Stress Distribution Analysis for Linear Viscoelastic Materials
The formulation of the differential or integro-differential equations governing the quasi-static stress analysis problem for linear viscoelastic bodies is considered, with particular reference to the initial conditions associated with sudden loading. If classical methods of solving the differential equations, such as the Laplace transform or integrating factor, are used, the need to evaluate the initial conditions after load application at t = 0+ presents difficulties. These can be avoided by working with the lower limit t = 0-, before load application, when the body is still undisturbed, and, in the case of direct integration of the equations, delta functions and their derivatives must then be incorporated into the analysis. Examples of both methods of approach are contrasted. The stress distribution in a spinning hollow circular cylinder with annihilating inner cavity is evaluated as an example which does not fall within the scope of the Laplace transform method of analysis. The procedures are justified through the application of the corresponding integral operators.
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