Configuration optimization of clamping members of frame-supported membrane structures

A method is presented for configuration optimization of frames that have specified properties on nodal displacements, stresses, and reaction forces against static loads. The conventional ground structure approach is first used for topology optimization. A feasible solution with a small number of members satisfying all the design requirements except the stress constraints is obtained by assigning artificially small upper-bound displacement, or by penalizing the stiffness of a thin member. This way, the well-known difficulty in topology optimization under stress constraints is successfully avoided. The nodal locations and cross-sectional areas of the feasible solution are next optimized to obtain an approximate optimal configuration under stress constraints. The proposed method is applied to the design of self-fastening clamping members for membrane structures modeled using frame elements. An optimization result is also presented for a clamping member that adjusts deformation of membrane by applying a clamping force with a vertically attached bolt.