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.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics