Structural shape design sensitivity analysis - A unified viewpoint

Abstract

Two major approaches for structural shape design sensitivity analysis the material derivative and control volume approaches are presented, analyzed and compared. Starting with a continuum formulation and a general response functional needing sensitivity analysis, the two approaches are derived. It is shown that the final design sensitivity expression for one approach can be obtained from the final expression for the other. Thus the two approaches are theoretically the same. Discretizations of the continuum expressions are discussed and it is shown that the two approaches can lead to different implementations for numerical calculations. The control volume approach appears to be more natural for computer implementation because it is viewed as an extension of the isoparametric formulation for finite element analysis to the design sensitivity analysis problem. This view point leads to a simple explanation of the method involving explicit design variations of the internal and external forces. Using this interpretation a general implementation of the method is suggested either outside an established finite element code or inside it.