A numerical method for form finding and shape optimization of reciprocal structures

Reciprocal structure is a special structural system that has a complex form. In this paper, a new numerical method is proposed for form finding and shape optimization of reciprocal structures. Two new parameters, contact point and contact vector, are introduced to describe the special lapping connections of the discrete bar elements of a reciprocal structure. Using these two parameters, it is easy to establish structural analysis model and conduct finite element analysis. The property of lapping connection is formulated according to the geometric condition. An error function is defined by uniting the connection lapping conditions, and the form finding problem of reciprocal structure can then be formulated as an optimization problem of minimizing the error function. The shape of a reciprocal structure is optimized by minimizing the total strain energy under static loads. Numerical examples demonstrate the effectiveness and applicability of the proposed method.