Direct limit analysis based topology optimization of foundations

Topology optimization of foundation structures is conducted using a direct limit analysis based optimization approach. Originally developed for plastic topology design of 2D superstructures and industrial structures, which are traditionally designed based on elasticity, the direct limit analysis based design method demonstrated strong intrinsic properties that make of it a promising alternative for topology design. Unlike existing methods the one proposed here is fundamentally conceived and developed in the framework of direct plastic limit analysis which is the natural and usual known framework for the analysis and design of geotechnical structures. The method is extended to handle foundation design by providing for the simultaneous presence of two materials: the soil and the reinforcement, governed by Coulomb failure law. Two types of designs are considered, namely, continuous and discrete. The first allows a range of graded densities of reinforcement that may in practice represent the types of mixtures used in soil improvement, such as cementation. In the discrete design the reinforcement consists exclusively of solid structural elements. A series of two dimensional example problems demonstrate the capabilities of the method to generate rational classical designs or uncommon but intuitively sound foundation configurations that could inspire designers to develop novel solutions.