This paper regards the minimum weight problem of spatial systems, known in the literature as Rozvany–Prager archgrids. Their architectural role is to transmit a load of fixed intensity to the line of supports located at the boundary of a given plane domain. The system consists of arches spaced apart from one another, hence the mechanics of such a system is that of a gridwork shell and not a shell continuum. Mathematically, description of an archgrid falls into the class of Michell frames. Therefore, in our approach, we make use of the plastic design paradigm – it states that optimal bar structure is at the verge of plastic failure, with bars uniformly stressed to the limit value in compression, or tension. In the case of archgrid optimization, only compression is allowed and this limitation introduces an additional design constraint. The main goal of this paper is computational, thus the general variational framework of the optimization problem is reformulated in the discrete setting, involving the methods of linear algebra. Numerics of the discrete approach to Rozvany–Prager archgrids is considered from the novel perspective based on second-order cone programming (SOCP). Procedures used for solving the examples are coded in MATLAB combined with MOSEK optimization toolbox for SOCP routines.

Tensile structures in general, achieve their load-carrying capability only after the process of initial form-finding. From the mechanical point of view, this process can be considered as a problem in statics. As cable systems are close siblings of trusses (cables, however, can carry tensile forces only), in our study we refer to equilibrium equation similar to those known from the theory of the latter. In particular, the paper regards designing pre-tensioned cable systems, with a goal to make them kinematically stable and such that the weight of so designed system is lowest possible. Unlike in typical topology optimization problems, our goal is not to optimize the structural layout against a particular applied load. However, our method uses much the same pattern. First, we formulate the variational problem of form-finding and next we describe the corresponding iterative numerical procedure for determining the optimum location of nodes of the cable system mesh. We base our study on the concept of force density which is a ratio of an axial force in cable segment to its length.