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Numerical Methods for Solving Dynamic Equilibrium Equations
Abstract
Once the number of degrees of freedom exceeds a certain number, it would be impossible to solve the dynamic equilibrium equation manually, hence the need to switch to a numerical resolution, whose general principle is to convert a dynamic equation into a static one. We are interested, for the dynamic analysis of the structures and the continuous media, in “one-step” algorithms rather than “multi-step” one. It is mainly because the systems to be solved are of large size and that it is important to minimize the number of operations and value to be memorized to the detriment, if necessary, of precision. A “one-step” algorithm, like that of Newmark, makes it possible to calculate the solution at time tn+1, starting from the solution at time tn. In addition to the disadvantage of requiring the storage of several steps, the “multi-step” algorithms such as that of Houbolt requires a startup procedure. This chapter allows the reader to enumerate and understand different numerical method with different examples.
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