Galerkin Solution to Geometrically Nonlinear Shallow Shell Equations

摘要

A laminated shallow shell approach that includes von Karman geometricnonlinearity and parabolic transverse shear deformation is posed in differential operator form. Trigonmetric series are assumed for each of the five shell displacement degrees freedom for the subsequent nonlinear galerkin solution resulting in 5n2 simultaneous algebraic equations where n is the number of displacement terms assumed in the series. The galerkin nonlinear solution is computationally intensive. The response of several laminate geometries subjected to transverse loadings are found. Thicker plates and shells generally exhibit more flexible response compared to thinner geometries in both linear and nonlinear analyses. The nondimensional shell response is examined by using the Batdorf-Stein shell parameter for laminated constructions. Quasi-isotropic shallow shells undergo significant transverse shear flexibility in the thicker geometries as given by the nondimensional shell crown deflection. However, the nondimensional crown deflection in the deeper shell response is not much influenced by shell thickness. For flat plates, geometric nonlinearity lessens the influence of transverse shear flexibility when compared to linear solutions due to membrane stretching resistance. (AN).