Abstract A large number of references dealing with the geometric stiffness matrix of the DKT finite element exist in the literature, where nearly all of them adopt an inconsistent form. While such a matrix may be part of the element to treat nonlinear problems in general, it is of crucial importance for linearized buckling analysis. The present work seems to be the first to obtain an explicit expression for this matrix in a consistent way. Numerical results on linear buckling of plates assess the element performance either with the proposed explicit consistent matrix, or with the most commonly used inconsistent matrix.

Abstract To discretize reinforced soil structures in plane strain and predict their collapse load, a simple three-node triangular finite element is formulated based on the static theorem of the limit analysis. The element satisfies the equilibrium equations and the mechanical boundary conditions in a weak sense. A modified Mohr-Coulomb yield surface is adopted to describe the reinforced soil behavior from a macromechanics point of view. It is also taken into account the possibility of tension failure of the reinforcement and failure of the reinforcement interface. The stated nonlinear convex optimization problem is cast as second-order cone programming. Numerical examples illustrate the predictive accuracy of the above scheme as well as the efficiency and speed of an interior-point method to reach optimal solutions.

Abstract Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch-Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical p-refinement is exploited.