# fea examples

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• FEA Good Modeling Practices

Issues and examples

Finite element model of a dual pinion gear.

• Finite Element Analysis (FEA)Good modeling and analysis procedures

FEA is a powerful analysis tool, but use it with care.

Warnings

ALL MODELS ARE WRONG! - SOME ARE USEFUL.

An FEA program allows an engineer to make mistakes at a rapid rate of speed. (R. Miller)

An error caused by misunderstanding or oversight is not correctible by mesh refinement or by use of a

more powerful computer. (Cook)

• Finite Element Analysis (FEA)Good modeling and analysis procedures

FEA is a versatile tool, but not the best analytical tool for every problem. (Cook)

An analysis is doomed to failure without sufficient consideration of all available

tools to determine which is most appropriate, and sufficient pre-analysis

planning to determine the required scope and level of complexity for the analysis

and the required accuracy of the solution.

• Basic Concepts in Finite Element Analysis

Divide and conquer - Simple linear equations like F=Kx are not valid on a large scale for a part with complex geometry but they can be valid for a small region of material within the complex part.

Therefore, if we break down a complex physical object into a large but finite number of small pieces (elements) for which simple equations can be solved with acceptable accuracy (where numerical approximations are valid), then build the structure back up (via nodal connectivity and transferring solutions from one element to the next to allow successive computation) we can create a meaningful solution for the entire complex object.

• AForE =AForE =

Basic Concepts in Finite Element Analysis

Finite elements are small interconnected geometrical entities connected to other elements through nodes (1D), boundary lines (2D), and boundary surfaces (3D).

Elements contain the material information and determine how the loads are transferred into displacements for all connected nodes

FEM is actually displacement analysis {F}=[K]{x} with node displacements determined by element "stretching", followed by load and stress calculations for the elements based on the nodal displacements and the material properties

• Basic Concepts in Finite Element Analysis

Nodes: basically coordinate locations,they locate/define the endpoints of all 1D elements and the corners of all 2D & 3D elements.

Since all info goes into model and is computed for the model on the nodal level (i.e. input nodal forces and output nodal displacements), at a minimum, nodes must be present at all locations where there are changes in geometry or where there are applied loads or boundary conditions.

AForE =AForE =

• Basic Concepts in Finite Element Analysis

Degrees of Freedom (DOF) & Associated Loads: DOFs are the unknown quantities associated with a node,

or the things that must be solved for mathematically. Associated loads are loads of the same direction and type

as the DOFs. For structural FEA the DOFs are displacements (or

rotations) and the associated loads are forces (or moments).

Boundary Condition (BC): A boundary condition for the model is the setting of a known value for a displacement or an associated load. For a particular node you can set either the load or the displacement but not both.

• Text: Building Better Products with FEA,by V. Adams & A. Askenazi,

Boundary Conditions: the loads and constraints that represent the effect of the surrounding environment on the model. (Everything else, that you have not modeled).

UNWANTED EFFECTS (p. 264-270)Overconstrained, redundant supports, excessive constraint tend to add stiffness to the model (stiffer than the real system) Also, prohibits Poisson contraction (making excessive stress) example of excessive constraint in thermal expansion

Underconstrained, understiffened, insufficient stiffness if rigid-body motion can occur, cracks, un-"glued" parts (p. 270) "Ask yourself if the parts that were not modeled could really allow the deformation that you are seeing." (p. 271) If you notice high stress near the boundary conditions, are they fictitious or real ?

Point load: local stress is infinite, but is meaningless (Fig. 8.6, p.272)If you are concerned with locations "far" removed from locations which have singularity, then you can use the point loads.

http://engr.bd.psu.edu/davej/classes/excessiveconstraint.html

• COMPARISON OF BOUNDARY CONDITION SCHEMES (p. 295-300)Considers various approaches for modeling a pin-in-a-hole

"... boundary conditions are arguably the toughest aspect of FEA"

• Basic Concepts in Finite Element Analysis

The number of equations in the mathematical model is equal to the number of unknown degrees of freedom (each node introduces 3 DOF for 3D brick elements).

All loadings such as pressures, thermal loadings, etc. must be converted to associated loads to allow solution of the displacement equations. This can either be done by the user or by the software, but all information becomes nodal information prior to solution.

The method requires the solution of large systems of simultaneous equations requires high-speed computers

(#eqns = (#DOF/node)*#nodes - # BCs)

• Figure 6: When a refinement point is defined at the center of the hole in the bracket model, the mesh is enhanced

surrounding it.

• Local mesh refinement

Finite element model of a dual pinion gear.

• Frame FEAMaximum Compression Stress 22 ksi

• 5 commandments of finite element modeling and analysis

1. Thou shalt use the simplest model (in terms of model complexity and scope, element type and mesh, etc.) that provides the information you are looking for.

2. Thou shalt verify the quality of the finite element mesh model both prior to the analysis and after results have been generated.

3. Thou shalt completely understand the assumptions inherent in the finite element method, understand the characteristics of any automatically constrained joints (especially those created between parts in an assembly during the automatic meshing process), and understand and correctly apply the boundary conditions and nodal loads.

4. Thou shalt verify the results of a finite element analysis both numerically and physically (plot displaced shape first!).

5. Thou shalt not use the results of an unverified finite element analysis for making design decisions, and thou shalt not present the results in a false or misleading way.

• Mesh Convergence Help:http://www.algor.com/service_support/hints_tips/mesh_convergence_study.asp

Help getting specific element and nodal results info:http://www.algor.com/service_support/hints_tips/inquire_results.asp

ALGOR Keystroke-Specific Tutorials:http://www.algor.com/service_support/tutorials/default.aspx

What can go wrong with FEA? (ME Magazine article)http://www.memagazine.org/backissues/may98/features/wrong/wrong.html

http://www.algor.com/service_support/hints_tips/mesh_convergence_study.asphttp://www.algor.com/service_support/hints_tips/inquire_results.asphttp://www.algor.com/service_support/tutorials/default.aspxhttp://www.memagazine.org/backissues/may98/features/wrong/wrong.html

Frame FEA