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Autor:
Allen C. Pipkin
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modern as well as the clas sical techniques of applied
Autor:
Allen C. Pipkin
This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematic
Autor:
M. G. Hilgers, Allen C. Pipkin
Publikováno v:
Quarterly of Applied Mathematics. 55:791-800
A theory of elastic sheets with bending stiffness has been proposed in which the strain energy density of the sheet includes a dependence on the second-order derivatives. To study the motion of such sheets, a kinetic energy is required that is accura
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::9cbb0540c37c56667232fa94e0be17a9
https://doi.org/10.1090/qam/1486549
https://doi.org/10.1090/qam/1486549
Autor:
Allen C. Pipkin, M. G. Hilgers
Publikováno v:
Quarterly of Applied Mathematics. 54:307-316
The strain energy per unit area for a deformed sheet of elastic material is estimated by representing the deformation as a power series in the thickness variable. The membrane energy is the lowest-order approximation obtained in this way. Strain-grad
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::99e7abb509a32703da174bfb7db86a4f
https://doi.org/10.1090/qam/1388018
https://doi.org/10.1090/qam/1388018
Autor:
Allen C. Pipkin
Publikováno v:
The Quarterly Journal of Mechanics and Applied Mathematics. 48:123-134
A relatively short segment at one end of a stretched string of viscoelastic material is stretched by an additional amount and then released. A loading wave propagates into the less-stretched region, followed by an unloading wave reflected from the en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0c46ffcd62fe8448ba5b6d500a07594e
https://doi.org/10.1093/qjmam/48.1.123
https://doi.org/10.1093/qjmam/48.1.123
Autor:
Allen C. Pipkin
Publikováno v:
IMA Journal of Applied Mathematics. 54:285-299
The relaxed theory of inextensible networks allow fibres to grow shorter, but not longer, in a deformation. Minimum energy and minimum complementary energy theorems for infinitesimal plane deformations of such networks are proved. It is shown that an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a4e0509ee102bd912d2f2d8eef8e0158
https://doi.org/10.1093/imamat/54.3.285
https://doi.org/10.1093/imamat/54.3.285
Autor:
Allen C. Pipkin
Publikováno v:
IMA Journal of Applied Mathematics. 52:297-308
The theory of plane stress for infinitesimal deformations of elastic membranes commonly yields solutions that are unstable with respect to out-of-plane perturbations. This can be remedied by replacing the elastic strain energy by a certain relaxed en
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::c33df34d51798e6274b46b7ba4bfc31c
https://doi.org/10.1093/imamat/52.3.297
https://doi.org/10.1093/imamat/52.3.297
Autor:
Allen C. Pipkin, M. G. Hilgers
Publikováno v:
Journal of Elasticity. 31:125-139
Necessary conditions for energy-minimizing deformations are derived for a theory of sheets in which the strain energy function depends on the second derivatives of the deformation as well as its first derivatives. All of these conditions are extensio
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https://explore.openaire.eu/search/publication?articleId=doi_________::cb87c84a8a48050aef08c378a32df10a
https://doi.org/10.1007/bf00041227
https://doi.org/10.1007/bf00041227
Autor:
Allen C. Pipkin
Publikováno v:
The Quarterly Journal of Mechanics and Applied Mathematics. 46:583-599
One dimensional wave propagation in nonlinear viscoelasticitic materials is discussed by using a nonlinear version of the compliance integral stress strain relation of linear viscoelasticity theory. The analysis is phrased in terms of longitudinal wa
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::424a15e55e7ea0d5db039e9627487428
https://doi.org/10.1093/qjmam/46.4.583
https://doi.org/10.1093/qjmam/46.4.583
Autor:
Allen C. Pipkin, M. G. Hilgers
Publikováno v:
Quarterly of Applied Mathematics. 50:389-400
For a membrane composed of elastic material with strain energy W W per unit initial volume, approximations to the energy per unit initial area are obtained by integrating W W through the thickness. The usual stretching energy M ( r , a ) M\left ( {{r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::5fc469b25b16fa20abd3c6da46e90695
https://doi.org/10.1090/qam/1162282
https://doi.org/10.1090/qam/1162282