Design Methodology of Flexible Structures by Spring-and-Segment Model

A design methodology of flexible structures is presented for the enrichment of the structural function by utilizing the mechanism realized by the large elastic deformation of flexible members. The flexible member is modeled by straight bar segments linked by virtual coil springs. Its large deformation is analyzed by the Lagrange multiplier method, the functional of which is constituted in line with the principle of stationary potential energy with constraints on geometrical boundary conditions. The sensitivity analysis is formulated especially for the solution obtained by the Lagrange multiplier method so as to approximate the change of the structural response in the first-order sense with respect to design variables. Owing to the sensitivity analysis, governing equation of the design variables to realize the prescribed structural performance is derived as the linear simultaneous equations. The solution of design variables is determined by the Moore-Penrose generalized inverse since the coefficient matrix becomes rectangular.