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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2014, Volume 55, Issue 3, Pages 140–145
(Mi pmtf1068)
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This article is cited in 1 scientific paper (total in 1 paper)
Constructing generalized Cesàro formulas for finite plane strains
D. V. Georgievskii Lomonosov Moscow State University, Moscow, 119991, Russia
Abstract:
The problem of finding the displacement vector from a system of nonlinear differential equations which includes displacement gradient components is studied. Expressions on the right side of this system for certain parameter values have the kinematic sense of Lagrange and Euler finite strain tensors. The task is to construct generalized Cesàro formulas for finite strains. The construction of the solution consists of two stages (algebraic and differential), and the second is performed for space whose dimension is greater than or equal to two. An algorithm for the inversion of the original system is proposed, and analytical constructions for the case of two-dimensional space are performed. The problem is solved at the first (algebraic) stage, i.e., an exact analytical expression for the displacement vector components is derived through the known finite strain tensor and an unknown scalar function having the kinematic sense of rotation. Necessary conditions for the existence of this relationship are formulated.
Keywords:
kinematics, Cauchy relations, finite strain tensors, Cesàro formulas, invariant, plane strain.
Received: 14.08.2013
Citation:
D. V. Georgievskii, “Constructing generalized Cesàro formulas for finite plane strains”, Prikl. Mekh. Tekh. Fiz., 55:3 (2014), 140–145; J. Appl. Mech. Tech. Phys., 55:3 (2014), 494–498
Linking options:
https://www.mathnet.ru/eng/pmtf1068 https://www.mathnet.ru/eng/pmtf/v55/i3/p140
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