Abstract:

In elastic bodies, stress is only a function of strain, while in viscoelastic bodies, stress depends on both strain and strain rate. By making various combinations of springs and dashpots with different material constants, it is possible to represent the mechanical behavior of materials such as high polymers, nylon fibers, concrete etc. In this study, which discusses the statically indeterminate axially loaded bar problem, whose mechanical behavior is represented using the Maxwell model, a solution technique that can be easily applied to even the most complex structural systems is proposed by using the total potential energy (TPE) theorem. The TPE expression in terms of the displacement of the nodes is obtained in the Laplace space. The solutions that minimize the TPE expression are the real displacements, and the Inverse Laplace transform method is applied to return to the time domain. The method has been tested on the sample problem and the results are presented. This method provides great convenience in obtaining the solution directly by following a few simple process steps, regardless of the change in the viscoelastic material model, the number of elements of the system and the type of loading.

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