A locking-free finite difference method on staggered grids for linear elasticity problems

2018 ◽  
Vol 76 (6) ◽  
pp. 1301-1320 ◽  
Author(s):  
Hongxing Rui ◽  
Ming Sun
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Linear Elasticity ◽  
Difference Method ◽  
Staggered Grids ◽  
Elasticity Problems

Solution of Structural Mechanics Problems by the Differential Quadrature Finite Difference Method

2000 ◽  
Author(s):  
Chang-New Chen
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Partial Differential Operator ◽  
Structural Mechanics ◽  
Plane Elasticity ◽  
Differential Quadrature ◽  
Difference Operators ◽  
Elasticity Problems ◽  
Nonuniform Plate

Abstract The differential quadrature finite difference method (DQFDM) has been proposed by the author. The finite difference operators are derived by the differential quadrature (DQ). They can be obtained by using the weighting coefficients for DQ discretizations. The derivation is straight and easy. By using different orders or the same order but different grid DQ discretizations for the same derivative or partial derivative, various finite difference operators for the same differential or partial differential operator can be obtained. Finite difference operators for unequally spaced and irregular grids can also be generated through the use of generic differential quadrature (GDQ). The derivation of higher order finite difference operators is also easy. By adopting the same order of approximation to all mathematical terms existing in the problem to be solved, excellent convergence can be obtained due to the consistent approximation. The DQFDM is effective for solving structural mechanics problems. The numerical simulations for solving anisotropic nonuniform plate problems and two-dimensional plane elasticity problems are carried out. Numerical results are presented. They demonstrate the DQFDM.

A Novel Finite Difference Method for Flow Calculation on Colocated Grids

2008 ◽  
Author(s):  
Z. Z. Xia ◽  
P. Zhang ◽  
R. Z. Wang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Numerical Solutions ◽  
Fluid Dynamic ◽  
Algebraic Equations ◽  
Duct Flow ◽  
Staggered Grids ◽  
Linear Algebraic Equations ◽  
Incomplete Lu Factorization

A new finite difference method, which removes the need for staggered grids in fluid dynamic computation, is presented. Pressure checker boarding is prevented through a dual-velocity scheme that incorporates the influence of pressure on velocity gradients. A supplementary velocity resulting from the discrete divergence of pressure gradient, together with the main velocity driven by the discretized pressure first-order gradient, is introduced for the discretization of continuity equation. The method in which linear algebraic equations are solved using incomplete LU factorization, removes the pressure-correction equation, and was applied to rectangle duct flow and natural convection in a cubic cavity. These numerical solutions are in excellent agreement with the analytical solutions and those of the algorithm on staggered grids. The new method is shown to be superior in convergence compared to the original one on staggered grids.

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