Variational approach by means of adjoint systems to structural optimization and sensitivity analysis. I - Variation of material parameters within fixed domain

For a linear elastic structure, the first variation of an arbitrary stress, strain and displacement functionals corresponding to variation of material parameters within specified domain is derived by using the solution for primary and adjoint systems. This variation is of fundamental importance in sensitivity analysis, optimal design and identification problems. Simple examples of optimal stiffness design and identification of stiffness parameters in beams are presented.