Structural analysis in the problems of gradient elasticity

DOI10.1134/s1995080223060446zbMath1525.74029OpenAlexW4387298769MaRDI QIDQ6095173

D. B. Volkov-Bogorodskiy

Publication date: 12 October 2023

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080223060446

zbMATH Keywords

generalized Helmholtz equationEshelby inclusion problemgeneralized Papkovich-Neuber representationbilinear energy functionalquasi-separation of variables methodTrefftz block approximation

Mathematics Subject Classification ID

Inhomogeneity in solid mechanics (74E05) Energy minimization in equilibrium problems in solid mechanics (74G65) Elastic materials (74B99) Numerical and other methods in solid mechanics (74S99)

Cites Work

• Exact solution of Eshelby-Christensen problem in gradient elasticity for composites with spherical inclusions
• Generalized Trefftz method in the gradient elasticity theory
• Generalized Eshelby problem in the gradient theory of elasticity
• Systems of functions consistent with inhomogeneities of elliptic and spheroidal shapes in problems of continuum mechanics
• Micro-structure in linear elasticity
• The determination of the elastic field of an ellipsoidal inclusion, and related problems
• Generalized finite element analysis with T-complete boundary solution functions
• Radial multipliers in solutions of the Helmholtz equations
• On trial functions applied in the generalized Trefftz method
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