TY - JOUR
T1 - Dimensional reduction for the beam in elasticity on a bounded domain
AU - Liu, K. M.
N1 - Funding Information:
This research was partially supported by National Science Council of the Republic of China under Grant No. NSC-86-2115-M-018-009.
PY - 2000/1
Y1 - 2000/1
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.
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U2 - 10.1016/s0898-1221(99)00320-x
DO - 10.1016/s0898-1221(99)00320-x
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 -