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

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. © 1990 Springer-Verlag.