Variational approach by means of adjoint systems to structural optimization and sensitivity analysis—II: Structure shape variation

Abstract For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of shape of external boundaries or interfaces is derived by using the solutions for primary and adjoint systems. The application to optimal design is next presented and the relevant optimally conditions are derived from general expressions. The path-independent integrals used in fracture mechanics are rederived as a particular case of general expressions.

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