Constrained finite element analysis with displacement mapping: application to thin-walled members with holes

A widely used approach to understand and analyze the complex behavior of a structural member is to decompose the complex phenomenon into simpler ones. In thin-walled members the deformations are frequently decomposed into the following behavior modes: global (G), distortional (D), local-plate (L), shear (S) and transverse extension (T). A practical realization of this approach is the constrained finite element method (cFEM). Whilst the cFEM is readily applicable for a wide range of problems, still, a disadvantage of the currently available cFEM is that it is based on a specific rectangular shell finite element. This imposes two major restrictions: (i) highly regular rectangular mesh is a must, and (ii) the potential benefits of the various available shell elements cannot be utilized. The aim of the reported research is to release these restrictions set by the cFEM-specific shell element. The idea is to use two discretizations and two corresponding basis function systems. One is an ordinary shell finite element discretization, the other is the specific cFEM discretization. The basis functions of the cFEM are transferred to the ordinary shell model, then the calculations are completed in the ordinary shell model but with using the cFEM basis functions. The key step is the transfer of the cFEM basis functions, which can be realized by mapping between the nodal displacements of the two shell models. In the paper the proposed method is briefly introduced and some proof-of-concept examples are presented, with a special focus on members with holes.

Learning Objectives:
To understand how modal decomposition can be performed in a thin-walled member modelled by arbitrary shell finite elements.

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