Growth method for size, topology, and geometry optimization of truss structures

The problem of optimally designing the topology of plane trusses has, in most cases, been dealt with as a size problem in which members are eliminated when their size tends to zero. This article presents a novel growth method for the optimal design in a sequential manner of size, geometry, and topology of plane trusses without the need of a ground structure. The method has been applied to single load case problems with stress and size constraints. It works sequentially by adding new joints and members optimally, requiring five basic steps: (1) domain specification, (2) topology and size optimization, (3) geometry optimization, (4) optimality verification, and (5) topology growth. To demonstrate the proposed growth method, three examples were carried out: Michell cantilever, Messerschmidt–Bölkow–Blohm beam, and Michell cantilever with fixed circular boundary. The results obtained with the proposed growth method agree perfectly with the analytical solutions. A Windows XP program, which demonstrates the method, can be downloaded from http://www.upct.es/~deyc/software/tto/.