Constrained finite element method with displacement mapping

Abstract

AbstractA widely used approach to understand and analyze the complex behavior of a structural member is to decompose the complex phenomenon into simpler ones, and then to interpret the complex phenomenon as the superposition of the simpler ones. Accordingly, the deformations of thin‐walled members are frequently decomposed into global, distortional, local‐plate, etc. modes. One well known practical technique is the constraining of shell models; the idea first appeared in the constrained finite strip method, then later in the constrained finite element method, or cFEM in short. While the cFEM was proved to be applicable for a wide range of problems, its disadvantage is that it requires a specific rectangular shell finite element. The aim of the reported research is to release the limits set by this specific shell element. The idea is to use two discretizations and two corresponding basis function systems. One is based on an ordinary shell finite element, the other one is on the cFEM shell elements. The basis functions of the cFEM are mapped to the ordinary shell model, then the calculations are completed in the ordinary shell model but with using the cFEM basis functions. In the paper the proposed method is briefly introduced and some proof‐of‐concept examples are presented.