A novel hybrid cellular automata–linear programming approach for the optimal sizing of planar truss structures

Abstract

This paper presents a novel hybrid cellular automata (CA) linear programming (LP) methodology for the size optimisation of planar truss structures. The method uses the nodal displacements and internal forces of the truss as the design variables of the optimisation problem. The objective function is the volume of the structure and the constraints of the original optimisation problem are recast in terms of the new decision variables in the two-phase step. Starting with an arbitrary set of nodal displacements and internal forces, these are updated in turn in an iterative two-phase process. In the first phase, the internal forces are kept fixed and the nodal displacements are found using a CA approach. In the second phase, a LP is used to find the set of internal forces of truss elements which minimises the total volume of the structure. The effectiveness and efficiency of the methodology is also examined with its application to some benchmark truss structures.

Keywords:

• size optimisation
• truss structures
• cellular automata
• Newton–Raphson method
• linear programming
• simplex method