FORM FINDING OF TENSION-COMPRESSION MIXED SHELLS BASED ON HYPERBOLIC EQUILIBRIUM EQUATIONS

This paper presents a form-finding method for shells resisting external loads through tension-compression mixed membrane stresses. The vertical equilibrium equation of the shell is expressed as a hyperbolic partial differential equation, which is discretized by the finite difference method to obtain a linear system of equations. Existence and uniqueness of the solution can be determined using the coefficient matrix of the equilibrium equations. By introducing regularization and smoothing terms, smooth shapes can be obtained even if the solutions are not unique. The validity of the proposed method is confirmed by comparison with the initial-boundary value problem for wave equations.