NDLI: Dynamic equations of the theory of thin prismatic bodies with expansion in the system of Legendre polynomials

Please wait, while we are loading the content...

Mechanics of Solids : Volume 52

Mechanics of Solids : Volume 51

Mechanics of Solids : Volume 50

Mechanics of Solids : Volume 49

Mechanics of Solids : Volume 48

Mechanics of Solids : Volume 47

Mechanics of Solids : Volume 46

Mechanics of Solids : Volume 46, Issue 6, December 2011

Mechanics of Solids : Volume 46, Issue 5, October 2011

Mechanics of Solids : Volume 46, Issue 4, August 2011

Mechanics of Solids : Volume 46, Issue 3, June 2011

On steady motions of a rigid body bearing three-degree-of-freedom control momentum gyroscopes and their stability

Continuum theory of dislocations and disclinations in nonlinearly elastic micropolar media

On the choice of coordinates in the analysis of plane plastic strain

Parameter identification in viscoelastic strain models for composite materials by analyzing impulsive loading of shells of revolution

Experimental-theoretical method for determining mechanical characteristics of spherical films and membranes of complex structure

Derivation of equations of state for ideal crystals of simple structure

Asymptotic computation of the inhomogeneity energy in a body in an external stress field

Prefracture zone for longitudinal shear cracks in structured materials

Model of symmetric crack formation in a plate and a wedge under bending by a point indenter

Formation of separation zones in an asymmetric motion of a body in an elastic medium

Nonlinear vibrations and stability of elastic and viscoelastic systems under random stationary loads

Dynamic interaction of bridges and high-speed trains

Dynamic equations of the theory of thin prismatic bodies with expansion in the system of Legendre polynomials

On the solution of boundary value problems of mechanics for the Poisson equation and related equations

Mechanics of Solids : Volume 46, Issue 2, April 2011

Mechanics of Solids : Volume 46, Issue 1, February 2011

Mechanics of Solids : Volume 45

Mechanics of Solids : Volume 44

Mechanics of Solids : Volume 43

Mechanics of Solids : Volume 42

Dynamic equations of the theory of thin prismatic bodies with expansion in the system of Legendre polynomials

Content Provider	Springer Nature Link
Author	Ulukhanyan, A. R.
Copyright Year	2011
Abstract	For a thin anisotropic body that is inhomogeneous with respect to curvilinear coordinates x $^{1}$ and x $^{2}$ and for an arbitrary homogeneous prismatic anisotropic elastic body of variable thickness with one small dimension in the case of the classical parametrization of its domain, we obtain the equations of motion of the Cosserat theory of elasticity in terms of moments with the kinematic boundary conditions of kinematic meaning and with boundary conditions of physical meaning taken into account.For prismatic bodies of constant thickness, these equations are used to obtain the system of zeroorder approximation equations for an isotropic medium. For the zero-order moments of the third components of the displacement and rotation vectors, fourth-order wave equations are obtained. In the classical theory, such equations are obtained in the first-order approximation for the zero- and first-order moments of the first invariant of the plane strain and for the third components of the displacement vector. In contrast to the Timoshenko type wave equation, in the equation for the zero-order moment of the third component of the displacement vector, the shear coefficient is k = 1. Moreover, the plate cylindrical rigidity coincides with the rigidity obtained by I. N. Vekua, and for Poisson’s ratio equal to 0.5, the coefficient multiplying the acceleration is zero.In the case of a transversally isotropic medium, in the first- and second-order approximations, the fourth- and sixth-order hyperbolic equations are obtained for the zero-, first-, and second-order moments of the first invariant of the plane strain and of the third component of the displacement vector, respectively. The matrix of velocities of the wave propagation in an infinitely transversally isotropic elastic medium is written in the principal directions, and this matrix shows that the coefficients of these equations can be expressed in terms of these velocities. Most of this paper was published in [1].
Starting Page	467
Ending Page	479
Page Count	13
File Format	PDF
ISSN	00256544
Journal	Mechanics of Solids
Volume Number	46
Issue Number	3
e-ISSN	19347936
Language	English
Publisher	Allerton Press, Inc.
Publisher Date	2011-07-27
Publisher Place	Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Cosserat theory prismatic body with one small dimension system of Legendre polynomials moments of function hyperbolic equation Mechanics
Content Type	Text
Resource Type	Article
Subject	Physics and Astronomy Mechanics of Materials

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Equations of motion and boundary conditions of physical meaning of micropolar theory of thin bodies with two small cuts

Homogenization of the equations of the Cosserat theory of elasticity of inhomogeneous bodies

A Note on the Legendre Series Solution of the Laplace Equation for Cylindrical Problems

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

Asymptotics of solutions of the three-dimensional elasticity equations for compressible and incompressible bodies

Application of Chebyshev polynomials to the theory of thin bodies

Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension

Spacetime Interpretation of Torsion in Prismatic Bodies

Poincare-chetayev equations and flexible multi-body systems.

Dynamic equations of the theory of thin prismatic bodies with expansion in the system of Legendre polynomials

Similar Documents

Equations of motion and boundary conditions of physical meaning of micropolar theory of thin bodies with two small cuts

Homogenization of the equations of the Cosserat theory of elasticity of inhomogeneous bodies

A Note on the Legendre Series Solution of the Laplace Equation for Cylindrical Problems

A Note on the Legendre Series Solution of the Biharmonic Equation for Cylindrical Problems

Asymptotics of solutions of the three-dimensional elasticity equations for compressible and incompressible bodies

Application of Chebyshev polynomials to the theory of thin bodies

Higher Order Mixed-Moment Approximations for the Fokker--Planck Equation in One Space Dimension

Spacetime Interpretation of Torsion in Prismatic Bodies

Poincare-chetayev equations and flexible multi-body systems.

Dynamic equations of the theory of thin prismatic bodies with expansion in the system of Legendre polynomials