Physically nonlinear and related approximate theories of elasticity, and their invariance properties

Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systemat...
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Gespeichert in:

Autor*in:	Casey, J. [verfasserIn] Naghdi, P. M.

Format:	Artikel
Sprache:	Englisch

Erschienen:	1985

Schlagwörter:	Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property

Anmerkung:	© Springer-Verlag 1985

Übergeordnetes Werk:	Enthalten in: Archive for rational mechanics and analysis - Springer-Verlag, 1957, 88(1985), 1 vom: März, Seite 59-82
Übergeordnetes Werk:	volume:88 ; year:1985 ; number:1 ; month:03 ; pages:59-82

Links:	Volltext

DOI / URN:	10.1007/BF00250682

Katalog-ID:	OLC2056402866

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allfields	10.1007/BF00250682 doi (DE-627)OLC2056402866 (DE-He213)BF00250682-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut Physically nonlinear and related approximate theories of elasticity, and their invariance properties 1985 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1985 Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 88(1985), 1 vom: März, Seite 59-82 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:88 year:1985 number:1 month:03 pages:59-82 https://doi.org/10.1007/BF00250682 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 88 1985 1 03 59-82
spelling	10.1007/BF00250682 doi (DE-627)OLC2056402866 (DE-He213)BF00250682-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut Physically nonlinear and related approximate theories of elasticity, and their invariance properties 1985 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1985 Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 88(1985), 1 vom: März, Seite 59-82 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:88 year:1985 number:1 month:03 pages:59-82 https://doi.org/10.1007/BF00250682 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 88 1985 1 03 59-82
allfields_unstemmed	10.1007/BF00250682 doi (DE-627)OLC2056402866 (DE-He213)BF00250682-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut Physically nonlinear and related approximate theories of elasticity, and their invariance properties 1985 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1985 Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 88(1985), 1 vom: März, Seite 59-82 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:88 year:1985 number:1 month:03 pages:59-82 https://doi.org/10.1007/BF00250682 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 88 1985 1 03 59-82
allfieldsGer	10.1007/BF00250682 doi (DE-627)OLC2056402866 (DE-He213)BF00250682-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut Physically nonlinear and related approximate theories of elasticity, and their invariance properties 1985 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1985 Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 88(1985), 1 vom: März, Seite 59-82 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:88 year:1985 number:1 month:03 pages:59-82 https://doi.org/10.1007/BF00250682 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 88 1985 1 03 59-82
allfieldsSound	10.1007/BF00250682 doi (DE-627)OLC2056402866 (DE-He213)BF00250682-p DE-627 ger DE-627 rakwb eng 530 510 VZ Casey, J. verfasserin aut Physically nonlinear and related approximate theories of elasticity, and their invariance properties 1985 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 1985 Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property Naghdi, P. M. aut Enthalten in Archive for rational mechanics and analysis Springer-Verlag, 1957 88(1985), 1 vom: März, Seite 59-82 (DE-627)129519618 (DE-600)212130-X (DE-576)014933004 0003-9527 nnns volume:88 year:1985 number:1 month:03 pages:59-82 https://doi.org/10.1007/BF00250682 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_11 GBV_ILN_20 GBV_ILN_21 GBV_ILN_22 GBV_ILN_30 GBV_ILN_31 GBV_ILN_32 GBV_ILN_40 GBV_ILN_59 GBV_ILN_65 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2010 GBV_ILN_2012 GBV_ILN_2016 GBV_ILN_2018 GBV_ILN_2020 GBV_ILN_2088 GBV_ILN_2409 GBV_ILN_4035 GBV_ILN_4036 GBV_ILN_4046 GBV_ILN_4126 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4310 GBV_ILN_4311 GBV_ILN_4313 GBV_ILN_4314 GBV_ILN_4315 GBV_ILN_4318 GBV_ILN_4319 GBV_ILN_4323 GBV_ILN_4325 GBV_ILN_4700 AR 88 1985 1 03 59-82
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author	Casey, J.
spellingShingle	Casey, J. ddc 530 misc Neural Network misc Complex System misc Nonlinear Dynamics misc Electromagnetism misc Invariance Property Physically nonlinear and related approximate theories of elasticity, and their invariance properties
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topic_title	530 510 VZ Physically nonlinear and related approximate theories of elasticity, and their invariance properties Neural Network Complex System Nonlinear Dynamics Electromagnetism Invariance Property
topic	ddc 530 misc Neural Network misc Complex System misc Nonlinear Dynamics misc Electromagnetism misc Invariance Property
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title	Physically nonlinear and related approximate theories of elasticity, and their invariance properties
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title_full	Physically nonlinear and related approximate theories of elasticity, and their invariance properties
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title_sort	physically nonlinear and related approximate theories of elasticity, and their invariance properties
title_auth	Physically nonlinear and related approximate theories of elasticity, and their invariance properties
abstract	Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. © Springer-Verlag 1985
abstractGer	Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. © Springer-Verlag 1985
abstract_unstemmed	Abstract The existing developments of physically nonlinear elasticity have several shortcomings. With the aim of remedying these deficiencies, a number of approximate theories of elasticity are discussed in the present paper and, in particular, a theory of physically nonlinear elasticity is systematically developed. More specifically, stress-strain relations for anisotropic physically nonlinear materials are derived. The method of Casey & Naghdi [1] is then applied to obtain properly invariant results. This method involves the use of auxiliary motions obtained by removing from any given motion the translation and rotation at any one particle, called a “pivot.” The auxiliary motions represent the original motions in the approximate theory. The connection between the transformation of fields under a change of pivot and invariance requirements associated with the auxiliary motions is investigated. © Springer-Verlag 1985
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title_short	Physically nonlinear and related approximate theories of elasticity, and their invariance properties
url	https://doi.org/10.1007/BF00250682
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