The 48th SNP Meeting

Invited Lecture

Dimension Reduction Techniques: Ideas and Applications

ROBERTO PARONI
Dipartimento di Architettura e Pianificazione
Palazzo del Pou Salit, Piazza Duomo 6
Università degli Studi di Sassari
07041 Alghero, Italy

Abstract. Approximate mechanical models for thin structures are hundreds of years old and go back to the pioneering works of Euler, D. Bernoulli, Navier and Kirchhoff. The classical theories are usually based on some a-priori assumptions, motivated by the smallness of certain dimensions with respect to others, on the deformation or on the induced stress field. In the last three decades a considerable amount of work has been done in order to rigorously justify the a-priori assumptions on which the classical theories are based; indeed several techniques have been introduced to make the dimension reduction rigorous. In this talk we review the common ideas behind these techniques and we illustrate some of them by considering a few dimension reduction problems.

Acknowledgement. This lecture was made possible through financial support from Pró-Reitoria de Pós-Graduação (PRPG/USP), Ministry of Science and Technology (MCT), and  National Council for Scientific and Technological Development (CNPq).