### 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 |
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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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Liu, K-M. (2000). Dimensional reduction for the beam in elasticity on a bounded domain.

*Computers and Mathematics with Applications*,*39*(1-2), 145-168.