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.

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 |