Event 20: Classical and Advanced Theories of Thin Structures: Mechanical and Mathematical Aspects

Download here the Course Program.

A fundamental problem in elasticity is to derive lower dimensional theories for thin structures, such as shells, plates and beams, from the fully three dimensional formulation of the problem. Classical approaches, which go back to the pioneering works in mechanics of Euler, D. Bernoulli and Navier, are based on some a-priori assumptions, motivated by the smallness of certain dimensions with respect to others, on the stress field or on the deformation of the body. In the last few decades a considerable amount of work has been done in order to rigorously justify the a-priori assumptions on which classical theories are based. In particular, approaches based on rigorous asymptotic expansion (mainly due to the French school) or inspired by the Gamma-convergence of energy functionals (proposed by E. De Giorgi in 1979) have been successfully used, in deriving one or two-dimensional classical mechanical models for thin structures in linear and non-linear elasticity starting from three-dimensional elasticity. Although numerous and interesting partial results have been obtained in studying problems of practical interest, several fundamental questions still remain unanswered and concern, for instance, the justification of mechanical models of damage and the generation of fractures inside a continuous body. Moreover, the enormous development of new materials (ferro-magnetic materials, shape memory alloys, self-assembly materials, nematic elastomers, etc) and nano-technologies opens the field of thin structures to new interesting and challenging problems, which have an important impact in material science and in practical engineering applications. The purpose of the course is to present an updated state-of-the-art overview of the general aspects and practical applications of the theories of thin structures, through the interaction of several topics, ranging from non-linear thin-films, shells, junctions, beams of different materials and in different contexts (elasticity, plasticity, etc.). Advanced problems like the optimal design and the modeling of thin films made of brittle or phase-transforming materials will be presented as well. The course is addressed to PhD students and researchers in the fields of continuum mechanics, structural engineering and applied mathematics interested in recent developments in linear and nonlinear elasticity, thin structures and asymptotic developments.

Fellowships

13 EU fellowships (10 Group 1, 2 Group 2, and 1 Group 3) are offered to young participants to attend the workshop.

When

2006-06-05 09:30 to
2006-06-09 18:30

Deadlines

Requests should be sent to CISM Secretariat by May 5, 2006 together with the applicant’s curriculum and a letter of recommendation by the head of the department or supervisor confirming that the institute cannot provide funding.

Where

CISM, Udine, Italy

Contact

Sara Guttilla

Contact Email

s.guttilla@cism.it

Contact Phone

+39 0432 248524

For more information, visit
http://www.cism.it