### Abstract

The dimensional reduction method is investigated for solving two-dimensionally linear, isotropic elasticity (Δu + (1 + λ/μ)▽▽ · u + ρu = 0) on domain Ω^{d} := Ω × (-d, d) ⊂ ℝ^{2} by semidiscretization techniques in the transverse direction, where ρ > 0 and Ω = (-a, a). The modelling error between the exact solution u and the dimensionally reduced solution u^{n} in E^{1} (Ω^{d}) is precisely obtained as d and n are fixed, where the norm ∥ · ∥_{E}1 is equivalent to the usual norm ∥ · ∥_{H}1. Numerical examples are presented.

Original language | English |
---|---|

Pages (from-to) | 145-168 |

Number of pages | 24 |

Journal | Computers and Mathematics with Applications |

Volume | 39 |

Issue number | 1-2 |

Publication status | Published - 2000 Jan 1 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*39*(1-2), 145-168.

}

*Computers and Mathematics with Applications*, vol. 39, no. 1-2, pp. 145-168.

**Dimensional reduction for the beam in elasticity on a bounded domain.** / Liu, Kang-Man.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Dimensional reduction for the beam in elasticity on a bounded domain

AU - Liu, Kang-Man

PY - 2000/1/1

Y1 - 2000/1/1

N2 - The dimensional reduction method is investigated for solving two-dimensionally linear, isotropic elasticity (Δu + (1 + λ/μ)▽▽ · u + ρu = 0) on domain Ωd := Ω × (-d, d) ⊂ ℝ2 by semidiscretization techniques in the transverse direction, where ρ > 0 and Ω = (-a, a). The modelling error between the exact solution u and the dimensionally reduced solution un in E1 (Ωd) is precisely obtained as d and n are fixed, where the norm ∥ · ∥E1 is equivalent to the usual norm ∥ · ∥H1. Numerical examples are presented.

AB - The dimensional reduction method is investigated for solving two-dimensionally linear, isotropic elasticity (Δu + (1 + λ/μ)▽▽ · u + ρu = 0) on domain Ωd := Ω × (-d, d) ⊂ ℝ2 by semidiscretization techniques in the transverse direction, where ρ > 0 and Ω = (-a, a). The modelling error between the exact solution u and the dimensionally reduced solution un in E1 (Ωd) is precisely obtained as d and n are fixed, where the norm ∥ · ∥E1 is equivalent to the usual norm ∥ · ∥H1. Numerical examples are presented.

UR - http://www.scopus.com/inward/record.url?scp=0039929681&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039929681&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0039929681

VL - 39

SP - 145

EP - 168

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 1-2

ER -