A new class of variational problems arising in the modeling of elastic multi-structures. (English) Zbl 0709.73100

The modeling of junctions between elastic structures is an important practical problem. In this paper elastic multistructures whose substructures have different dimensions (three-dimensional bodies, two- dimensional plates and shells, one-dimensional rods) are analysed as a coupled pluri-dimensional problem. A three-dimensional elastic structure consisting of a three-dimensional portion connected to a thin plate is treated in detailed form. A limit problem is formulated to solve the variational equations of the above mentioned elastic multi-structure. The obtained numerical results are discussed and some computations are also analysed. The main result of the paper is a new variational formulation of multi-structures; by using this formulation the problem is simultaneously posed over a three-dimensional set and a two-dimensional set.
Reviewer: I.Ecsedi


74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
74E30 Composite and mixture properties
65K10 Numerical optimization and variational techniques
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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