Design goals:

Minimum, maximum, or optimal values of performance parameters

Minimum mass of the part.

Maximum utilization of allowable stress and deformation.

Design optimization procedure proposes values for design parameters in accordance with design goals and considering design limits.

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