Fields in Non-Degenerate 1D-3D Elastic Multi-Structures
Vladimir Arkad'evich Kozlov · The Quarterly Journal of Mechanics and Applied Mathematics · 2001
We analyse 1D–3D elastic multi‐structures defined as solids involving finite‐size three‐dimensional elastic regions connected with thin rods. In the limit, when the thickness of the thin rods tends to zero, one has a union of a three‐dimensional region and a set of thin rods. Classes of degenerate and non‐degenerate multi‐structures are specified, and asymptotic expansions of solutions of mixed boundary‐value problems of linear elasticity are constructed. Asymptotic analysis, given in this work, provides rigorous justification of the existing engineering pile‐structure models, and it also enables one to construct new models of high accuracy.