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arXiv · 2407.00441

The weak form of the SDOF and MDOF equation of motion, part I: Theory

Nikolaos Karaliolios·Dimitrios L. Karabalis
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Abstract

The weak form of the SDOF and MDOF equations of motion are obtained. The original initial conditions problem is transformed into a boundary value problem. The boundary value problem is then solved and transformed back to the initial conditions one. Subsequently, a general method for obtaining numerical methods using an arbitrary number of linearly independent approximating functions is outlined. This is part one of a series of three papers, in the second of which a numerical method is obtained, using Bernstein polynomials of arbitrarily high order. The numerical evidence for the convergence of the method will be presented in the third part paper.

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Nikolaos Karaliolios, Dimitrios L. Karabalis. 2024-06-29. The weak form of the SDOF and MDOF equation of motion, part I: Theory. https://arxiv.org/abs/2407.00441

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