Optimal material layout – applied on reinforced concrete slabs

Abstract

This paper introduces a general, finite-element-based optimisation tool for improving the material layout of concrete structures. The application presented is general and exemplified by material optimisation of reinforced concrete slabs. By utilising the optimisation tool, it is possible to determine the optimal material layout of a slab at the ultimate load state based on simple inputs such as outer geometry, boundary conditions, multiple load cases and design domains. The material layout of the optimal design can either be fully orthotropic or isotropic, or a combination with a predefined coupling between design domains and reinforcement directions. The implementation is a lower bound formulation, resulting in a convex optimisation problem that consists of a number of linear constraints from the equilibrium equations and a number of convex non-linear constraints from the yield criteria. By utilising the capabilities of the non-linear interior point method, the non-linear convex yield criteria can be handled directly in the optimal solution process. Further, a graphical user interface is introduced, providing the design engineer with a practical tool for designing optimal structures. Finally, a number of reinforced concrete slab examples validate the method described and show the potential to save large amounts of material in constructions.