This presents an overview on numerical methods based strong, week and weakened weak (W2) formulations. Comparisons of W2 formulations with the strong and weak formulations will be presented. Properties of different types of numerical methods. We will also present a family of recent W2 models known as S-PIM and S-FEM that important for automations in computation including, spatial and temporal stability and convergence, softening effects induced by various types of smoothing domains, upper bound properties leading to certified solutions real-time computational models, and insensitivity to the quality of mesh allowing effective uses of triangular/tetrahedral meshes. Examples will be presented for simulating engineered material behavior at various extreme situations, fluid structural interaction problems, cracks in engineering aerospace structural systems, and crystal plasticity for metallic polycrystalline used in jet engines.

Keywords(optional): numerical methods, FEM, meshfree, weakened weak formulation, S-FEM, S-PIM, modeling and simulation

References

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