An Analytical Solution for Anisotropic Composite Plate of Crack under Bending and Twisting

2011 ◽  
Vol 197-198 ◽  
pp. 1567-1572
Author(s):  
Xue Xia Zhang ◽  
Xiao Chao Cui ◽  
Wei Yang Yang ◽  
Wen Bin Zhao
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Composite Plate ◽  
Boundary Value ◽  
Crack Tip ◽  
Theoretical Research ◽  
Partial Differential ◽  
Anisotropic Composite ◽  
Variable Function

Analysis of mechanical behaviors near crack tip for linear elastic anisotropic composite plate under bending loadings and twisting loadings was done. By introducing proper deflection function, the mechanical problem reduced to the boundary value problem of partial differential equation. The mixed mode stress intensity factor at the crack tip were presented under bending loadings and twisting loadings at infinity. By solving boundary value problem of partial differential equation and using a complex variable function method, the expressions for bending moments, strains and displacements near crack tip are derived. The obtained results are used to the theoretical research and experimental analysis of the fracture problems of composite plate.

scholarly journals Antiplane Problem of Periodically Stacked Parallel Cracks in an Infinite Orthotropic Plate

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Long Wu ◽  
Pengcheng Du
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Hyperbolic Function ◽  
Partial Differential ◽  
Parallel Cracks ◽  
Antiplane Problem ◽  
Variable Function ◽  
Analytic Expressions

The antiplane problem of the periodic parallel cracks in an infinite linear elastic orthotropic composite plate is studied in this paper. The antiplane problem is turned into the boundary value problem of partial differential equation. By constructing proper Westergaard stress function and using the periodicity of the hyperbolic function, the antiplane problem of the periodic parallel cracks degenerates into an algebra problem. Using the complex variable function method and the undetermined coefficients method, as well as with the help of boundary conditions, the boundary value problem of partial differential equation can be solved, and the analytic expressions for stress intensity factor, stress, and displacement near the periodical parallel cracks tip are obtained. When the cracks spacing tends to infinity, the antiplane problem of the periodic parallel cracks degenerates into the case of the antiplane problem of a single central crack.

scholarly journals A note on the nonlocal boundary value problem for a third order partial differential equation

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 801-808 ◽  
Author(s):  
Kh. Belakroum ◽  
A. Ashyralyev ◽  
A. Guezane-Lakoud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Stability Estimates ◽  
Order Partial Differential Equation ◽  
Nonlocal Boundary Value Problem ◽  
Third Order ◽  
Partial Differential

The nonlocal boundary-value problem for a third order partial differential equation in a Hilbert space with a self-adjoint positive definite operator is considered. Applying operator approach, the theorem on stability for solution of this nonlocal boundary value problem is established. In applications, the stability estimates for the solution of three nonlocal boundary value problems for third order partial differential equations are obtained.

scholarly journals A segmented Adomian algorithm for the boundary value problem of a second-order partial differential equation on a plane triangle area

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yin-shan Yun ◽  
Ying Wen ◽  
Temuer Chaolu ◽  
Randolph Rach
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Groundwater Flow ◽  
Boundary Value ◽  
Flow Region ◽  
Second Order ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Adomian Decomposition

Abstract For the boundary value problem (BVP) of a second-order partial differential equation on a plane triangle area, we propose a new algorithm based on the Adomian decomposition method (ADM) combined with a segmented technique. In addition, we present a new theorem that ensures the convergence of the algorithm. By this algorithm, the model for the effect of regional recharge on the plane triangle groundwater flow region is solved, from which we obtain the segmented exact solution of the problem, which satisfies the governing equation and all of the specified boundary conditions. Then, by the algorithm combined with Taylor’s formula, the heterogeneous aquifer model on the plane triangle groundwater flow region is considered, from which we obtain the segmented high-precision approximate solution of the problem.

scholarly journals Comparison results for nonlinear divergence structure elliptic PDE’s

2019 ◽  
Vol 9 (1) ◽  
pp. 438-448 ◽  
Author(s):  
Yichen Liu ◽  
Monica Marras ◽  
Giovanni Porru
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Elliptic Partial Differential Equation ◽  
Comparison Result ◽  
Partial Differential ◽  
Laplace Equations ◽  
Comparison Results ◽  
Divergence Structure

Abstract First we prove a comparison result for a nonlinear divergence structure elliptic partial differential equation. Next we find an estimate of the solution of a boundary value problem in a domain Ω in terms of the solution of a related symmetric boundary value problem in a ball B having the same measure as Ω. For p-Laplace equations, the corresponding result is due to Giorgio Talenti. In a special (radial) case we also prove a reverse comparison result.

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