We present new rectangular mixed finite elements for linear elasticity. The approach is based on a modification of the Hellinger-Reissner functional in which the symmetry of the stress field is enforced weakly through the introduction of a Lagrange multiplier. The elements are analogues of the lowest order elements described in Arnold, Falk and Winther [ Mixed finite element methods for linear ...

A triangular mixed finite element model for the elasto-plastic analysis of Kirchhoff plates is presented. The proposed discretization is based on rigid in bending elements connected by means of rotational springs between the inter-element sides and constant bending moments on the influence area of each node. The continuity of the normal bending moment through the sides allows a standard Helling...

Size-dependent longitudinal and torsional vibrations of nano-beams are examined by two-phase mixture integral elasticity. A new and efficient elastodynamic model is conceived by convexly combining the local phase with strain- and stress-driven purely nonlocal phases. The proposed stress-driven nonlocal integral mixture leads to well-posed structural problems for any value of the scale parameter...

A carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular FEM models, and to reconstruct a strain field with an adjustable parameter a. A novel Galerkin-like weakform derived from the Hellinger–Reissner variational principle is proposed for establishing the discretized system equations. The new weak form is very simple, possesses the same goo...

Abstract In this paper, we study the approximation of eigenvalues arising from mixed Hellinger–Reissner elasticity problem by using a simple finite element introduced recently one authors. We prove that method converges when residual type error estimator is considered and decays optimally with respect to number degrees freedom. A postprocessing technique originally proposed in different context...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

this paper is devoted to the spectral theory (more precisely, tothe variational theory of the spectrum) of guided waves in anelastic half cylinder.  we use variational methods to investigateseveral aspects of propagating waves, including localization (seefigure 1), existence criteria and the formulas to find them. weapproach the problem using two complementary methods: thevariational methods fo...

The hybrid stress boundary element method (HSBEM) was introduced in 1987 on the basis of the Hellinger-Reissner potential, as a generalization of Pian’s hybrid finite element method. This new two-field formulation makes use of fundamental solutions to interpolate the stress field in the domain of an elastic body, which ends up discretized as a superelement with arbitrary shape and arbitrary num...

Abstract In this paper, mixed formulations are presented in the framework of isogeometric Reissner–Mindlin plates and shells with aim alleviating membrane shear locking. The based on Hellinger-Reissner functional use stress resultants as additional unknowns, which have to be interpolated appropriate approximation spaces. unknowns can eliminated by static condensation. analysis condensation is p...