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Modeling and numerical analysis of junctions between elastic structures. (English) Zbl 0707.73045
Industrial and applied mathematics, Proc. 1st Int. Conf., ICIAM, Paris/Fr. 1987, 62-74 (1988).
Summary: [For the entire collection see Zbl 0664.00003.]
We consider a problem in three-dimensional linearized elasticity, posed over a domain consisting of a plate with thickness \(2\epsilon\), inserted into a solid whose Lamé constants are independent of \(\epsilon\). If the Lamé constants of the material constituting the plate vary as \(\epsilon^{-3}\), the solution of the three-dimensional problem converges, as \(\epsilon\) approaches zero, to the solution of a coupled, “pluri-dimensional” problem of a new type, posed simultaneously over a three-dimensional open set with a slit and a two-dimensional open set. Other problems are also amenable to the same method, such as junctions between plates and rods, and folded plates.

74E30 Composite and mixture properties
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
65K10 Numerical optimization and variational techniques