The displacement initial-boundary value problem in bending of thermoelastic plates weakened by cracks
type: Item
instance of: scholarly article
title: The displacement initial-boundary value problem in bending of thermoelastic plates weakened by cracks
zbMATH Open document ID: 1159.35014
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-10-06T00:00:00Z
review text: The authors consider the initial-boundary value problem in a vector form with the edge-of-the-crack Dirichlet boundary conditions for bending of a thermoelastic plate \[ \begin{aligned} &\mathbb{B}_0\partial_t^2\mathbf{U}(x,t)+\mathbb{B}_1\partial_t\mathbf{U}(x,t)+\mathbb{A}\mathbf{U}(x,t) =\mathbf{Q},\;(x,t)\in S\times (0,\infty),\\ &\mathbf{U}(x,0)=\partial_t\mathbf{U}(x,0)=0,\;x\in S,\\ &\mathbf{U}^+(x,t)=\mathbf{F}^+(x,t),\;\mathbf{U}^-(x,t)=\mathbf{F}^-(x,t),\;(x,t)\in \partial S_0\times (0,\infty),\end{aligned} \] \(\mathbf{U}=(\mathbf{u}^T,u_4)^T,\;\mathbf{u}=(u_1,u_2,u_3)^T,\;u_4(x,t)=\frac{12}{h^3}\int_{-h/2}^{h/2}x_3\theta(x,x_3,t)dx_3,\;x=(x_1,x_2),\;\) \( \mathbb{B}_0=\text{diag}\{\frac{\rho}{12}h^2,\frac{\rho}{12}h^2,\rho,0\}\;\) and the matrices \(\mathbb{B}_1,\;\mathbb{A}\) contain the first-order and the second-order partial derivatives with respect to \(x_1,\;x_2\) respectively. The crack is modeled by an open connected arc \(\partial S_0\subset \partial S.\) The unique solvability in spaces of distributions is proved by means of combination of the Laplace transformation and variational methods.
reviewed by: Igor Bock
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 74K20
Mathematics Subject Classification ID: 74F05
Mathematics Subject Classification ID: 35L20
zbMATH DE Number: 5349088
zbMATH Keywords: crack
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: unique solvability
author: Igor Chudinovich
author: C. Constanda
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.07.023
OpenAlex ID: W2049250072
cites work: Q3995422
cites work: THERMAL EFFECTS IN MINDLIN-TYPE PLATES
cites work: Potential Representations of Solutions for Dynamic Bending of Elastic Plates Weakened by Cracks
cites work: Q4502418
cites work: Q4658079
cites work: The Cauchy problem in the theory of thermoelastic plates with transverse shear deformation
cites work: Q5628582
cites work: Q5679204
DOI: 10.1016/J.JMAA.2008.07.023
Recommended article: The traction initial-boundary value problem for bending of thermoelastic plates with cracks
Recommended article: Boundary Integral Equations for Thermoelastic Plates with Cracks
Recommended article: The equilibrium problem for a thermoelastic plate with a crack
Recommended article: The third boundary problem on equilibrium of a thermoelastic plate with a crack
Recommended article: Boundary equations in dynamic problems for thermoelastic media with cracks
Recommended article: Q3814905
Recommended article: Solvability of initial-boundary value problems for bending of thermoelastic plates with mixed boundary conditions
Recommended article: Q3700935
Recommended article: Q5480877
Recommended article: On plane displacement boundary value problem of quasi–static linear thermoelasticity
description: scientific article; zbMATH DE number 5349088