Abstract
This paper concerns simultaneous geometry and topology optimization of truss structures. To be specific, coordinates of truss nodes and axial stress resultants are admitted as design variables in the optimization process. Within this scope, two- and three-dimensional systems are considered; the latter also include cable nets in tension. In the analysis of such structures, curvilinear elements are represented as polygonal chains of straight members. Such approach is legitimate in light of computational line of discussion in the paper, and it also allows for a consistent description of statics in terms of the theory of trusses. Combining the optimal design of truss geometry and topology in one numerical algorithm results in a highly nonlinear problem involving algebraic functions. However, employing the idea of force densities—i.e., ratios of axial stress resultants to member lengths—makes it possible to recast the problem into the computationally less demanding form involving polynomials. The computational part of the study was performed in Scilab and MATLAB. The results obtained show that the proposed approach to optimal design of trusses and truss-like structures is scientifically reliable and may be used by civil engineers and architects.
Published Version
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