We present a family of pairs of finite element spaces for the unaltered Hellinger–Reissner variational principle using polynomial shape functions on a single triangular mesh for stress and displacement. There is a member of the family for each polynomial degree, beginning with degree two for the stress and degree one for the displacement, and each is stable and affords optimal order approximati...

The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced fibre-reinforced com...

In this paper, a generalized particle system (GPS) method, a general method to describe multiple strong form representation based particle methods is described. Gradient, divergence, and Laplacian operators used in various strong form based particle method such as moving particle semi-implicit (MPS) method, smooth particle hydrodynamics (SPH), and peridynamics, can be described by the GPS metho...

Abstrac-Based on a variational principle, a new approach to derive the exact boundary equation for the analysis of nonlinear Reissner plates and a related existing criterion for the solution of the boundary integral equation is presented in this paper. In this procedure, the boundary and the domain of the plate are discredited to solve the nonlinear problems. All unknown variables are at the bo...

In this paper, we extend the hybridization procedure proposed in [D. N. Arnold and F. Brezzi, Mixed nonconforming finite element methods: Implementation, postprocessing error estimates, ESAIM Math. Model. Numer. Anal. 19 (1985) 7–32] to Virtual Element Method for linear elasticity problems based on Hellinger–Reissner principle. To illustrate such a technique, focus specific 2D scheme, but other...