A new class of variational problems arising in the modeling of elastic multi-structures

Abstract

Summary.It is shown how elastic multi-structures that comprise substructures of possibly different "dimensions" (three-dimensional structures, plates, rods) are modeled by coupled, pluri-dimensional, variational problems of a new type. Following recent work by the author, H. LeDret, and R. Nzengwa, we describe here in detail one such problem, which is simultaneously posed over a threedimensional open set with a slit and a two-dimensional open set. The numerical analysis of such problems is also discussed and finally, some numerical results are presented.

Mathematical model of coupled plates meeting at an angle 0 < θ < π and its finite element method

“…In Feng [l, 21, the mechanical and mathematical models of composite structures have been proposed in general. Ciarlet [3,4] and LeDret [5] have dealt with the field by the asymptotic analysis. In our recent paper [6], a composite elastic structure consisting of coupled plates meeting at a right angle and its finite element approximations are considered using the approach proposed by Feng [1,2].…”