Analysis of a Modified First-Order System Least Squares Method for Linear Elasticity with Improved Momentum Balance

The Nonlinear Bending Analysis for Circular Nano Plates Based on Modified Coupled Stress and Three- Dimensional Elasticity Theories

In this paper, the nonlinear bending analysis for annular circular nano plates is conducted based on the modified coupled stress and three-dimensional elasticity theories. For this purpose, the equilibrium equations, considering nonlinear strain terms, are calculated using the least energy potential method and solved by the numerical semi-analytical polynomial method. According to the previous ...

First-Order System Least Squares For Linear Elasticity: Numerical Results

Two first-order system least squares (FOSLS) methods based on L norms are applied to various boundary value problems of planar linear elasticity. Both use finite element discretization and multigrid solution methods. They are two-stage algorithms that solve first for the displacement flux variable (the gradient of displacement, which easily yields the deformation and stress variables), then for...

NEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS

We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...

First-Order System Least Squares for the Stress-Displacement Formulation: Linear Elasticity

First-Order System Least Squares (FOSLS) for Spatial Linear Elasticity: Pure Traction

This paper develops first-order system least-squares (FOSLS) functionals for solving the pure traction problem in three-dimensional linear elasticity. It is a direct extension of an earlier paper on planar elasticity [Z. Cai, T. A. Manteuffel, S. F. McCormick, and S. V. Parter, SIAM J. Numer. Anal., 35 (1998), pp. 320–335]. Two functionals are developed, one involving L norms of the first-order...