Structural topology optimization subjected to relaxed stress and design variables

Sustainability, the ability of humans to live within our means, becomes a major concern for engineers and designers now a day's. Engineering optimization, which uses techniques of selecting best elements from set of alternatives to achieve design goals, is one means for sustainability. Structural topology optimization, which is one type of engineering optimization, deals with finding optimal layout of a structure through optimal material distribution with a given design domain. Topology optimization problems have been formulated and solved by means of compliance minimization. There are some efforts for formulating and solving a topology optimization problem with stress constraints. Though formulating an optimization problems with stress constraints seems acceptable and reliable from engineering point of view it has been facing challenges associated with high nonlinear local stress constraints and design variables. In this paper an optimization problem is formulated to minimize volume based on von mises stress theory subjected to stress constraints for two dimensional problems. A mathematical model which takes into consideration the singularity phenomenon associated with the design variables and stress constraints is developed. The results of the model is compared to the results of the compliance based approach by solving two numerical cases. The numerical results shows that the proposed method has comparable efficiency and accuracy by having less transition elements and securing elements in the design domain free from stress failure. © 2006-2016 Asian Research Publishing Network (ARPN).