A 99 line code for discretized Michell truss optimization written in Mathematica

Abstract

The main purpose of the paper is to provide an easy-to-use code for topological optimization of the least weight trusses, written in the Mathematica programming language. The main idea of the presented approach consists in using a fixed ground structure and the linear programming formulation of the optimization problem. The solver is based on the fast interior point method. The strong effort is done to create the effective generator of the computational model utilizing the high regularity of the ground structure and the high sparsity of the geometric matrix. The efficiency and reliability of the algorithm is confirmed in several numerical tests. Due to a linear programming formulation of the optimization problem the method presented in the paper assures finding the global optimum, hence it may be considered as the useful tool for verification of results obtained in other ways. The appended complete Mathematica code of the program developed will be supplied by the Publisher on SpringerLink.

Optimal design of a class of symmetric plane frameworks of least weight

“…Let us emphasize that the sole comparison of the volumes is not sufficient. The numerical layouts found in Sokół andLewiński (2010, 2011) and Sokół andRozvany (2011, 2012) compare favorably with analytical results reported in the Introduction of the present paper. In contrast, the numerical predictions of bar layouts shown in Figs.…”

“…The members of the unknown structures should be stressed up to given limits ±σ p and should lie above the line linking the supports. Since this problem has been previously discussed in the remarkable paper by McConnel (1974) including the numerical solutions comparing favorably with those obtained by the present authors (2010) and by Sokół (2011) with using much better software and hardware, one can name this problem shortly: McConnel's problem.…”

“…The supports may be sliding in the horizontal direction with no effect on the form of the solutions in all cases shown Authors of the Discussion suggest. It has been recently solved in Sokół andRozvany (2011, 2012). Let us emphasize that the solutions shown in Fig.…”

“…The solutions of Fig. 3 have been constructed by using analytical method of Sokół and Lewiński (2010) and justified by the numerical method of Sokół (2011). The upper figure in Fig.…”

New analytical benchmarks for topology optimization and their implications. Part I: bi-symmetric trusses with two point loads between supports

“…They were performed using an improved version of the program developed by Sokół (2011a). This newer version of the program makes use of the 'adaptive ground structure' approach, similar to that proposed by Gilbert and Tyas (2003), however, it applies a different strategy of adding-removing of the active bars from a huge number of potential members of the full ground structure.…”