FORM GENERATION OF PIECEWISE DEVELOPABLE SURFACES USING EQUILIBRIUM EQUATIONS OF SHELLS

Abstract

A form generation method is proposed for generating piecewise developable surfaces based on the membrane theory of shells. Design parameters are the principal stresses of horizontal projected stresses and load distribution. The Gaussian curvature of discrete surfaces is used to evaluate developability. It is shown that simple smooth developable surfaces can be generated by appropriately specifying the principal stresses. More complex developable surfaces can also be generated by minimizing the sum of squares of the Gaussian curvature of the surface. Numerical example confirms that piecewise developable surfaces can be generated by applying line loads along the internal boundaries.