Report on parallel processing oriented generalized design sensitivity analysis method for multibody dynamic systems.

This volume provides the international multibody dynamics community with an up-to-date view on the state of the art in this rapidly growing field of research which now plays a central role in the modeling, analysis, simulation and optimization of mechanical systems in a variety of fields and for a wide range of industrial applications. This book contains selected contributions delivered at the ECCOMAS Thematic Conference on Multibody Dynamics, which was held in Brussels, Belgium and organized by the Université catholique de Louvain, from 4th to 7th July 2011. Each paper reflects the State-of-Art in the application of Multibody Dynamics to different areas of engineering. They are enlarged and revised versions of the communications, which were enhanced in terms of self-containment and tutorial quality by the authors. The result is a comprehensive text that constitutes a valuable reference for researchers and design engineers which helps to appraise the potential for the application of multibody dynamics methodologies to a wide range of areas of scientific and engineering relevance.

In this report, the technical objective is the derivation of a systematic and unified theory and organization of a corresponding general computer program for the design of constrained dynamic systems by judicious selection of the most suitable methods from the following branches of mathematics and mechanics: (a) Optimization Methods, (b) Rigid Body Mechanics, (c) Numerical Integration Methods, and (d) Matrix Manipulation Methods. Accordingly, a method of formulating and automatically integrating the equations of motion and design sensitivity adjoint equations for general constrained dynamic systems is presented. Design sensitivity analysis is carried out using a state-space method that has previously been used for design optimization of linear structural systems. Application of efficient sparse matrix computational methods is shown to be suitable for both dynamic and design sensitivity analyses and for interactive strained system is treated with three degrees of freedom. Algebraic equations prescribing constraints between various bodies are then written and a Lagrangian formulation is used to write the dynamical equations of motion for each body of the system. A stiff predictor-corrector numerical integration (GEAR) algorithm is used for numerical integration of mixed systems of nonlinear differential equations of motion and algebraic equations of constraint (together with spring-damper relations and other user-supplied equations).

Sensitivity analysis and optimal shape design are key issues in engineering that have been affected by advances in numerical tools currently available. This book, and its supplementary online files, presents basic optimization techniques that can be used to compute the sensitivity of a given design to local change, or to improve its performance by local optimization of these data. The relevance and scope of these techniques have improved dramatically in recent years because of progress in discretization strategies, optimization algorithms, automatic differentiation, software availability, and the power of personal computers. Numerical Methods in Sensitivity Analysis and Shape Optimization will be of interest to graduate students involved in mathematical modeling and simulation, as well as engineers and researchers in applied mathematics looking for an up-to-date introduction to optimization techniques, sensitivity analysis, and optimal design.