Finite element methods (FEM) are powerful tools for solving complex structural problems, but how do you know which one is best for your project? In this article, you'll learn some criteria and tips to compare different FEM approaches and choose the one that suits your needs and goals.
FEM is a numerical technique that divides a domain into smaller elements and applies equations to each element to approximate the behavior of the whole system. FEM can handle various types of problems, such as linear or nonlinear, static or dynamic, elastic or plastic, and so on. However, not all FEM methods are equally efficient or accurate for every problem.
FEM methods come in many forms, but some of the most popular are Lagrangian FEM, Eulerian FEM, and ALE FEM. Lagrangian FEM uses fixed nodes and elements that deform with the material, making it ideal for problems with small deformations and simple geometries. However, it may struggle with mesh distortion or locking issues for large deformations or complex geometries. Eulerian FEM uses fixed elements and nodes that move with the material, making it suitable for problems with large deformations and fluid-like behavior. It may lack accuracy or stability for small deformations or solid-like behavior. ALE FEM combines the advantages of Lagrangian and Eulerian methods by using moving elements and nodes that can adapt to the material deformation. This makes it great for problems with large deformations and complex geometries, though it may require more computational resources and mesh refinement.
When comparing different FEM methods, you should consider criteria that reflect your problem characteristics and desired outcomes. Accuracy, for example, can be measured by comparing the FEM results with analytical solutions or experimental data. Efficiency can be measured by comparing the computational time, memory usage, and convergence rate of the FEM methods. To evaluate robustness, you can test the FEM methods for different scenarios, boundary conditions, and parameters. Flexibility can be measured by evaluating the FEM methods for different types of problems, geometries, materials, and loads. By considering these criteria, you can determine which FEM method best meets your needs.
To compare different FEM methods effectively and avoid common pitfalls and biases, it is essential to use consistent units, scales, and dimensions for all FEM methods and comparisons. Additionally, you should ensure that the mesh size, shape, and quality are appropriate for each FEM method and problem. Furthermore, you should use the right element type, order, and formulation for each FEM method and problem. It is also important to use the right solver type, settings, and tolerances for each FEM method and problem. Finally, post-processing tools and techniques should be used to visualize and analyze the FEM results and comparisons.
To illustrate how to compare different FEM methods, let's look at some examples of problems that can benefit from different FEM approaches. For instance, buckling of a thin-walled cylinder requires large deformations and nonlinear behavior, making an ALE FEM method more accurate and robust than a Lagrangian or Eulerian FEM method. On the other hand, fluid-structure interaction of a dam involves fluid-like and solid-like behavior, so an Eulerian FEM method is more efficient and flexible than a Lagrangian or ALE FEM method. Additionally, fracture of a concrete beam involves complex geometries and material properties, so a Lagrangian FEM method with special elements and formulations is more suitable and realistic than an Eulerian or ALE FEM method.