The National Natural Science Foundation of China, No. 11372060, 2014-2016
Skeletal structures composed of fiber reinforced polymer composites are the ideal configuration of the load bearing structures of lightweight spacecrafts. The natural frequency is one of the most important performances which need to be considered in its design procedure. The multi-scale optimization model is established for the skeletal structure composed of a series of tubes of fiber reinforced polymer composites with constraints of exact natural frequency in which the light weight is chosen as the design objective and the structural topology and the ply angles of the composite are chosen as the design variables at the macro and micro scales in this project. The strong singular optima are revealed for the optimization problem of skeletal structures with natural frequency constraints through the exact dynamic stiffness method. And the forming mechanism of the singular optimum will be researched. Some particular forms of area/moment of inertia-density interpolation schemes and the continuation technique of the parameters, which can restore the connectedness of the feasible domain, are proposed. Based on the proposed optimization model, the probability of finding the strongly singular optimum with gradient-based algorithms can be increased. The stiffness parameters of beam are introduced into the optimization formulation to deal with the non-convex difficulty when the ply angles of the composite are chosen as the design variables. The mapping relations will be established between the spaces of stiffness parameters and ply angles to increase the probability of finding the global optimum with gradient-based algorithms. The research of this project will provide new theoretical model and numerical algorithm for the lightweight design of the skeletal composite structures with natural frequency.