In this paper, the compressive behavior of composite laminates with multiple through-the-width delaminations is investigated analytically. The analytical method is based on the CLPT theory and its formulation is developed on the basis of the Rayleigh-Ritz approximation technique to analyze the buckling and post-buckling behavior of the delaminated laminates. The method can handle both local buc...

Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which the motion of an ice sheet or glacier is determined by the balance of stresses acting on the ice at any instant in time. However, there is also an equivalent and alternative formulation of mechanics where the equations of motion are instead found by invoking a variational princ...

We consider a parallel method for solving generalized eigenvalue problems that arise from large-scale molecular orbital computations. We use a moment-based method that finds several eigenvalues and their corresponding eigenvectors in a given domain, which is suitable for master-worker type parallel programming models. We also show the efficiency of the Rayleigh-Ritz procedure for improving the ...

We introduce a variational method for approximating distribution functions of dynamics with a “Liouville operator” L̂, in terms of a nonequilibrium action functional for two independent (left and right) trial states. The method is valid for deterministic or stochastic Markov dynamics, and for stationary or time-dependent distributions. A practical Rayleigh-Ritz procedure is advanced, whose input...

Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, sharp non-asymptotic convergence estimates are known. These estimates require a properly scaled preconditioner. In t...

Iterative algorithms for large-scale eigenpair computation are mostly based subspace projections consisting of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz (RR) projection step that extracts approximate eigenpairs. A predominant methodology for the SU step makes use of Krylov subspaces that builds orthonormal bases pie...

This paper discusses a few algorithms for updating the approximate Singular Value Decomposition (SVD) in the context of information retrieval by Latent Semantic Indexing (LSI) methods. A unifying framework is considered which is based on Rayleigh-Ritz projection methods. First, a Rayleigh-Ritz approach for the SVD is discussed and it is then used to interpret the Zha-Simon algorithms [SIAM J. S...

We consider a parallel method for solving generalized eigenvalue problems that arise from molecular orbital computations. We use a moment-based method that finds several eigenvalues and their corresponding eigenvectors in a given domain, which is suitable for masterworker type parallel programming models. The computation of eigenvalues using explicit moments is sometimes numerically unstable. W...

The paper considers problem of buckling a thin elastic cylindrical shell, supported by rings various stiffness. approximate solution for clamping edge was obtained with analytical Rayleigh-Ritz method. parameters the optimal distribution mass structure between shell and stiffeners are found in order to maximize critical pressure. Frames zero eccentricity considered. solutions compared finite el...

Using  principle  of  minimum  total  potential  energy  approach  in conjunction  with  Rayleigh-Ritz  method,  the  electro-thermo- mechanical  axial  buckling  behavior  of  piezoelectric  polymeric cylindrical  shell  reinforced  with  double-walled  boron-nitride nanotube  (DWBNNT)  is  investigated. Coupling  between  electrical and mechanical  fields  are  considered  according  to  ...