A simple layout optimization formulation for load-carrying tensegrity structures

Traditional tensegrity structures comprise isolated compression members lying inside a continuous network of tension members. In this contribution, a simple numerical layout optimization formulation is presented and used to identify the topologies of minimum volume tensegrity structures designed to carry external applied loads. Binary variables and associated constraints are used to limit (usually to one) the number of compressive elements connecting a node. A computationally efficient two-stage procedure employing mixed integer linear programming (MILP) is used to identify structures capable of carrying both externally applied loads and the self-stresses present when these loads are removed. Although tensegrity structures are often regarded as inherently ‘optimal’, the presence of additional constraints in the optimization formulation means that they can never be more optimal than traditional, non-tensegrity, structures. The proposed procedure is programmed in a MATLAB script (available for download) and a range of examples are used to demonstrate the efficacy of the approach presented

Layout optimization of structures with distributed self-weight, lumped masses and frictional supports

The well-known ‘ground structure’-based truss layout optimization method has recently been extended to allow accurate modelling of distributed self-weight. By incorporating equally stressed catenaries in the ground structure, non-conservative errors caused by neglecting bending effects within members carrying their own weight are eliminated. However, in cases where the self-weight of a structure has a favourable role in supporting the applied loads, solutions that include convoluted arrangements of overlapping elements may often be generated. To address this, an enhanced layout optimization formulation is proposed that explicitly allows inclusion of favourable unstressed masses, such as counterweights. Frictional supports are also modelled and the cost of abutments and anchorages taken account of in the formulation. The efficacy of the proposed methodology is demonstrated through application to benchmark examples and to the conceptual design of a simplified long-span bridge structure, considering both ground anchored and self-anchored alternatives

Adaptive topology optimization of fail-safe truss structures

Avoidance of disproportionate and progressive collapse, often termed ‘fail-safe design’, is a key consideration in the design of buildings and infrastructure. This paper addresses the problem of fail-safe truss topology optimization in the setting of plastic design, where damage is defined as a moveable circular region in which members are considered to have zero strength for that particular load case. A rigorous and computationally efficient iterative solution strategy is employed in both the dual (member adding) and primal (damage-case adding) problems simultaneously, which allows cases of high complexity and many damage cases (maximum of 16290 potential members and 16291 damage cases) to be solved to the global optimum. Common member-based damage definitions (e.g. damage to any one member) are shown to be highly dependent on the nodal grid; in the limiting case completely negating the effect of the fail-safe constraints. The method proposed in this article does not have such limitations, enabling a more sophisticated and robust treatment of fail-safe design. Moreover, the global minimization and high resolutions create new benchmarks for the least-material designs of ‘fail-safe’ structures using rigid-plastic materials. A number of example structures are considered (short cantilever, square cantilever, multi-span truss), and the effects of damage radius, location, and structure rationalisation are discussed

LayOpt : an educational web-app for truss layout optimization

A new interactive truss layout optimization web-app has been developed for educational use. This has been designed to be used on a range of devices, from mobile phones to desktop PCs. Truss designs are first generated via numerical layout optimization and then rationalized via geometry optimization. It is then shown that these designs can be simplified using a computationally inexpensive process that allows the user to control the trade-off between complexity and structural volume. The process involves the use of smooth Heaviside representations of member existence variables, with nodal slack forces employed that allow unstable intermediate truss structures. Full details of the web-app are provided in this contribution, from underlying formulation to cloud computing implementation. A range of numerical examples are used to demonstrate the efficacy of the web-app, and to show how it can potentially be used in educational and practical engineering settings

Layout optimization of long-span structures subject to self-weight and multiple load-cases

Layout optimization provides a powerful means of identifying materially efficient structures. It has the potential to be particularly valuable when long-span structures are involved, since self-weight represents a significant proportion of the overall loading. However, previously proposed numerical layout optimization methods neglect or make non-conservative approximations in their modelling of self-weight and/or multiple load-cases. Combining these effects presents challenges that are not encountered when they are considered separately. In this paper, three formulations are presented to address this. One formulation makes use of equal stress catenary elements, whilst the other two make use of elements with bending resistance. Strengths and weaknesses of each formulation are discussed. Finally, an approach that combines formulations is proposed to more closely model real-world behaviour and to reduce computational expense. The efficacy of this approach is demonstrated through application to a number of 2D- and 3D-structural design problems