Models such as this housing can be divided along an axis of symmetry to reduce model size and run times.
Models such as this housing can be divided along an axis of symmetry to reduce model size and run times.
 
Each node supports translation along and rotation about an X, Y, and Z axis for a total of six degrees of freedom. The sum number of the DOF from all nodes also provides an estimate of model size.
Each node supports translation along and rotation about an X, Y, and Z axis for a total of six degrees of freedom. The sum number of the DOF from all nodes also provides an estimate of model size.

In this article, Ted Fryberger, a consulting engineer and instructor with DeepSoft Inc., Columbia, Md. (www.deepsoftinc.com), makes suggestions for establishing an FEA program. (The first part of this series appeared in the February 5 issue - "At square one with FEA - part 1.")

The following steps are a necessity for each analysis, says Fryberger. "Think of these as the tactical portion of the job," he suggests. For each analysis, users must:

  • Define the geometry.
  • Select element types and set element properties.
  • Create surface and internal meshes.
  • Specify loads.
  • Specify boundary conditions.
  • Select materials and specify material properties.
  • Check the input data.
  • Run the analysis.
  • Evaluate the results.
  • Modify and iterate until confident the model is providing accurate results.
  • Check results for accuracy by independent means.

Meshing is more than redefining a model with elements. It's a discretization because the element supports specific types of geometry and analyses. Nodes are often the intersecting points at the corners of common FEA elements. Higher-order elements support midside nodes for additional computation points. One measure of problem size and complexity is the total number of nodes or elements.

FEA model geometry must closely mimic the product geometry. However, the fine detail necessary in solid models is often omitted from FEA models depending on detail size and the analysis objectives. A wide range of elements are available for differing geometry, boundary conditions, and analyses.

Fryberger says it's normal to go through numerous iterations before the analysis completes. "It is helpful to have an initial coarse mesh of relatively large elements to evaluate before deciding where to enhance the mesh for increased accuracy in subsequent runs," he says. Once the basic model is running accurately it's a good idea to create similar models that allow evaluating specialized or "what if" scenarios.

Structural loads include point loads and moments applied at nodes, pressure loads applied to element surfaces, and accelerations applied to the entire model. Thermal, fluid, electrostatic, and electromagnetic analyses support their own appropriate load types. Specific element types normally allow only certain types of loads. For example, fluid elements cannot carry structural loads.

Boundary conditions (BCs) describe how the model is grounded, attached to something else, or how portions of the model attach to or interact with each other. BCs can be completely fixed or constrained for specific degrees of freedom. Every node has up to six degrees of freedom (DOF), three for translation along the X, Y, and Z axes and three for rotation about the same axes. Not all element types support all six DOF. BCs can be used to constrain specific DOF at each node. For example, a node with a fixed BC will not support translation or rotation along or about any of the three axes. Fixing a BC is a way to more-accurately model the real world.

Look for model symmetry. Model geometry can be broken along lines of symmetry, if they exist, to create a physically smaller model that still does a good job of predicting stresses. This is desirable if the model will be so large that it won't run on the computer at hand or runs too slowly. For example a missile radome (nose cone) is an axisymmetric body of revolution, so engineers normally don't have to do a full-blown 3D FEA model of it, only a 2D profile of revolution. Stress distributions within this 2D profile will be uniform throughout the entire 360° of revolution. For example, at any angle of rotation around the circumference of the radome the 2D stress or temperature distribution will be identical. Geometry, loads, boundary conditions, and materials must all be uniformly applied to use symmetry.

"Other ways of applying symmetry are with half, and quarter symmetry models," says Fryberger. "For the oceanographic instrumentation housing in an accompanying image, we could have used half symmetry after slicing the model in half along its longitudinal axis." This works because the model geometry, loads, boundary conditions, and materials are all uniform and symmetrical about the cutting plane. When using symmetry you must apply appropriate BCs along the cut edge to account for material removed from the model. 2D plane stress and plane strain models are other examples where symmetry works well.

"If there are only some stations of interest along this 2D radome profile mentioned earlier, we could generate a few 1D models through the wall just at these locations of interest," he says. "So depending on product geometry, loading, boundary conditions, and what you are looking for, you may not have to do full-blown 3D FEA." One-dimensional and 2D models will always be smaller than 3D models and will run faster, but they require knowledge of the part to be analyzed and loading conditions.

"Generally I specify model size this way: Small models have 50k nodes or less, medium-size models run from 50k to 200k nodes, and large-size models have more than 200k nodes, many types of dynamic analyses, and any nonlinear analysis," says Fryberger. Dynamic and nonlinear models normally require iterative solver runs which always increase run times compared to a static analysis. And count on fully automatic mesh generators to create larger models in terms of number of nodes and elements compared to a manually created model mesh.

Model geometry can be created directly in FEA software using built-in CAD or solid-modeling tools, separate 2D or 3D CAD software, or a 3D solid modeler. "The choice is largely personal preference although 3D-solid modelers are clearly preferred by many including myself," says Fryberger. A stand-alone 3D solid modeler provides the most power and flexibility for creating geometry and modifying parameters. Stand-alone CAD packages may be more familiar to designers or engineers than the FEA-supplied tools.

"With FEA-supplied CAD tools you do not have to purchase a second software package, learn to use it, and there are no data-translation issues," he adds. Also some FEA packages such as Ansys and Nastran support model text file input as an alternative to graphically creating model geometry.

Specifying material properties means checking or assigning values for mass density, modulus of elasticity, Poisson's ratio, shear modulus of elasticity, and thermal expansion coefficient.The final installment of this series will work through a detailed sample problem to show how the ideas presented here work.




A Brief FEA Glossary

These terms are most often encountered in a discussion of FEA results.

Static -- loads of a fixed magnitude or those that change so slowly with time they can be treated as constant.
Dynamic -- loads that vary with time.
Linear -- all portions of the model, geometry, materials, and boundary conditions must behave linearly.
Nonlinear -- one or more portions of the model that behave in a nonlinear fashion.
Steady state -- analysis results valid for long term, usually some period after an initial transient period.
Transient -- results in a period of change.
Multiphysics -- a single analysis simultaneously encompassing more than one physical phenomena. Loading could include any combination of structural, thermal, fluid, electrostatic, and electromagnetic phenomena.
Structural -- analyses that finds model displacements and resultant stresses.
Thermal -- finds temperature profiles and heat fluxes.
Fluidic -- finds velocity flows and pressure distributions.
Electrostatic -- finds voltage potentials.
Electromagnetic -- finds magnetic fields.
Solver -- a math engine or collection of algorithms that solves the force, geometry stiffness, and displacement matrices in a structural problem.
Preprocessor -- an FEA software module used to create geometry, apply loads, boundary conditions, and check input data.
Postprocessor -- an FEA software module used to view analysis results and check output data.