Optimal vault problem – form finding through 2D convex program

• Optimization of vaults is equivalent to a 2D convex problem optimal membrane. The surface the graph membrane's deflection function. are proved solve Prager . discretized and reformulated as conic quadratic program. With MATLAB code precise grid-shell approximations given. This work puts forward form finding designing least-volume vault that structure spanning over plane region, which via pure compression transfers vertically tracking load supporting boundary. Through duality scheme, developed recently for design pre-stressed membranes, reduced pair mutually dual problems formulated on reference region. constructed upon solutions those both minimum volume compliance; analytical examples measure-theoretic approach, such 3D by carries transmissible load. ground method applied furnishes discrete, programs leading grid-shells. By adopting member-adding adaptive technique, this efficiently tackled numerically. computer demonstrated number where highly found.