# Dimensional reduction for the plate in elasticity on an unbounded domain

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

The dimensional reduction method is investigated for solving boundary value problems of the plate in elasticity on domain Ω(d) := R2 x (-d, d) by replacing the problems with systems of equations in R2. The basic tool to analyze the dimensional reduction technique for problems on an unbounded domain Ω(d) is the use of Fourier-transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depends on the smoothness of the data on the faces.

Original language English 1-22 22 Mathematical and Computer Modelling 30 5-6 https://doi.org/10.1016/S0895-7177(99)00144-2 Published - 1999 Sep 1

### Fingerprint

Dimensional Reduction
Unbounded Domain
Elasticity
Fourier Transformation
Hilbert spaces
Reduction Method
Boundary value problems
System of equations
Error Estimates
Smoothness
Rate of Convergence
Exact Solution
Hilbert space
Boundary Value Problem
Face

### All Science Journal Classification (ASJC) codes

• Modelling and Simulation
• Computer Science Applications

### Cite this

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title = "Dimensional reduction for the plate in elasticity on an unbounded domain",
abstract = "The dimensional reduction method is investigated for solving boundary value problems of the plate in elasticity on domain Ω(d) := R2 x (-d, d) by replacing the problems with systems of equations in R2. The basic tool to analyze the dimensional reduction technique for problems on an unbounded domain Ω(d) is the use of Fourier-transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depends on the smoothness of the data on the faces.",
author = "Liu, {K. M.}",
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language = "English",
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journal = "Mathematical and Computer Modelling",
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In: Mathematical and Computer Modelling, Vol. 30, No. 5-6, 01.09.1999, p. 1-22.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Dimensional reduction for the plate in elasticity on an unbounded domain

AU - Liu, K. M.

PY - 1999/9/1

Y1 - 1999/9/1

N2 - The dimensional reduction method is investigated for solving boundary value problems of the plate in elasticity on domain Ω(d) := R2 x (-d, d) by replacing the problems with systems of equations in R2. The basic tool to analyze the dimensional reduction technique for problems on an unbounded domain Ω(d) is the use of Fourier-transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depends on the smoothness of the data on the faces.

AB - The dimensional reduction method is investigated for solving boundary value problems of the plate in elasticity on domain Ω(d) := R2 x (-d, d) by replacing the problems with systems of equations in R2. The basic tool to analyze the dimensional reduction technique for problems on an unbounded domain Ω(d) is the use of Fourier-transformation. The error estimates between the exact solution and the dimensionally reduced solution in a Hilbert space are obtained when d and N are given. The rates of convergence depends on the smoothness of the data on the faces.

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DO - 10.1016/S0895-7177(99)00144-2

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