Finite element analysis of no-tension structures as a topology optimization problem

摘要

An alternative numerical approach is presented for the analysis of no-tension masonry-like solids. Whereas most of the strategies available in the literature resort to non-linear finite element techniques, the proposed approach re-formulates the problem within the framework of topology optimization. The equilibrium of a two-dimensional no-tension body is found searching for the distribution of an equivalent orthotropic material, in which tensile principal stresses are not allowed by prescribing negligible stiffness in the relevant direction, such that the potential energy of the solid is minimized. Unlike many conventional approaches that deal with the tough non-linearity of the problem through step-wise incremental analyses, the proposed method efficiently solves the effect of compatible loads through a one-shot energy-based optimization. Analytical and numerical benchmarks from the literature are investigated to assess the effectiveness of the proposed procedure and to discuss convergence features and possible applications inspired by the limit analysis of masonry-like structures.