Abstract
The various approaches to the solution of viscoelastic boundary value problems discussed in the last chapter for bars and beams carry over to the solution of problems in two and three dimensions. In particular, if the solution to a similar problem for an elastic material already exists, the correspondence principle may be invoked and with the use of Laplace or Fourier transforms a solution can be found. Such solutions can be used with confidence but one must be cognizant of the general equations of elasticity and the methods of solutions for elasticity problems in two and three dimensions as well as any assumptions that might often be applied. To provide all of the necessary information and background for multidimensional elasticity theory is beyond the scope of this text but the procedures needed will be outlined in the following sections.
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Notes
- 1.
† Note that in this and the following equations the comma is used in the subscripts on stress to be able to write both the radial and hoop stresses in one equation. Since the form of these stresses differs only by a minus sign, it is preferred to emphasize their similarity by this nonstandard notation rather than write the two equations separately.
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Brinson, H.F., Brinson, L.C. (2015). Viscoelastic Stress Analysis in Two and Three Dimensions. In: Polymer Engineering Science and Viscoelasticity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-7485-3_9
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