Computation of critical loads and buckling modes using hybrid-mixed stress finite element models

•A hybrid-mixed stress finite element model is presented.•Independent approximation of stress and displacement fields.•Static geometrical non-linear analysis and linear stability.•Use of effective p-refinement procedures.•Legendre polynomials are used to define the approximation bases.

This work presents a hybrid mixed stress finite element model for the linear stability analysis of frame structures and Reissner–Mindlin plate bending problems. This model approximates the stress and displacement fields in the domain and the displacement field on the static boundary. Legendre polynomials are used to define all approximation bases, in order to compute analytical solutions for all structural operators. It enables also the implementation of highly efficient p-refinement procedures. A material linear behaviour is assumed and to validate the model and to illustrate its potential, numerical tests are presented and compared with analytical and numerical solutions.