Budapest Tech
John 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
László Horváth www.nik.hu

Definition
Main features
Analysis in model space
Short story
The FEM/FEA process
Finite elements mesh
Parameters to be calculated
Finite elements
Loads and boundary conditions
Examples for analysis and visualization of results
Optimizing shapes

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

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.

Source: www.catia.com

Source: www.catia.com

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.

Creating model for analysis (preprocessing)
Preparation of geometric model
Preparation of FEM
Convert model from outside source
Definition of loads and
Boundary conditions
New geometric model
Simplified regions
New entities
Mesh generation
Selection of material properties
Checking for consistency and correctness
Optimizing the FEM
Automatic
Automatic correction
Refining mesh
FEM
Postprocessing
Processing of results for engineers
Color coding of intervals for parameter values
Construction of data sets and tables
Visualization of variation in time
Graphical visualization of
2D és 3D functions

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.

Stress
Deformation, gradient
Pressure
Internal force
Reaction force
Torque
Deformation energy
Natural frequency
Temperature, gradient
Heat flow
Magnetic field
By layers at composites

One-dimensional
Planar
Shell
Solid

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).
Concentrated 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.
Mechanical restraints restrict movements in specified directions and result reaction forces.
Definition of degrees of freedom . Nonrestrained nodes have six degrees of freedom.
Automatic contact recognition .

Source: www.catia.com

Source: www.catia.com

Source: www.catia.com

Source: www.catia.com

Source: www.catia.com

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 v d a b c a b
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.