How can you select the right finite element method and mesh size for spacecraft structural analysis?

1 Finite element method

Finite element method (FEM) is a numerical technique that divides a complex structure into smaller and simpler elements, and then solves the equations of equilibrium and compatibility for each element. FEM can handle various types of structures, such as beams, plates, shells, and solids, and various types of loads, such as thermal, mechanical, and acoustic. However, not all FEM formulations are equally suitable for all structures and loads. For example, some FEM formulations may be more accurate or efficient for thin or thick structures, or for linear or nonlinear problems. Therefore, you need to choose the FEM formulation that best matches the characteristics and requirements of your spacecraft structure.

3 Mesh convergence

Mesh convergence is a process that helps you determine the optimal mesh size for your FEM model. Mesh convergence means that the results of FEM (such as displacements, stresses, or strains) do not change significantly when the mesh size is refined or coarsened. To perform mesh convergence, you need to run FEM with different mesh sizes and compare the results. You can use various criteria to measure the convergence, such as percentage difference, norm error, or factor of safety. You can also use various methods to refine or coarsen the mesh, such as global or local refinement, or adaptive or uniform refinement. The optimal mesh size is the one that satisfies the convergence criteria and meets the accuracy and efficiency requirements.

5 Structure types

Different types of spacecraft structures may require different FEM formulations and mesh sizes. For example, for thin-walled structures, such as spacecraft panels or skins, you may use shell elements, which are two-dimensional elements that can model the bending and membrane behavior of thin structures. For thick-walled structures, such as spacecraft frames or bulkheads, you may use solid elements, which are three-dimensional elements that can model the full stress and strain state of thick structures. For beam-like structures, such as spacecraft booms or trusses, you may use beam elements, which are one-dimensional elements that can model the axial and bending behavior of slender structures. For each structure type, you need to select the appropriate FEM formulation and mesh size that can capture the relevant structural behavior and load effects.

6 Load types

Different types of loads may also affect the FEM formulation and mesh size selection. For example, for static loads, such as gravity or pressure, you may use linear FEM, which assumes that the structure behaves linearly and does not undergo large deformations or material nonlinearities. For dynamic loads, such as vibrations or shocks, you may use nonlinear FEM, which accounts for the nonlinear effects of large deformations, material nonlinearities, or contact interactions. For thermal loads, such as heat flux or temperature gradients, you may use coupled FEM, which couples the thermal and mechanical analyses and considers the thermal expansion or contraction of the structure. For each load type, you need to select the FEM formulation and mesh size that can model the load magnitude, direction, and duration.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?