Research on Ratio-Extremum Algorithm for Topology Optimization of Continuum Structures Including Active Constraint Identification

Abstract

To obtain the topology optimization algorithm of continuum structure which can effectively identify the effective constraints and quickly converge, based on the original Ratio-Extremum algorithm theory based on truss structure optimization, the emitter algorithm theory is introduced into the topology optimization of continuum structure. Firstly, taking pseudo density as design variables, mathematical model of the minimization mass with constraints of nodal displacements and element stresses is constructed. Secondly, according to essential extremum conditions of Dual objective function, iterative optimization direction and analytical step-size of constraint multipliers are derived. And, according to essential extremum conditions of Generalized Lagrange function, iterative optimization direction and analytical step-size of pseudo densities are derived. Analytical step-sizes are used to avoid one-dimensional optimization and then the calculation quantity of iterative optimization can be decreased. Thirdly, first-order partial derivatives of nodal displacement and element equivalent stress constraints with respect to pseudo densities are given. After that, by using self-compiled MATLAB program for continuum structure analysis, partial derivative calculation and optimization iteration, 4 optimization examples of different beam structures are used to show the changes of active nodal displacement and element equivalent stress constraints, and structural mass in the optimization iteration process, and to show the effectiveness of Ratio-Extremum algorithm in topology optimization of continuum structures.