Two discontinuous Galerkin schemes for linear elastic waves in two and three dimensions with Dirichlet and optional Neumann boundary conditions are formulated: a pure displacement formulation and a mixed formulation with the displacement and a pressure parameter as variables. The schemes are implemented for two dimensions using Concepts with piecewise linear orthogonal basis functions for the d...

This paper is concerned with an efficient dual boundary element method for 2d crack problems under antiplane shear loading. The dual equations are the displacement and the traction boundary integral equations. When the displacement equation is applied on the outer boundary and the traction equation on one of the crack surfaces, general crack problems with anti-plane shear loading can be solved ...

This paper presents a variational multiscale method for developing stabilized finite element formulations for small strain inelasticity. The multiscale method arises from a decomposition of the displacement field into coarse (resolved) and fine (unresolved) scales. The resulting finite element formulation allows arbitrary combinations of interpolation functions for the displacement and pressure...

ABSTRACT A new finite element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that utilizes a scalar electric potential as nodal variables, this new formulation implements a vector potential from which components of electric displacement are derived. For linear piezoelectric materials with positive definite material ...

In this paper, a new nite-element formulation for the solution of electromechanical boundary value problems is presented. As opposed to the standard formulation that uses scalar electric potential as nodal variables, this new formulation implements a vector potential from which components of electric displacement are derived. For linear piezoelectric materials with positive de nite material mod...

This paper presents a method to compute consistent response sensitivities of force-based finite element models of structural frame systems to both material constitutive and discrete loading parameters. It has been shown that force-based frame elements are superior to classical displacement-based elements in the sense that they enable, at no significant additional costs, a drastic reduction in t...

The boundary element method (BEM) for linear elasticity in its curent usage is based on the boundary integral equation for displacements. The stress field in the interior of the body is computed by differentiating the displacement field at the source point in the BEM formulation, via the strain field. However, at the boundary, this method gives rise to a hypersingular integral relation which be...

The rapid layout synthesis of microresonators from high-level engineering specifications is demonstrated. Functional parameters such as resonant frequency, quality factor, and displacement amplitude at resonance are satisfied while simultaneously minimizing a user-specified objective function. A synthesis tool implementing the optimization-based formulation can be used to explore micromechanica...

A first-order system least squares formulation for the Signorini problem modeling frictionless contact in linear elasticity is studied. In addition to the displacement field, the stress tensor is used as an independent process variable. A contact boundary term is added to the usual least squares functional in order to achieve coercivity and continuity in appropriate norms. The discrete function...

A quasi-static mixed boundary value problem of incremental elasto-plasticity for a continuously inhomogeneous body is considered. Using the two-operator Green-Betti formula and the fundamental solution of a reference homogeneous linear elasticity problem, with frozen initial or tangent elastic coefficients, a boundary-domain integro-differential formulation of the elasto-plastic problem is pres...