A method for shape design of free-form shells under self-weight is presented, without resorting to any parametric shape representations. The graph surface is discretized into a polyhedral surface with quadrilateral mesh. Membrane stresses which satisfy the equilibrium in the horizontal plane are given based on Pucher’s formulation, and the equilibrium equation in the vertical direction is solved. Desirable distributions of thrusts on the boundaries of a surface can easily be specified. Successive over-relaxation method is used for solving Pucher’s formulation discretized by the finite-difference method. It is shown in the numerical examples that various equilibrium shapes can be generated.
