CHAPTER 2 Literature Review
2.3 The Process of Finite Element Analysis
FEA programs can perform complex analyses in relatively small amounts of time. Their user interfaces have become more aesthetically pleasing, convenient and, for a user with the necessary theoretical background, self-explanatory (Mac Donald, 2011). This section will examine the computational finite element analysis process and focus more on the practical procedure of going from a physical problem to generating a corresponding finite element solution. It was decided to conduct a further study into the practical procedures of conducting a computational FEA so that reliable models may be generated in this research.
Figure 2-4 represents the basic overview of the FEA process, adapted from (Mac Donald, 2011).
Figure 2-4. Basic overview of the computational FEA process
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1. Understand the Physical Problem: The accuracy of the entire process is based purely on the expertise of the analyst displayed at this step of the analysis. The design objective must be outlined. The purpose of the study as well as the quantities of interest must be known.
This step should see the analyst identifying all the distinctive features of the domain. The material properties and loading conditions must also be identified (Mac Donald, 2011).
2. Determine the Mathematical Model: Once the essential features of the physical model have been identified, it is necessary to translate these into a mathematical representation of the problem. This stage involves two tasks. Firstly, it is required that the problem domain be defined i.e. the physical shape of the problem. This step usually entails the creation of appropriated CAD geometry or an assemblage of nodes and elements. Secondly, a mathematical formulation best representing the physical problem must be selected. A practical example would be the requirement of plane strain on an axisymmetric component.
This can be achieved using a two-dimensional element model which can be used due to the presence of symmetry. The identification of what element type to use at this point before discretization is crucial as it greatly influences solution time and computational cost of the model (Mac Donald, 2011).
3. Finite Element Solution of the Model: This step encompasses various aspects of the creation of the finite element model process as seen in Figure 2-4. The first step in this process is the finite element model creation. This starts off with model discretization. Once the element type and mathematical formulation is selected, the next step is to actually divide the model into the specified elements. Most commercial FEA software can automatically discretize the model using automatic mesh generators. Auto-meshing cannot necessarily predict occurrences such as areas of localized stress and will in such cases not be able to rationalize the need for mesh refinement. Thus the analyst will need to specify refinement based on the understanding of the physical problem as well as engineering experience (Mac Donald, 2011). Table 2-1 shows an overview of typical structural finite elements.
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Table 2-1. Overview of typical structural finite elements
Basic Shape Representative Geometry Application
Point Mass Elements
Line
Truss/ Spar Element Spring Element Beam Elements Pipe Elements Axisymmetric Shell Elements
2-D Contact Elements 2-D surface Effect Elements
Area
Triangular Quadrilateral
2-D Surface Element - Plane Stress
- Plane Strain - Axisymmetric - Plate Element
Volume
Tetrahedral Hexahedral
3-D Solid Element
Following discretization, boundary conditions are applied to the model. The locations and types of boundary conditions are based on the understating of the physical problem. Table 2-2 shows typical constraints that are encountered and Table 2-3 shows several loading conditions that can be applied in structural FEA problems. The contents of these tables were both adapted from (Mac Donald, 2011).
Once the model is created, the computational strategy must be selected. For each particular problem, the user must select a particular solution method, and if applicable, the time step or load step size. At this point, the solver is generally set to solve the problem. A common problem experienced with non-linear or transient problems is solution convergence within the given time steps. Generally there would not be any indication of how to fix the error and hence fixing the error would rely on the experience of the analyst (Mac Donald, 2011). Once results are obtained, an experienced analyst would be able to assess the quality of results and make a judgement as to the acceptability of the results. If it is seen that there is a potential that key areas were not adequately captured by the mesh or that the solution results deviate from what was expected then the model parameters should be refined in order to better analyse the problem (Mac Donald, 2011).
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Table 2-2. Typical boundary constraints encountered in Structural FEA
Boundary
Constraint Description
Fixed Support This is the most basic type of boundary condition. It constrains a specified region of the model in all degrees of freedom (DOF)
Frictionless Support
This constraint allows for only one degree of freedom to be constrained. It is useful when modelling effects of adjoining structures to prevent the model moving across boundaries.
Symmetry Constraint These are frictionless constraints imposed on symmetry cut planes.
Multipoint Constraint (MPC) / Coupled DOF
Applying a constraint to a single node will result in stress concentrations (singularities) around the node. An MPC avoids singularities by creating a master node, to which a constraint is applied, and multiple slave nodes. The slave nodes follow the behaviour of the master, thus coupling the nodes.
Forced Displacement
A location in space where a selected group of nodes will be at the end of the analysis is specified, rather than a force or pressure.
This forces nodes to move to a location and hold this position.
Constraints with Coordinate Systems
These are constraints that are assigned to a defined coordinate system. These constrains are useful when applying supports that are inclined at an angle to the global coordinate system.
Time-Varying Constraints
This implies that the constraint changes in some manner during the course of the simulation. An example of this is contact problems. A model will be unconstrained until it comes into contact with other bodies.
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Table 2-3. Typical Loads encountered in Structural FEA
Load Type Description
Force
This is the most basic type of load. Forces can be applied as single values for static analyses with small deflections or time varying when large deflections are expected.
Moment Moments/Torque can be directly applied to nodes provided they have free rotational degrees of freedom.
Pressure
These loads can be applied to edges of 2-D and faces of 3-D geometry. Pressure loads generally act perpendicularly to the edge or surface selected.
Velocity
Linear velocities can be applied to groups of nodes. These are usually only used for non-linear analyses such as impact analysis or material forming analysis.
Acceleration Acceleration loads are also used in dynamic analyses and impact analyses. The most common acceleration load used is gravity
Non-Linear Loads
There are 3 types of non-linear effect loads.
Large deformation loads, which cause the structure to greatly deform and hence need to be applied incrementally.
Contact loads, which occur when two bodies intersect and deform against each other.
Follower forces, which are locally defined in relation to a node.
This force will adjust its orientation as the structure deforms to maintain a specific application angle relative to the chosen node.
Multiple Loads and Load Steps
The structure has multiple loads specified. These can all be applied in one load step simultaneously or over multiple load steps,
separately. The loads can be anything from forces to pressure loads etc.
4. Interpretation of Results, Post-Processing: In this step, the results must be interpreted before any information can be used to make design decisions. One must determine if the model accurately represents the physical problem. In the results of a structural FEA, each node in the finite element mesh will have a corresponding displacement. Post processing converts these displacements into more useful results such as contour plots of stress or strain throughout the domain.
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It is important to check results and determine if the results obtained are realistic. An analyst should ask certain questions about the result such as:
• Has the yield or ultimate tensile stress been exceeded?
• Are displacement magnitudes excessive?
• Are stresses/strains excessively large?
• Do stresses /strains transition smoothly throughout the domain?
• Are expected errors acceptable?
Figure 2-5 shows a general procedure for the interpretation of structural FEA results adapted from (Mac Donald, 2011)
Figure 2-5. General procedure for the interpretation of post-processing structural FEA results
If the model is checked and found to be viable based on the obtained results, then the next stage is to validate the solution results against experimental results or analytical solutions. If the error observed is too significant then assumptions made at the beginning of the modelling process must be re-evaluated and further analysis cycles would be required.
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