Finite Deflection Discrete Element Analysis Of Shells
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Finite Deflection, Discrete Element Analysis of Shells
A discrete element analysis method for predicting the nonlinear response of thin elastic shells is presented. The displacement patterns for a shell element, the edges of which must be parallel to orthogonal curvilinear coordinates, are expressed in terms of products of one-dimensional Hermite interpolation polynomials and undetermined nodal displacement parameters. Geometric admissibility of the displacement state of an assemblage of these discrete elements is conveniently satisfied. Special treatment is given to the particular cases of flat rectangular plate and circular cylindrical shell discrete elements. The use of a potential energy principle permits the incorporation of geometric nonlinearity, thus providing the capability for predicting finite displacements and post-buckling behavior. Numerical solutions are obtained by direct minimization of the total discretized potential energy. Several numerical examples, both linear and nonlinear, which indicate the effectiveness of the analysis are considered. The applicability of this discrete element analysis method to predicting the elastic post-buckling behavior of integrally stiffened shells is provided by the assumed element displacement patterns.