A computational procedure for flexible beams with frictional contact constraints

Abstract

SUMMARYThis paper deals with the application of a parametric quadratic programming (PQP) I N T R O D U C T I O NWith the introduction of stronger, light weight and flexible synthetic materials the geometrically non-linear analysis of frames, buildings, many machine parts and structural components has become essential. In some engineering applications, these flexible structures will undergo frictional contacts. This adds another type of non-linearity. Owing to the highly non-lincar behaviour and the complex geometry of such structural components, detailed analysis of their structural behaviour requires efficient, robust and above all reliable numerical solvers. The aim of this paper is to offer the formulation and numerical solution of a class of geometrically non-linear beam structures subjected to frictional contact constraints.The most common methods of treating geometrically non-linear contact problems are based o n either the Lagrange multiplier method or on the penalty function method. When the former is employed. the conditions are enforced by augmenting the Lagrangian multipliers as additional system variables. However, this engenders computational difficulties as the resulting solution matrix contains zero diagonal terms corresponding to the Lagrange multipliers, in addition to the increased numbcr of unknowns as the Lagrange multipliers are part of the unknown solution vector.

Engineering and Economic Applications of Complementarity Problems

“…Recent references on these problems include [3,16,17,91,92]. Contact problems with Coulomb friction have been treated extensively by Klarbring and his colleagues [18,82,90,93,94,95,96,97] as well as in [4,108,109,111,115,116,145,187,191]. Mathematical programming techniques used for solving the latter problems include linear complementarity methods, sequential quadratic programming algorithms, Newton methods for generalized equations, and B-differentiable equations.…”