Homogenization of a thin plate reinforced with periodic families of rigid rods
The asymptotics of the solution to the elastic bending problem for a thin plate reinforced with several periodic families of closely spaced but disjoint rods are constructed and justified, the result of homogenization being substantially different from the case when the rods are welded together into a single periodic mesh. The material in the rods is assumed to be appreciably more rigid than that in the plate. An averaged fourth-order differential operator is obtained from summing the nonelliptic operators generated by each of the families of the rods. This operator is shown to be elliptic if and only if the rods from at least two families are nonparallel. As a simplified example, the paper examines a similar stationary heat conduction problem. Bibliography: 24 titles.
- OSTI ID:
- 21612744
- Journal Information:
- Sbornik. Mathematics, Vol. 202, Issue 8; Other Information: DOI: 10.1070/SM2011v202n08ABEH004181; Country of input: International Atomic Energy Agency (IAEA); ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
Similar Records
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II