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 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.
| 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 |
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All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics
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Dimensional reduction for the beam in elasticity on a bounded domain. / Liu, Kang-Man.
In: Computers and Mathematics with Applications, Vol. 39, No. 1-2, 01.01.2000, p. 145-168.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 -