Shape optimization method of free-form cable-braced grid shells based on the translational surfaces technique

Abstract

Cable-braced grid shells, being a new type of single-layer reticulated shell, are widely used in glass roofs. However, research on the shape optimization of free-form cable-braced grid shells is relatively lacking. This paper describes a shape optimization method for cable-braced free-form grid shells, with strain energy used as the optimization object, structural height used as the optimization variable, and the conjugate gradient method used as the optimization algorithm. According to the shape forming method for grid shells, their shape optimization can be realized only by adjusting the generatrix and directrix, not by optimizing the whole surface. The B-spline curve method is used to model the generatrix and directrix and maintain an optimized surface fairing. The following conclusions can be drawn from this study. First, the structural mechanical behavior of grid shells can be significantly improved with rapid convergence using the proposed shape optimization method. Second, the plane quadrilateral mesh is maintained and fewer optimization variables are needed during the proposed shape optimization method. Finally, the optimized surface is fairing and the mechanical properties of the optimized surface are somewhat decreased when using the B-spline curve method.