In this paper we introduce new finite elements to approximate the Hellinger Reissner formulation of elastictiy. The elements are the vector valued tangential continuous Nédélec elements for the displacements, and symmetric, tensor valued, normal-normal continuous elements for the stresses. These elements do neither suffer from volume locking as the Poisson ratio approaches 12 , nor suffer from ...

A modified first-order system least squares formulation for linear elasticity, obtained by adding the antisymmetric displacement gradient in the test space, is analyzed. This approach leads to surprisingly small momentum balance error compared to standard least squares approaches. It is shown that the modified least squares formulation is well-posed and its performance is illustrated by adaptiv...

Increasing applications of laminated composite structures necessitate the development equivalent single layer (ESL) models that can achieve similar accuracy but are more computationally efficient than 3D or layer-wise models. Most ESL displacement-based do not guarantee interfacial continuity shear stresses within laminates. A possible remedy is enforcement interlaminar equilibrium in variation...

Powell–Sabin B-splines are enjoying an increased use in the analysis of solids and fluids, including fracture propagation. However, B-spline interpolation does not hold Kronecker delta property and, therefore, imposition Dirichlet boundary conditions is as straightforward for standard finite elements. Herein, we discuss applicability various approaches developed to date weak analyses which empl...

The Arnold–Winther element successfully discretizes the Hellinger–Reissner variational formulation of linear elasticity; its development was one key early breakthroughs finite exterior calculus. Despite great utility, it is not available in standard software, because degrees freedom are preserved under Piola push-forward. In this work we apply novel transformation theory recently developed by K...

In this paper we prove that if $X $ is a Banach space, then for every lower semi-continuous bounded below function $f, $ there exists a $left(varphi_1, varphi_2right)$-convex function $g, $ with arbitrarily small norm,  such that $f + g $ attains its strong minimum on $X. $ This result extends some of the  well-known varitional principles as that of Ekeland [On the variational principle,  J. Ma...

A new low order membrane nite element is presented. The element formulation is based on the variational principle of Hughes and Brezzi employing an independent rotation eld. In the present work nonconforming interpolation is used for the drill rotation eld. Both triangular and quadrilateral elements are considered. Combined with the Reissner-Mindlin plate bending element of O~ nate, Zarate and ...

We use the three-dimensional Hellinger}Reissner mixed variational principle to derive a Kth order (K"0, 1, 2,2) shear and normal deformable plate theory. The balance laws, the constitutive relations and the boundary conditions for the plate theory are deduced. The constitutive relations incorporate the shear and the normal tractions applied on the top and the bottom surfaces of the plate. For a...