By using the simplified Reissner's equation of axisymmetric shells of revolution, the nonlinear bending of a corrugated annular plate with a large boundary corrugation and a non-deformable rigid body at the center under compound load are investigated. The nonlinear boundary value problem of the comigated diaphragm reduces to the nonlinear integral equations by applying the method of Green's function. To solve the integral equations, a so-called interpolated parameter important to prevent divergence is introduced into the iterative format. Computation shows that when loads are small, any, value of interpolated parameter can assure the convergence of iteration. Interpolated parameter equal or almost equal to 1 yields a faster convergence rate; when loads are large,interpolated parameter cannot be taken too large in order to assure convergence. The characteristic curves of the comugated diaphragm for different load combinations are given. The obtained characteristic curves are available for reference to design. It can be concluded that the deflection is larger when the diaphragm is acted by both uniform load and concentrated load than when it is acted only by uniform load. The solution method can be applied to corrugated shells of arbitrary diametral sections.
Hamada M, Seguchi Y, Ito S, et al. Numerical method for nonlinear axisymmetric bending of arbitrary shells of revolution and large deflection analyses of corrugated diaphragm and bellows[J]. Bulletin of JSME,1968,11(43): 24-33.
Bihari I, Elbert A. Deformation of circular corrugated plates and shells[J]. Periodica Polytech Mech Eng Mas, 1978,22(2): 123-143.
LIU Ren-huai, YUAN Hong. Nonlinear bending of corrugated annular plate with large boundary corrugation[J].Appl Mech Eng, 1997,2(3):353-367.
Libai A, Simmonds J G.The Nonlinear Theory of Elastic Shells of One Spatial Dimension[M]. Boston: Academic Press, 1988, 206-212.
Simmonds J G, Libai A. A simplified version of Reissner's non-linear equations for a first-approximation theory of shells of revolution[J]. Comput Mech,1987,2(2):99-103.