An algorithm for programming the element matrices of doubly curved quadrilateral shell finite elements

Abstract

AbstractThis paper describes an algorithm which reduces the apparently diverse and complicated matrix calculations required to evaluate the finite element matrices of doubly curved quadrilateral shell finite elements to a few basic manipulations which are then repeated a large number of times. The algorithm can be transcribed particularly quickly into computer code. It lends itself to a structured programming approach and the flexibility of the ensuing coding is high. The accuracy of the code can be ascertained with relative ease and fault‐finding is comparatively straightforward; hence, a high degree of confidence can be placed in its execution. The element chosen to illustrate the application of the algorithm is a particularly difficult example. It is expected that the algorithm described would be useful in a wide variety of finite element computer program applications.