Direct computation of stresses in linear elasticity

Direct Computation of Stresses in Elasticity

We describe and analyze an approach to the pure Neumann problem of three-dimensional linearized elasticity, whose novelty consists in considering the strain tensor field as the sole unknown, instead of the displacement vector field as is customary. This approach leads to a well-posed quadratic minimization problem of a new type, constrained by a weak form of the classical Saint Venant compatibi...

Shape Gradient Computation in Isogeometric Analysis for Linear Elasticity

The transfer of geometrical data from CAD (Computer Aided Design) to FEA (Finite-Element Analysis) is a bottleneck of automated design optimization procedures, yielding a loss of accuracy and cumbersome software couplings. Isogeometric analysis methods propose a new paradigm that allows to overcome these difficulties by using a unique geometrical representation that yields a direct relationship...

On the existence of solution in the linear elasticity with surface stresses

Integrability of Displacement and Stresses in Linear and Nonlinear Elasticity with Mixed Boundary Conditions

Equations of linear and nonlinear infinitesimal elasticity with mixed boundary conditions are considered. The bounded domain is assumed to have a Lipschitz boundary and to satisfy additional regularity assumptions. W 1,p regularity for the displacements and Lp regularity for the stresses is proved for some p > 2.

On the Strong Closure of Strains and Stresses in Linear Elasticity

We consider the following special problem related to the optimal layout problems of materials: Given two elastic materials, C 1 and C 2 the corresponding elasticity tensors, and a force ~ f, nd the strong closure of strains and stresses as the distribution of the materials varies or, alternatively, nd the sets of elasticity tensors which generate these strong closures. In this paper, it is show...