An inverse method for optimizing elastic properties considering multiple loading conditions and displacement criteria

Significant research effort has been devoted to topology optimization of two- and three-dimensional structural elements subject to various design and loading criteria. While the field of topology optimization has been tremendously successful over the years, literature focusing on the optimization of spatially-varying elastic material properties in structures subject to multiple loading states is scarce. In this article, we contribute to the state of the art in material optimization by proposing a numerical regime for optimizing the distribution of the elastic modulus in structural elements subject to multiple loading conditions and design displacement criteria. Such displacement criteria (target displacement fields prescribed by the designer) may result from factors related to structural codes, occupant comfort, proximity of adjacent structures, etc. In this work, we utilize a constrained least-squares framework to solve the optimization problem for N loading conditions and design displacement targets. This approach is formulated in a straight-forward manner such that it may be applied in a broad suite of design problems with unique geometries, loading conditions, and displacement criteria. To test the approach, a suite of optimization problems are solved to demonstrate solutions considering N=2 for different geometries and boundary conditions.