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An optimization approach is presented for form-finding of tensegrity structures. It is shown that various equilibrium shapes can be easily found by solving a forced-deformation analysis problem formulated as a minimization problem considering the nodal coordinates as design variables. The objective function is defined in terms of the member lengths, and it can be regarded as the total strain energy corresponding to fictitious elastic material properties. The self-equilibrium forces can be found from the optimality conditions of the nonlinear programming problem. Stability of the self-equilibrium shape is investigated based on the local convexity of the objective function. Similarity between form-finding problem of a structure with zero-unstressed-length cables and the problem of minimum square-length network is also discussed. Furthermore, folding of a structure with small unstressed-length cables is approximately simulated using affine transformation of equilibrium shape. [ABSTRACT FROM AUTHOR]

An optimization approach is presented for force design of tensegrity structures by enumeration of the vertices of the feasible region of the prestresses, which is defined as the linear combinations of the coefficients of the self-equilibrium force vectors. The unilateral properties of the stresses in cables and struts are taken into consideration. In order to design the stiffest structure against uncertain external loads as well as specific external loads, a multiobjective optimization problem is formulated for simultaneous maximization of the lowest eigenvalue of the tangent stiffness matrix and minimization of the compliance against a specified set of external loads. In the numerical example, Pareto optimal solutions are found by enumerating the vertices of the feasible region of prestresses of a tensegrity grid, and the monotonicity properties of the objective functions are investigated. [ABSTRACT FROM AUTHOR]

An algorithm based on Semi-Definite Programming (SDP) formulation is proposed for optimum design of structures for specified linear buckling load factors. Optimal trusses and frames are computed by using the primal-dual interior-point method based on SDP scheme. It is well known that optimizing structures under buckling constraints is difficult because of the non-differentiability of buckling load factors for the case of multimodal solutions. The examples studied indicate that optimum designs with multiple buckling load factors can be found with no difficulty by successively solving the SDP problems. [ABSTRACT FROM AUTHOR]