Abstract
In the investigation reported here novel techniques for the computation of highly nonlinear response statistics, such as mean square and covariance of generalized displacements of large scale discretized plate and shell structures have been developed. The techniques combine the versatile finite element method and the stochastic central difference method as well as derivatives of the latter such that complex aerospace and naval structures under intensive transient disturbances represented as nonstationary random processes can be considered. The flat triangular plate finite element is of the Mindlin type and is based on the hybrid strain formulation. The updated Lagrangiah hybrid strain based formulation is capable of dealing with deformations of finite rotations and finite strains. Explicit expressions for the consistent element mass and stiff matrices were previously obtained, and therefore no numerical matrix inversion and integration is necessary in the element matrix derivation. Several additional features are novel. First, the so-called averaged deterministic central difference scheme is employed in the co-ordinate updating process for large deformations. Second, application of the time co-ordinate transformation in conjunction with the stochastic central difference method enables one to deal with highly stiff discretized structures. Third, application of the adaptive time schemes makes it convenient to solve a wide variety of highly nonlinear systems. Finally, the recursive nature of the stochastic central difference method makes it possible to deal with a wide class of nonstationary random process.
On the Asymptotic Spectrum of Finite Element Matrix Sequences
