Velocity-based reciprocal theorems in elastodynamics and BIEM implementation issues |
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Authors: | Christos G Panagiotopoulos G D Manolis |
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Institution: | 1. Department of Civil Engineering, Aristotle University of Thessaloniki, Panepistimioupolis, P.O. Box 502, 54124, Thessaloniki, Greece
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Abstract: | Reciprocal theorems in elastodynamics are introduced as extensions of respective theorems from elastostatics. Inasmuch as
the latter is a subset of the former, the aim here is to present an elastodynamic reciprocal theorem that also includes elastostatics
as a special case when the time variable becomes irrelevant. This is accomplished by introducing a velocity-based reciprocal
theorem, whose basic properties are subsequently explored. The next step is to use this theorem and formulate a numerical
approach based on boundary integral equation statements and compare them with existing formulations based on conventional
reciprocity relations. The applications presented here involve the standard mechanical oscillator and the unidimensional axial
element as two simple, yet important problems of structural dynamics. Along with the numerical results, a thorough stability
analysis of the corresponding time-stepping algorithms is formulated. In both cases, the superior performance of the methodologies
built on velocity-based reciprocal theorems is clearly demonstrated. |
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Keywords: | |
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