Sensitivity analysis of 3D frictional contact with BEM using complex-step differentiation

Abstract

This paper presents a study of the complex step differentiation method applied to a parameter sensitivity analysis for 3D elastic contact problem. The analysis is performed with the Boundary Element Method (BEM) using discontinuous elements and the Generalized Newton Method with line search (GNMls). A standard BEM implementation is used and the contact restrictions are fulfilled through the augmented Lagrangian method. This methodology in conjunction with the BEM avoids the calculation of the nonlinear derivatives during the solution process, allowing a fast and reliable solution procedure. The parameter sensitivity is evaluated using complex-step differentiation. This well-known method approximates the derivative of a function analogously to the standard finite differences method, with the advantages of being numerically exact and nearly insensitive to the step-size. As an example, a Hertz-type problem is solved and the sensitivity of the contact pressures with respect to the Young Modulus variation is evaluated. The obtained results are compared with analytical and numerical solutions found in the literature.