Large finite elements method for the solution of problems in the theory of elasticity

Abstract

In contrast to conventional finite element (CFE) formulations, the large finite element (LFE) concept is based on subdividing the region under consideration into a small number of LFE and using in each of them an appropriate parametric displacement field such that the governing differential problem equations are satisfied a priori (Trefftz's method). Where relevant, known local solutions in the vicinity of a stress concentration or stress singularity are used as a convenient expansion basis. The boundary conditions, as well as the continuity across the interfaces, are implicitly imposed by an appropriate variational functional. The LFE concept attempts to combine the flexibility of the conventional FE method with the accuracy and high convergence rate of the Trefftz's method. The paper summarises the principal results obtained and shows that the practical efficiency of the LFE analysis is superior to a CFE solution, for both regular and singular problems.