Abstract
Use of the material derivative concept of continuum mechanics to relate variations in structural shape to measures of structural performance is reviewed. Alternate formulations of design sensitivity analysis are obtained in the form of boundary integrals and domain integrals. Theoretical implications of the resulting formulations are developed to include the dependence of performance on only normal variation of the boundary and the need for evaluation of trace operators for projection of stress and strain related quantities onto the boundary. Computational implications of shape design sensitivity formulations are investigated, including compatibility of design sensitivity analysis with finite element and boundary element methods of structural analysis, parameterization of boundary shape and parameterization of design velocity fields. Implementation of shape design sensitivity analysis using finite element computer codes is discussed. Recent numerical results are used to illustrate the accuracy that is achievable using methods for material derivative shape design sensitivity analysis.
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