Rationalization of trusses generated via layout optimization

Abstract

Numerical layout optimization provides a computationally efficient and generally applicable means of identifying the optimal arrangement of bars in a truss. When the plastic layout optimization formulation is used, a wide variety of problem types can be solved using linear programming. However, the solutions obtained are frequently quite complex, particularly when fine numerical discretizations are employed. To address this, the efficacy of two rationalization techniques are explored in this paper: (i) introduction of 'joint lengths', and (ii) application of geometry optimization. In the former case this involves the use of a modified layout optimization formulation, which remains linear, whilst in the latter case a non-linear optimization post-processing step, involving adjusting the locations of nodes in the layout optimized solution, is undertaken. The two rationalization techniques are applied to example problems involving both point and distributed loads, self-weight and multiple load cases. It is demonstrated that the introduction of joint lengths reduces structural complexity at negligible computational cost, though generally leads to increased volumes. Conversely, the use of geometry optimization carries a computational cost but is effective in reducing both structural complexity and the computed volume.

Optimum structure for a uniform load over multiple spans

“…5 shows relatively coarse resolution numerical solutions. These have been rendered even clearer via application of a geometry optimization post-processing step, which involves rationalizing the solution by adjusting the positions of nodes (He and Gilbert 2015); full details of the numerical solutions are included in the electronic supplementary information.…”

Application of layout optimization to the design of additively manufactured metallic components

“…The main drawback of the strategy adopted here is that some iterations were required in order to obtain a viable design solution. However, the need for iteration could potentially be reduced through the use of a geometry optimization rationalization step (this involves adjusting the positions of nodes, which in turn leads to removal of many thin elements (He and Gilbert 2015). This could potentially replace the sizing optimization step described in Section 3.3.…”

“…When attempting to yield a practical solution various rationalization techniques can be applied (e.g. He and Gilbert 2015), or alternatively, the optimization can simply be performed with a coarse nodal discretization and, provided the layout obtained is practical, and the associated volume lies within an acceptable percentage of the reference volume, then it can be deemed acceptable. For this initial investigation any solution that fell within 20 % of the reference volume was deemed to be potentially acceptable.…”

Automatic rationalization of yield-line patterns identified using discontinuity layout optimization

“…These distinguishing features can be expected to ensure that performance is much improved. Note also that the proposed procedure is similar to the procedure recently proposed for rationalizing trusses identified using layout optimization (He and Gilbert 2015); also the use of a geometry optimization step to improve very coarse resolution DLO solutions has recently been proposed for in-plane analysis problems by Bauer and Lackner (2015).…”