Shape optimization of no-tension arches subjected to in-plane loading

In this paper a novel method for the shape optimization of tapered arches subjected to in-plane gravity (self-weight) and horizontal loading through compressive internal loading is presented. The arch is discretized into beam elements, and axial deformation is assumed to be small. The curved shape of the tapered arch is discretized into a centroidal B-spline curve with beam elements. Constraints are imposed for allowable axial force and bending moment in the arch so that only compressive stress exists in the section. The computational cost for optimization is reduced, and the convergence property is improved by considering the locations of the control points of B-spline curves as design variables. The height of section is also modeled using a B-spline function. A section update algorithm is introduced in the optimization procedure to account for the contact and separation phenomena and to further speed up the computation process. The objective function to minimize the total strain energy of the arch under self-weight and horizontal loading. Numerical examples are presented that demonstrate the effectiveness of the proposed method. To validate the findings, the properties of the obtained optimal shapes are compared to shapes obtained by a graphic statics approach.