A CONTINUUM MECHANICAL-BASED FORMULATION OF THE VARIATIONAL SENSITIVITY ANALYSIS IN STRUCTURAL OPTIMIZATION .1. ANALYSIS

A variational formulation of shape design sensitivity analysis is outl ined, starting from a differential geometry-based representation of co ntinuum mechanics. A rigorous analysis using convected curvilinear coo rdinates yields a decomposition of all continuum mechanical functions into independent geometry and displacement mappings. Using this repres entation of geometry and displacements defined on a fixed parameter sp ace, their influence on physical quantities can easily be separated. C onsequently, the variations of continuum mechanical quantities with re spect to either geometry or displacements can be performed similarly u sing the well-known linearization techniques in nonlinear mechanics. T he proposed methodology for performing variational design sensitivity analysis is formulated for general nonlinear hyperelastic material beh aviour using either the Lagrangian or Eulerian description. The differ ences and similarities of the formulation presented compared with the material derivative approach and the domain parametrization approach a re highlighted and discussed.