Dimensional reduction for the beam in elasticity on a bounded domain

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Abstract

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 E1d) is precisely obtained as d and n are fixed, where the norm ∥ · ∥E1 is equivalent to the usual norm ∥ · ∥H1. Numerical examples are presented.

Original languageEnglish
Pages (from-to)145-168
Number of pages24
JournalComputers and Mathematics with Applications
Volume39
Issue number1-2
Publication statusPublished - 2000 Jan 1

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All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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