NDLI: Lamé’s strain potential method for plane gradient elasticity problems

Content Provider	Springer Nature Link
Author	Papargyri Beskou, Sofia Tsipoulos, Stefas
Copyright Year	2014
Abstract	The method of Lamé’s strain potential for solving analytically a certain class of problems of classical elasticity is extended here to plane gradient elasticity of the simple Mindlin’s type with just one constant (internal length) in addition to the two classical elastic moduli. According to this method, the strains are expressed as second-order derivatives of a scalar function (Lamé’s strain potential). Thus, combining compatibility, equilibrium and stress–strain equations under plane stress or plane strain conditions and zero body forces, one can prove that this strain potential satisfies an equation of the fourth order instead of the second one for the classical case. General solutions of this equation in Cartesian and polar coordinates are provided. Four examples, two in Cartesian and two in axisymmetric polar coordinates, are presented to illustrate the method and demonstrate its advantages and limitations.
Starting Page	1399
Ending Page	1419
Page Count	21
File Format	PDF
ISSN	09391533
Journal	Archive of Applied Mechanics
Volume Number	85
Issue Number	9
e-ISSN	14320681
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-11-27
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Lamé’s strain potential Gradient elasticity Analytical solutions Cartesian and polar coordinates Boundary value problems Plane stress and plane strain Theoretical and Applied Mechanics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanical Engineering

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