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.

Editorial

“…Here Makrodimopoulos (2015) seeks to assess how well Hodge and Belytschko's formulation performs when used in conjunction with modern computing facilities and optimisation algorithms. In fact, it is shown that the Hodge and Belytschko formulation compares favourably with a number of recently proposed methods, and it is also shown that it can be extended to model reinforced concrete slabs, by using the Neilsen failure criteria.In the paper by Dollerup et al (2015), an optimisation-based design procedure for reinforced concrete slabs is proposed. The lack of suitable computer-based tools for the design of reinforced concrete slabs has led some practitioners to turn to elastic methods, even when ultimate limit state behaviour is of primary importance.…”

“…In the paper by Dollerup et al (2015), an optimisation-based design procedure for reinforced concrete slabs is proposed. The lack of suitable computer-based tools for the design of reinforced concrete slabs has led some practitioners to turn to elastic methods, even when ultimate limit state behaviour is of primary importance.…”

“…This can lead to complex reinforcement layouts and/or to very conservative designs. Dollerup et al (2015) describe a lower bound limit analysis/design formulation capable of treating multiple load cases, and demonstrate its efficacy by applying it to various slab design problems. It is shown that it can be used to identify slab designs with significantly reduced required moment capacities (and hence; for example, steel reinforcement).…”