An integer programming model for truss topology optimization

Ana M. Faustino*

Joaquim J. Júdice

† Isabel M. Ribeiro*

A. Serra Neves ‡

* Secção de Matemática do Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal afausti@fe.up.pt

iribeiro@fe.up.pt

† Departamento de Matemática da Universidade de Coimbra and Instituto de Telecomunicações, Coimbra, Portugal joaquim.judice@co.it.pt  

‡ Secção de Materiais de Construção do Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Porto asneves@fe.up.pt  

 

Abstract

In this paper a truss-structure model is described for finding a kinematically stable structure with optimal topology and cross-sectional size and minimum volume. The underlying model findsapplicationsinsomecivil engineering structuraldesignproblemsand takes into consideration all the conditions associated with the limit states usually presented in structural safety codes. Ultimate limit states are treated applying plasticity theory, while serviceability limit states are dealt with via elasticity theory. The admissible solution space is discretised using bar elements. A 0 − 1 variable is assigned to each one of these elements, in order to indicate if it is or not included in the solution. The mathematical formulation of the model leads to a mixed 0 1 integer nonlinear program with a nonlinear objective function and linear and bilinear constraints. It is shown that this problem can be reduced into a mixed 0 1 integer linear program by exploiting the so– called reformulation–linearization technique. Some computational experience is included to highlight the importance of these formulations in practice.

Keywords: Truss topology optimization, integer programming, reformulation-linearization technique.

 

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