NONLINEAR STABILITY OF CORRUGATED DIAPHRAGMS

By using the large deflection theory of axisymmetric shallow shells of revolution, the nonlinear stability of a corrugated diaphragm under arbitrary load and boundary conditions is investigated. The nonlinear boundary value problem of the corrugated diaphragm reduces to the nonlinear integral equations using Green's function. To solve the integral equations, expansion method is used to obtain Green's function. Then the integral equations are reduced to the form with degenerate core by expanding Green's function into a series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton's iterative method is utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, the central deflection is taken as the control parameter. Corresponding loads are obtained by increasing deflection step by step. As a numerical example, the local instability phenomenon of corrugated diaphragm with plane central region and three corrugations is studied. The snapping instability of corrugated diaphragm because of existence of defect is discussed, which is analogous to the total instability phenomenon in shallow spherical shells. The present work is expected to be useful for design of corrugated diaphragms.