Errors Modeling and Accuracy
MEEM4405 Introduction to Finite Element Analysis
Convergence Requirements
If a mesh is repeatedly refined, will the results converge to a solution? Yes, if the elements used pass the patch test.
MEEM4405 Introduction to Finite Element Analysis
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Convergence Requirements
In a patch test, the FE model must have:
A simple arrangement of elements with one internal node Supports sufficient to stop rigid body motion Work equivalent loads consistent with a constant state of stress (and strain)
To pass the test, the results must exactly represent the correct constant stress (and strain), within numerical error.
MEEM4405 Introduction to Finite Element Analysis
Infinite Media
If the FE model is embedded in a medium that can be considered infinite, do one of the following:
Make CD a very large distance from AB, so that it does not influence the results (may have problems) Use Infinite Elements, a type of isoparametric element Connect FE model with Boundary Element model
MEEM4405 Introduction to Finite Element Analysis
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Substructures
Substructuring allows analyzing a large FE model as a collection of components.
MEEM4405 Introduction to Finite Element Analysis
Substructures
Substructuring works as follows:
1. Divide the model into parts (substructures) 2. Create a FE model of each substructure. Solve for dofs of nodes shared with other substructures in terms of internal node dofs. 3. Assembly a global model with only shared nodes. 4. Solve the global model, then use the solutions of the shared dofs to solve for the internal dofs. Then post-process for stresses and strains.
In effect, each substructure is a superelement for the global model.
MEEM4405 Introduction to Finite Element Analysis
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Substructures
Substructures should be chosen so as to minimize the number of shared nodes. Substructures do NOT introduce additional approximations. Substructures can be useful for:
When there is not sufficient computer power to handle the whole model. When different departments or companies are working on different parts of the design. When only a small part of the model is nonlinear. When there is repetition of substructures.
MEEM4405 Introduction to Finite Element Analysis
Symmetry
If the problem has symmetry in geometry, support conditions and loading, it may only be necessary to model a fraction of the problem. Support Conditions on planes of symmetry must be chosen appropriately. The must results be known to also be symmetric.
MEEM4405 Introduction to Finite Element Analysis
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Structure and Element Behavior
To do a proper FE analysis, the analyst must understand how the structure is likely to behave and how elements are able to behave. E.g. If the analyst knows the stress varies linearly, Q6 elements will work, but if they vary quadratically, Q8 elements must be used.
MEEM4405 Introduction to Finite Element Analysis
Structure Behaviour
If beam flanges are wide, y = My/I is not accurate. Beam elements will not give accurate results. In this case, plate/shell elements should be used.
MEEM4405 Introduction to Finite Element Analysis
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Structure Behaviour
A curved I-beam reacts to moments as shown, therefore shell elements would be more accurate than beam elements. Pipe bends react to moments as shown. Use shell elements or specialized beam elements with correction factors.
MEEM4405 Introduction to Finite Element Analysis
Structure Behaviour
If the load is not applied directly below the shear center, the channel will twist. Use shell elements instead of beam elements.
MEEM4405 Introduction to Finite Element Analysis
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Structure Behaviour
A thin-walled cylindrical tank has high flexural stresses at the base. Use a finer mesh where there are discontinuities or abrupt changes in the structure.
MEEM4405 Introduction to Finite Element Analysis
Structure Behaviour
If a simply-supported plate is thin, we need to use shell elem...