Hamiltonian Structure and Conservation Laws of Three-Dimensional Linear Elasticity Theory

2021 ◽  
pp. 99-123
Author(s):  
D. O. Bykov ◽  
V. N. Grebenev ◽  
S. B. Medvedev
Keyword(s):  
Conservation Laws ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Hamiltonian Structure ◽  
Three Dimensional ◽  
Linear Elasticity Theory

Linear elasticity theory of cubic quasicrystals

1993 ◽  
Vol 48 (10) ◽  
pp. 6999-7002 ◽  
Author(s):  
Wenge Yang ◽  
Renhui Wang ◽  
Di-hua Ding ◽  
Chengzheng Hu
Keyword(s):  
Elasticity Theory ◽  
Linear Elasticity ◽  
Linear Elasticity Theory

Monolayerwise application of linear elasticity theory well describes strongly deformed lipid membranes and the effect of solvent

Soft Matter ◽  
2020 ◽  
Vol 16 (5) ◽  
pp. 1179-1189 ◽  
Author(s):  
Timur R. Galimzyanov ◽  
Pavel V. Bashkirov ◽  
Paul S. Blank ◽  
Joshua Zimmerberg ◽  
Oleg V. Batishchev ◽  
...  
Keyword(s):  
Elasticity Theory ◽  
Linear Theory ◽  
Linear Elasticity ◽  
Lipid Membranes ◽  
Bilayer Membrane ◽  
Theory Of Elasticity ◽  
Linear Elasticity Theory ◽  
Effect Of Solvent ◽  
Model Based ◽  
Membrane Deformations

The linear theory of elasticity can be expanded through the range from weak to strong bilayer membrane deformations using a generalized Helfrich model based on monolayer membrane additivity.

Conservation laws of linear elasticity in stress formulations

2005 ◽  
Vol 461 (2053) ◽  
pp. 99-116 ◽  
Author(s):  
Shaofan Li ◽  
Anurag Gupta ◽  
Xanthippi Markenscoff
Keyword(s):  
Conservation Laws ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Cauchy Stress ◽  
General Boundary Conditions ◽  
Cauchy Stress Tensor ◽  
Equilibrium Equations ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Three Dimensional Elasticity

In this paper, we present new conservation laws of linear elasticity which have been discovered. These newly discovered conservation laws are expressed solely in terms of the Cauchy stress tensor, and they are genuine, non–trivial conservation laws that are intrinsically different from the displacement conservation laws previously known. They represent the variational symmetry conditions of combined Beltrami–Michell compatibility equations and the equilibrium equations. To derive these conservation laws, Noether's theorem is extended to partial differential equations of a tensorial field with general boundary conditions. By applying the tensorial version of Noether's theorem to Pobedrja's stress formulation of three–dimensional elasticity, a class of new conservation laws in terms of stresses has been obtained.

Linear elasticity theory of pentagonal quasicrystals

1987 ◽  
Vol 35 (16) ◽  
pp. 8609-8620 ◽  
Author(s):  
Piali De ◽  
Robert A. Pelcovits
Keyword(s):  
Elasticity Theory ◽  
Linear Elasticity ◽  
Linear Elasticity Theory

Integro-differential approach to solving problems of linear elasticity theory

2005 ◽  
Vol 50 (10) ◽  
pp. 535-538 ◽  
Author(s):  
G. V. Kostin ◽  
V. V. Saurin
Keyword(s):  
Elasticity Theory ◽  
Linear Elasticity ◽  
Linear Elasticity Theory ◽  
Differential Approach

scholarly journals Boundary value problems for the Lamé-Navier system in fractal domains

2021 ◽  
Vol 6 (10) ◽  
pp. 10449-10465
Author(s):  
Ricardo Abreu Blaya ◽  
◽  
J. A. Mendez-Bermudez ◽  
Arsenio Moreno García ◽  
José M. Sigarreta ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problems ◽  
Elasticity Theory ◽  
Linear Elasticity ◽  
Clifford Analysis ◽  
Boundary Value ◽  
Representation Formula ◽  
Linear Elasticity Theory ◽  
Fractal Domains

<abstract><p>The aim of this paper is to establish a representation formula for the solutions of the Lamé-Navier system in linear elasticity theory. We also study boundary value problems for such a system in a bounded domain $ \Omega\subset {\mathbb R}^3 $, allowing a very general geometric behavior of its boundary. Our method exploits the connections between this system and some classes of second order partial differential equations arising in Clifford analysis.</p></abstract>

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