Sensitivity analysis and optimal design with account for varying shape and support conditions

The present article deals with an extended class of design problems when besides material or dimensional variables, also structure shape, external support conditions, action through initial distortions is considered. In particular, a problem of mixed boundary conditions is discussed when imposed strength and stiffness requirements may lead to conflicting design decisions The sensitivity analysis for both linear and non-linear structures provides a uniform variational approach to such variety of problems by generating expressions of functional gradients explicitly in terms of state fields of primary and adjoint structures.