Biharmonic Solutions of Certain Integro‐Differential Equations of Linear Viscoelasticity
作者:
Alexander S. Elder,
期刊:
Transactions of the Society of Rheology
(AIP Available online 1964)
卷期:
Volume 8,
issue 1
页码: 101-115
ISSN:0148-6055
年代: 1964
DOI:10.1122/1.548971
出版商: The Society of Rheology
数据来源: AIP
摘要:
A stress function theory for linearly viscoelastic solids is developed in this paper. If body forces and inertial forces are neglected, the stresses, strains, and displacements are biharmonic functions of the space variables. The displacements are expressed in terms of harmonic functions by an extension of the Neuber‐Papkovitch theory. Axially symmetric stresses and strains are given in terms of a single biharmonic function. As the analysis does not involve boundary conditions, it is valid for problems involving moving leads and moving boundaries. The theory may be used to formulate stress analysis problems in terms of Volterra integral equations, using creep or relaxation functions as the kernel. The integral equations governing the stresses in a viscoelastic propellant grain subjected to the combined effects of internal pressure and erosion are derived.
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