Dimensional reduction for the plate in elasticity on an unbounded domain

K. M. Liu

doi:10.1016/S0895-7177(99)00144-2

Dimensional reduction for the plate in elasticity on an unbounded domain

K. M. Liu

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	1-22
Number of pages	22
Journal	Mathematical and Computer Modelling
Volume	30
Issue number	5-6
DOIs	https://doi.org/10.1016/S0895-7177(99)00144-2
Publication status	Published - 1999 Sep

All Science Journal Classification (ASJC) codes

Modelling and Simulation
Computer Science Applications

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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.}",

note = "Funding Information: This research was partially supported by the National Science Council of the Republic of China under Grant No. NSC-87-2115-M-018-008. The author wishes to thank the referees for their helpful suggestions.",

year = "1999",

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N1 - Funding Information: This research was partially supported by the National Science Council of the Republic of China under Grant No. NSC-87-2115-M-018-008. The author wishes to thank the referees for their helpful suggestions.

PY - 1999/9

Y1 - 1999/9

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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