Ana Faustino
Secção de Matemática do Dep. Eng. Civil - Faculdade de Engenharia da Universidade do Porto

Joaquim J. Júdice
Departamento de Matemática da Universidade de Coimbra e Instituto de Telecomunicações - Polo de Coimbra

Isabel M. Ribeiro
Secção de Matemática do Dep. Eng. Civil - Faculdade de Engenharia da Universidade do Porto

A. Serra Neves
Secção de Materiais de Construção do Dep. Eng. Civil - Faculdade de Engenharia da Universidade do Porto

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 finds applications in some civil engineering structural design problems and 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.