Combined gradient-stochastic optimization with negative circular masks for large deformation topologies


Anupam Saxena, Mechanical Engineering, Indian Institute of Technology Kanpur, Kanpur 208016, India.



Topology optimization of large deformation two-dimensional continua is presented using a combined gradient-stochastic search with negative circular masks. The possibility of generating perfect black and white topologies is explored while attaining the efficiency of first-order and second-order search algorithms. The design region is modeled with honeycomb tessellation to thwart the known connectivity singularities such as the checkerboards and point flexures. Mask shrinkage is incorporated for ease in density transition between gradient and stochastic steps. Notches at continuum boundaries are moderated through multiple use of a simple boundary smoothing method. A neo-Hookean elasticity model is employed to simulate the material nonlinearities in large displacement continua. With examples on stiff beams and large deformation compliant mechanisms, it is illustrated that perfectly binary, connected and smooth topologies can be obtained within a few hundred design evaluations.Copyright © 2012 John Wiley & Sons, Ltd.