A meshless local Petrov-Galerkin (MLPG) method is applied to solve problems of Reissner-Mindlin shells under thermal loading. Both stationary and thermal shock loads are analyzed here. Functionally graded materials with a continuous variation of properties in the shell thickness direction are considered here. A weak formulation for the set of governing equations in the Reissner-Mindlin theory i...

A novel spectral element technique is examined in which the test functions are different from the approximating elements. Examples are given for a simple 1D Helmholtz equation, Burger's Equation with a small viscosity, and for Darcy's Equation with a discontinous hydraulic conductivity. 1. Polynomial Approximation. Spectral element approximations have been shown to be an eeective tool for the a...

We present a space-time certified reduced basis method for long-time integration of parametrized noncoercive parabolic equations with quadratic nonlinearity. We first consider a finite element discretization based on discontinuous Galerkin time integration and introduce associated Petrov-Galerkin space-time trialand test-space norms which yields optimal and asymptotically mesh independent stabi...

this paper deals with the dynamic analysis of stress field in cylindrically layeredstructures reinforced by carbon nanotube (clsrcn) subjected to mechanical shock loading.application of meshless local integral equations based on meshless local petrov-galerkin(mlpg) method is developed for dynamic stress analysis in this article. analysis is carriedout in frequency domain by applying the laplace...

Model-reduction techniques aim to reduce the computational complexity of simulating dynamical systems by applying a (Petrov–)Galerkin projection process that enforces dynamics evolve in low-dimensional subspace original state space. Frequently, resulting reduced-order model (ROM) violates intrinsic physical properties full-order (e.g., global conservation, Lagrangian structure, state-variable b...

We present a unified analysis for family of variational time discretization methods, including discontinuous Galerkin methods and continuous Galerkin-Petrov applied to non-stiff initial value problems. Besides the well-definedness global error superconvergence properties are analyzed under rather weak abstract assumptions which also allow considerations wide variety quadrature formulas. Numeric...