Optimal design of foundations by means of nonlinear calculation methods

Abstract

This paper proposes using the defining equations from the theory of adaptive evolution of mechanical systems (which is based on the variational principles of nonlinear structural mechanics) to design the shape and size of foundations. It presents an expression for finding the potential energy of a system and the deformation energy density, as well as the variational Lagrange equation. The paper formulates a nonlinear boundary problem solved by finite-element analysis. The solution imposes a constraint on the modulus of elasticity to take into account the physico-mechanical properties of the materials. A calculation algorithm and an ADPL program are written for ANSYS. The paper also presents a solution to the problem of finding the rational foundation shaped for the case of plain strain. The solution-derived rational foundation shape is shown. The authors plot the stresses and energy densities as a function of evolution at the onset and finish of iterative processes. Note that the resulting foundation shape is more stable, more accurately positioned in the soil, and can carry a greater load compared to more conventional shapes.