Load-Path-Based Topology Optimization of Two-Dimensional Continuum Structures

Abstract

The connection between topology optimization and load transfer is established in this work. The load transfer functions are used as an intermediate variable for topology optimization. This approach uses the total variation to minimize different objective functions such as the norm of the stress tensor and deviatoric principal stress subjected to equilibrium. To attain the topology of the microstructure, the principal load paths that follow the optimized principal stress directions are calculated. The principal vector field has singularities that are removed by an interpolation scheme. The optimal periodic microstructure is constructed using the load functions and the microstructures’ dimensions. The first advantage of this scheme is that using the load functions reduces the number of equilibrium constraints from two to one and reduces the number of variables from three stress tensor components to two load functions, leading to computational cost savings. The second advantage is that the nonlinear elliptic partial differential equations derived from the total variation equations are solved using the Gauss–Newton method, which has a quadratic convergence, speeding up the convergence toward the optimal structure. The third feature of the load-path-based optimization method is that the equilibrium and optimization problems are solved simultaneously.