Accession Number : AD0714927

Title :   On the Formal Structure of Continuum Mechanics. Part I. Deformation Theory,

Corporate Author : POLITECNICO DI MILANO (ITALY) ISTITUTO DI MATEMATICA

Personal Author(s) : Tonti,Enzo

Report Date : 14 JAN 1970

Pagination or Media Count : 13

Abstract : The purpose of the paper is to give an operator form to the equations of statics of continuous media in the case of small deformations (linear case) and of large deformations (non linear), aiming to obtain a unitary view of many known results in linear and nonlinear mechanics. In this paper an operator version of compatibility equations for large deformations, is given introducing a nonlinear operator that will be shown to be of the potential type. Some new results follow, namely a variational formulation of compatibility conditions extending a similar result obtained by the author in the small deformation theory. This formulation in three-dimensional space is similar to that of Einstein describing the gravitational field in space-time. An operational version of Bianchi's identities and a construction of boundary compatibility conditions are also given. (Author)

Descriptors :   (*DEFORMATION, *CONTINUUM MECHANICS), TENSOR ANALYSIS, OPERATORS(MATHEMATICS), STRAIN(MECHANICS), PARTIAL DIFFERENTIAL EQUATIONS, ITALY

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE