scholarly journals HOMOGENIZATION OF ELASTIC PLATE EQUATION∗

2018 ◽  
Vol 23 (2) ◽  
pp. 190-204 ◽  
Author(s):  
Krešimir Burazin ◽  
Jelena Jankov ◽  
Marko Vrdoljak
Keyword(s):  
Elliptic Equations ◽  
Homogenization Theory ◽  
Transverse Load ◽  
Plate Equation ◽  
Pure Bending ◽  
Push Forward ◽  
Fourth Order Elliptic Equation ◽  
Second Order Elliptic Problems ◽  
Kirchhoff Model ◽  
Stationary Plate

We are interested in general homogenization theory for fourth-order elliptic equation describing the Kirchhoff model for pure bending of a thin solid symmetric plate under a transverse load. Such theory is well-developed for second-order elliptic problems, while some results for general elliptic equations were established by Zhikov, Kozlov, Oleinik and Ngoan (1979). We push forward an approach of Antoni´c and Balenovi´c (1999, 2000) by proving a number of properties of H-convergence for stationary plate equation.

On the Linear Buckling of Circular Cylindrical Shells Under Asymmetric Axial Compressive Stress Distributions

1966 ◽  
Vol 70 (672) ◽  
pp. 1095-1097 ◽  
Author(s):  
D. J. Johns
Keyword(s):  
Compressive Stress ◽  
Cylindrical Shells ◽  
Bending Moment ◽  
Transverse Load ◽  
Stress Distributions ◽  
Pure Bending ◽  
Linear Buckling ◽  
Circular Cylindrical Shells ◽  
Axial Compressive Stress

The linear buckling of circular cylindrical shells is considered with particular attention to the cantilever shell subjected to either a pure bending moment (M) or transverse load (P)—see Fig. 1. It is believed that the conclusions reached have wider application to more general loading cases.

scholarly journals Sign-Changing Solutions for a Fourth-Order Elliptic Equation with Hardy Singular Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Ruichang Pei ◽  
Jihui Zhang
Keyword(s):  
Elliptic Equation ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Order Elliptic Equation ◽  
Singular Terms ◽  
Existence And Multiplicity ◽  
Minimax Methods ◽  
Fourth Order Elliptic Equation ◽  
Sign Changing Solutions

The existence and multiplicity of sign-changing solutions for a class of fourth elliptic equations with Hardy singular terms are established by using the minimax methods.

Fourth-order Elliptic Equations

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
A. Harrabi
Keyword(s):  
Elliptic Equation ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Existence Result ◽  
Order Elliptic Equation ◽  
Palais Smale Condition ◽  
Fourth Order Elliptic Equation ◽  
Fourth Order Elliptic Equations

AbstractWe prove an existence result for a fourth order elliptic equation where the associated functional does not satisfy the Palais-Smale condition. We use some truncations argument and L

Restricted Additive Schwarz Preconditioner for Elliptic Equations with Jump Coefficients

2016 ◽  
Vol 8 (6) ◽  
pp. 1072-1083 ◽  
Author(s):  
Zhiyong Liu ◽  
Yinnian He
Keyword(s):  
Convergence Rate ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Elliptic Equations ◽  
Preconditioned Conjugate Gradient ◽  
Additive Schwarz ◽  
Large Jump ◽  
Second Order Elliptic Problems ◽  
Schwarz Preconditioner

AbstractThis paper provides a proof of robustness of the restricted additive Schwarz preconditioner with harmonic overlap (RASHO) for the second order elliptic problems with jump coefficients. By analyzing the eigenvalue distribution of the RASHO preconditioner, we prove that the convergence rate of preconditioned conjugate gradient method with RASHO preconditioner is uniform with respect to the large jump and meshsize.

scholarly journals On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Yuanfang Ru ◽  
Fanglei Wang ◽  
Yunhai Wang ◽  
Tianqing An
Keyword(s):  
Elliptic Equation ◽  
Iterative Method ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Mountain Pass Lemma ◽  
Order Elliptic Equation ◽  
Kirchhoff Type ◽  
Fourth Order Elliptic Equation ◽  
Fourth Order Elliptic Equations

We consider a nonlocal fourth-order elliptic equation of Kirchhoff type with dependence on the gradient and Laplacian Δ2u-a+b∫Ω∇u2dxΔu=fx,u,∇u,Δu, in Ω, u=0, Δu=0, on ∂Ω, where a, b are positive constants. We will show that there exists b⁎>0 such that the problem has a nontrivial solution for 0<b<b⁎ through an iterative method based on the mountain pass lemma and truncation method developed by De Figueiredo et al., 2004.

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