Mechanical and structural engineers have always strived to make as efficient use of material as possible, e.g. by making structures as light as possible yet able to carry the loads subjected to them. In the past, the search for more efficient structures was a trial-and-error process. However, in the last two decades computational tools based on optimization theory have been developed that make it possible to find optimal structures more or less automatically. Due to the high cost savings and performance gains that may be achieved, such tools are finding increasing industrial use.This textbook gives an introduction to all three classes of geometry optimization problems of mechanical structures: sizing, shape and topology optimization. The style is explicit and concrete, focusing on problem formulations and numerical solution methods. The treatment is detailed enough to enable readers to write their own implementations. On the book's homepage, programs may be downloaded that further facilitate the learning of the material covered.The mathematical prerequisites are kept to a bare minimum, making the book suitable for undergraduate, or beginning graduate, students of mechanical or structural engineering. Practicing engineers working with structural optimization software would also benefit from reading this book."--Publisher's website.

In this work we reformulate the incremental, small strain, J2-plasticity problem with linear kinematic and nonlinear isotropic hardening as a set of unconstrained, nonsmooth equations. The reformulation is done using the minimum function. The system of equations obtained is piecewise smooth which enables Pang's Newton method for B-differentiable equations to be used. The method proposed in this work is compared with the familiar radial return method. It is shown, for linear kinematic and isotropic hardening, that this method represents a piecewise smooth mapping as well. Thus, nonsmooth Newton methods with proven global convergence properties are applicable. In addition, local quadratic convergence (even to nondifferentiable points) of the standard implementation of the radial return method is established. Numerical tests indicate that our method is as efficient as the radial return method, albeit more sensitive to parameter changes. © 2002 Elsevier Science B.V. All rights reserved.

In this paper we reformulate the frictional contact problem for elasto-plastic bodies as a set of unconstrained, non-smooth equations. The equations are semi-smooth so that Pang's Newton method for B-differentiable equations can be applied. An algorithm based on this method is described in detail. An example demonstrating the efficiency of the algorithm is presented. © 2002 Elsevier Science Ltd. All rights reserved.