The topical problem of optimizing the stress state in a bimaterial plate by proper
shaping of the matrix/inclusion interface is considered with respect to a recently
advanced criterion of minimizing the global variations of the contact stresses.
Mathematically, the variations provide an integral-type assessment of the local
stresses which requires less computational effort than direct minimization of the
stress concentration factor. The proposed criterion can thus be easily incorporated in
the numerical optimization scheme previously proposed by the author for similar
inverse problems. It consists of an efficient complex-valued direct solver and an
ordinary evolutionary search enhanced with an economical shape parametrization
tool. The attendant problem of optimizing the effective shear moduli is also
solved for comparison purposes. Though methodologically the paper continues
the previous works of the author, the primary emphasis is now placed on
developing a systematic optimization approach to obtain comprehensive
numerical results for nonbiaxial loadings. This setup is of special interest since
it differs drastically from the biaxial case, where the analytically known
equistress interfaces serve as an efficient benchmark for both theory and
computations. Consequently, given the lack of structurally specific analytical
assessments, the simulations performed for a wide range of values of the governing
parameters provide detailed numerical insight into the chosen case. The
elastic behavior of the optimal square-symmetric structures with strongly
contrasting well-ordered constituents is conveniently detailed in a set of
figures.
