Otimização topológica aplicada em um braço robótico flexível

Abstract

This work aims to apply the topology optimization method, to find the best distribution of material in a flexible robotic arm, which maximize or minimize an objective function and meeting a pre-established volume restriction. First we adopt a static model minimizing the compliance and further the study is extended to the dynamic case with the minimization of the dynamic compliance and maximizing natural frequency of the structure. For the three problems, the robotic arm is idealized as a beam located in a two-dimensional domain and in the static model extends the study also for three-dimensional case. These domains are discretized in a finite number of subdomains called finite elements, choosing, due to the geometry of the structure, by the quadrilateral finite elements (two-dimensional domain) and cubic finite elements (three-dimensional domain). In the formulation of problems the SIMP (Solid Isotropic Material with Penalization) material model is used, which admits pseudo-density finite elements as design variables. Design variables in the static problem updated by heuristic method called Optimality Criteria and dynamic problems we use the Sequential Linear Programming. It applies also the sensitivity filter to prevent possible numerical complications interfere with the optimal topologies. Numerical results were obtained through algorithms developed in Matlab software. The accomplished simulations show that the optimal topologies found are well defined, meet the convergence criteri set in the algorithms, can be used as designs in the manufacture of structures and agree with the results similar work done in the literature.