Asymptotic analysis of boundary-value problems in thin perforated domains with rapidly varying thickness

DOI10.1007/s11072-010-0101-5zbMath1334.74057OpenAlexW2058695663MaRDI QIDQ275359

Taras A. Mel'nyk, A. V. Popov

Publication date: 26 April 2016

Published in: Nonlinear Oscillations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11072-010-0101-5

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Plates (74K20) Degenerate elliptic equations (35J70) PDEs in connection with mechanics of deformable solids (35Q74) Homogenization and oscillations in dynamical problems of solid mechanics (74Q10)

Related Items

Spectrum of a singularly perturbed periodic thin waveguide, Thin domains with non-smooth periodic oscillatory boundaries, Homogenization of a locally periodic oscillating boundary, Elliptic and parabolic problems in thin domains with doubly weak oscillatory boundary, Localization of eigenfunctions in a thin cylinder with a locally periodic oscillating boundary, Quasilinear problems with nonlinear boundary conditions in higher-dimensional thin domains with corrugated boundaries, A reiterated homogenization problem for the \(p\)-Laplacian equation in corrugated thin domains, The \(p\)-Laplacian equation in thin domains: the unfolding approach, Locally periodic thin domains with varying period, Refinement strategies related to cubic tetrahedral meshes, The Neumann problem in thin domains with very highly oscillatory boundaries, Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary, An optimal control problem in a tubular thin domain with rough boundary, A Strange Vertex Condition Coming from Nowhere, Oscillating PDE in a rough domain with a curved interface: Homogenization of an Optimal Control Problem, Upscaling of a double porosity problem with jumps in thin porous media, Thin domains with doubly oscillatory boundary, Homogenization of a nonlinear monotone problem in a locally periodic domain via unfolding method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory
• Weighted Korn's inequality for a thin plate with a rough surface.
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• Thin elastic and periodic plates
• A new model for thin plates with rapidly varying thickness. II. A convergence proof