Generalized Finite Element Method on Hybrid Stress Approach: Formulation and Numerical Performance

Abstract

The framework of the Generalized Finite Element Method (GFEM) is applied to a nonconventional Hybrid Stress Formulation (HSF) aiming linear plane analysis. In the original HSF two approximation fields are involved: stresses in the domain and displacements on the static boundary. The main features of the HSF are that the stress field satisfies equilibrium condition in the domain, while equilibrium on the common boundaries between elements is enforced in a weak form. In the combined GFEM-HSF approach the enrichment of the displacement boundary field is provided by the product of the partition of unity (PU) and a basis of polynomials enrichment functions. Quadrilateral and triangular finite elements with selective nodal enrichment are then derived. The numerical performance of the HSF with nodal enrichment formulation is tested in several examples. The numerical investigation focuses mainly a sensitivity analysis of the results to mesh distortion. Relating to this aspect some mesh distortion conditions imposed over plane stress beam-bending benchmarks are addressed. In addition, considering both computational and numerical aspects, one conclude that GFEM-HSF can provide good alternative to conventional displacement based formulations for plane linear analysis .