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

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

A numerical study on optimum shape of steel slit dampers

Steel slit dampers are among the passive energy dissipating devices that have been proposed to improve seismic performance of steel structures. Several experimental and numerical studies have also been carried out to investigate capacity of the dampers in energy dissipation. In this article, a numerical model is developed to obtain optimum boundary shape of the dampers. To achieve this, isogeometric analysis method is utilized as a powerful tool in precise modeling of complex geometries for the purpose of non-linear analysis of the dampers. A conventional steel slit damper shape is modeled by non-uniform rational B-splines, and then, the shape is optimized with the aim of maximizing the structural energy dissipation under a volume constraint. To verify the model, measurements of an experimental test in literature are compared with the model results. A mathematical-based approach is employed for the optimization process and analytical shape sensitivity analysis is performed. As a result of optimization process, a new steel slit damper is suggested and its performance is evaluated via comparing with other shapes suggested in the literature.

Shape sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity

This work is devoted to the study of the void identification problem from partially overdetermined boundary data in the 2D-elastostatic case. In a first part, a shape identifiability result from a Cauchy data is presented, i.e. with traction field and boundary displacement as measurements. Then this geometric inverse problem is tackled by the minimization of two cost functionals, an energy gap functional and an {L^{2}} -gap functional, which enable the reconstruction of voids under Navier’s boundary conditions. The shape derivatives of these cost functionals are computed for the purpose of sensitivity analysis.