A new family of locking-free finite elements for shear deformable Reissner-Mindlin plates is presented. The elements are based on the "tangential-displacement normal-normal-stress" formulation of elasticity. In this formulation, the bending moments are treated as separate unknowns. The degrees of freedom for the plate element are the nodal values of the deflection, tangential components of the ...

The solutions of fluid-structure interaction problems, using displacement-based finite element formulations for acoustic fluids, may contain spurious non-zero frequencies. To remove this deficiency, we present here a new formulation based on a three-field discretization using displacements, pressure and a “vorticity moment” as variables with an appropriate treatment of the boundary conditions. ...

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...

Automatic hexahedral mesh generation for complex geometries is still a challenging problem, and therefore tetrahedral or mixed meshes are preferred. Unfortunately the standard formulation of the linear tetrahedral element exhibits volumetric locking in case of almost incompressible materials. In this paper we propose a new linear tetrahedral element based on the average nodal Jacobian. This ele...

The recently proposed expanded mixed formulation for numerical solution of second order elliptic problems is here extended to fourth order elliptic problems. This expanded formulation for the diierential problems under consideration diiers from the classical formulation in that three variables are treated, i.e., the displacement and the stress and moment tensors. It works for the case where the...

Modern structural optimization problems can usually be formulated in several alternative, but equivalent, ways leading to identical solutions. The chosen formulation may affect significantly the solution process, and is characterized by the independent variables and analysis equations used, as well as the form of constraints. A comprehensive study for different available schemes to structural o...

Koiter's asymptotic method enables the calculation and deep understanding of initial post-buckling behaviour thin-walled structures. For single-mode analysis, Budiansky (1974) presented a clear general formulation for method, based on expansion total potential energy function. The from is herein revisited expanded multi-modal primordial importance in structures with clustered bifurcation modes....

In this work, the rectangular nonconforming Wilson element in solving incompress-ible elastic equation is analyzed. Although the element does not satisses the inf-sup condition (in a mixed formulation), it still can be used to compute the displacement successfully. If a simple post-processing is applied, the pressure converges, too. An optimal convergence rate is established for both displaceme...