Second-order cone programming formulations for a class of problems in structural optimization

This paper provides efficient and easy to implement formulations for two problems in structural optimization as second-order cone programming (SOCP) problems based on the minimum compliance method and derived using the principle of complementary enEPSRC grant EP/E004547/1 Early stages of the developments of this paper are provided in the recent conference paper of Makrodimopoulos et al (2008) A. Makrodimopoulos (corresponding author) School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-595194 Fax : ++44-(0)2380-594813 E-mail: [email protected] A. Bhaskar School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-593825 Fax : ++44-(0)2380-594813 E-mail: [email protected] A.J. Keane School of Engineering Sciences, University of Southampton Tel.: ++44-(0)2380-592944 Fax : ++44-(0)2380-594813 E-mail: [email protected] ergy. In truss optimization both single and multiple loads (where we optimize the worst-case compliance) are considered. By using a heuristic which is based on the SOCP duality we can consider a simple ground structure and add only the members which improve the compliance of the structure. It is also shown that thickness optimization is a problem similar to truss optimization. Examples are given to illustrate the method developed in this paper.