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.

MSC:

 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