平板の幾何学的非線形問題の一解法(I)

概要

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Since the famous paper on the postbuckling behavior of an elastic rectangular plate was published by von Karman, much work has been done on the various geometrically nonlinear problems such as large deflection, postbuckling, soap-through and dynamic stability of elastic plates due to lateral as well as inplane loadings. Most of these studies are based on the Energy method proposed by E.Trefftz, K.Marguerre and others in which solution can be found by the stationary condition of the total potential energy of a given plate whose deflection is assumed in the form of known functional series with unknown coefficients. Numerical calculation in this method, however, is so laborious that problems of simple plate shapes, boundary conditions as well as loading conditions were only considered before high-speed digital computers became available. A practical method of solution on the general nonlinear problem of elastic plates with arbitrary shape, boundary and loading conditions is proposed in this paper by extending the method proposed by K.Marguerre, E.Trefftz and others. Displacement functions used are constructed by combined use of the finite element method and Rayleigh-Ritz's procedure.
社団法人日本船舶海洋工学会の論文