It is well recognized that the governing differential equations of 3D elasticity problems can be solved only for a narrow range of problems. Among the methods based on weak form solutions, the Finite Element Method (FEM) has been probably the most popular. Although FEM is versatile and applicable to arbitrary geometries, boundary conditions and material heterogeneity, it can sometimes be very expensive from a computational standpoint. There are other limitations to FEM as well. For example, the conventional FEM may not capture stress singularities or all necessary high-frequency wave modes of interest, which can play an important role in the correct characterization of the entire vibration pattern of a structure.
In this domain, MUL2 has been working in the development of methods based on closed-form solutions as well as numerical methods using frequency-dependent shape functions, i.e., dynamic shape functions.
Illustrative tools for the (numerically exact) static and dynamic resolution of beams and plates are available in the software section of this website.