Two-scale shape optimisation based on numerical homogenisation techniques and variational sensitivity analysis

Abstract This contribution presents a theoretical and computational framework for two-scale shape optimisation of nonlinear elastic structures. Particularly, minimum compliance problems with composite (matrix-inclusion) microstructures subjected to static loads volume-type design constraints are focused. A homogenisation-based FE $$^2$$ 2 scheme is extended by an enhanced formulation variational (shape) sensitivity analysis based on Noll ’s intrinsic, frame-free continuum mechanics. The obtained overall information couples variations across micro- macroscopic scales. numerical example demonstrates the capabilities proposed framework. investigations involve mesh morphing parametrisation at both macro- microscopic