Constrained and Unconstrained Optimization Formulations for Structural Elements in Unilateral Contact with an Elastic Foundation

Abstract

In this work, two numerical methodologies are proposed for the solution of unilateral contact problems between a structural member (beam or arch) and an elastic foundation. In the first approach, the finite element method is used to discretize the structure and elastic foundation and the contact problem is formulated as a constrained optimization problem. Only the original variables of the problem are used, subjected to inequality constraints, and the relevant equations are written as a linear complementary problem (LCP). The second approach is based on the Ritz method, where the coordinates defining the limits of the contact regions are considered as additional variables of the problem. The contact problem here is treated as an unconstrained optimum design problem. These proposed methodologies are then tested and compared using results from specific problems involving structures under unilateral contact constraints.

Effects of New Tunnelling on a Buried Pipeline with Joints and Its Detachment

“…The existing solutions to this problem are highly sophisticated mathematical analyses. Some distinct approaches may be found in the literature: direct approaches, numerical simulations and mathematical models [30][31][32][33][34][35][36][37][38]. To deal with the problem, a set of transcendental equations or inequalities, and an iterative technique is utilized in all approaches.…”