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A Unified Representation of Variational Principles in Non‐Linear Elasticity
Author(s) -
Bufler H.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(200001)80:1<53::aid-zamm53>3.0.co;2-4
Subject(s) - statics , mathematics , discretization , eigenvalues and eigenvectors , boundary value problem , elasticity (physics) , variational principle , representation (politics) , kinematics , linear elasticity , mathematical analysis , classical mechanics , finite element method , physics , quantum mechanics , politics , political science , law , thermodynamics
In elastomechanics there exist besides of the classical variational principles so‐called generalized (extended, mixed) ones which are used mainly for the discretization of boundary and eigenvalue problems. These principles can be constructed together with their incremental versions systematically from the canonical basic equations characterized by four special operators (statics, kinematics, material, loading), and the boundary‐ and (eventually) transition conditions. Under certain assumptions they can be strengthened to complementary extremum principles. The proposed abstract and unified formulation holds true for all kinds of elastic structures and, additionally, for related problems and facilitates the construction of the corresponding variational principles. At last the relevance of drilling degrees of freedom is discussed.