Form generation of piecewise developable surfaces with curved boundaries based on equilibrium equations of membrane shells

Developable surface is generated from a plane by a process of bending deformation that does not involve any in-plane deformation. Developable surface is characterized by vanishing Gaussian curvature throughout the surface. The use of developable surfaces offers a benefit of facilitating the simple fabrication and construction of building materials when designing structures with complex geometries, such as free-form shells. Several studies have proposed generating piecewise developable surfaces that consist of multiple developable surface patches. In this study, we extend our method to generate piecewise developable surfaces with curved boundaries based on the membrane theory of shells. Design parameters are the principal stresses of horizontal projected stresses. Developability of a surface is evaluated using the Gaussian curvature of discrete surfaces in discrete differential geometry. Developable surfaces are obtained by minimizing the sum of squares of the Gaussian curvature at grid points. It is shown that smooth developable surfaces can be generated by appropriately specifying the principal stresses. Additionally, it is shown that the application of line loads along the internal boundaries can create areas of discontinuity in the slope of the shell surface and provide piecewise developable surfaces. Furthermore, we evaluate mechanical properties of generated developable shell surface by finite element analysis.