Analysis Of Elastic Solids Research Articles

Derivation of exact expressions for two-dimensional singular and finite-part integrals applicable in solid mechanics

The purpose of this paper is to develop exact expressions for the evaluation of singular and finite-part integrals appearing in the stress analysis of elastic solids. A numerical solution is presented for the solution of problems in three dimensional elastostatics. The kernels of the integral equation solution are given in the case where the surfaces of the solid are discretized with flat triangular elements. Exact expressions are derived for the singular and finite-part integrals over a triangular domain. The availability of exact expressions for these integrals will increase the accuracy of the numerical results without the need of any cubature formulae. Finally, the example considered in the paper indicates the excellent approximation obtained by the method even when using only a few classical elements.

Design with Several Eigenvalue Constraints by Finite Elements and Linear Programming

Abstract A finite element discretization, combined with a powerful numerical eigenvalue procedure, has proved to be a unified approach to eigenvalue analysis of elastic solids. Treating the sensitivity analysis as an integrated part of this approach, one obtains gradients of the eigenvalues without any new eigenvalue analysis. This forms the necessary information for an optimal redesign which is formulated as a linear programming problem. By a sequence of optimal redesigns, one then obtains a solution to the problem of optimal design or a solution to an inverse eigenvalue problem. Taking as an example the vibration of Timoshenko beams, we focus on the gradient functions, on the dependence of slenderness, and on the inherent problem of local optima.