Análisis de un método compuesto de integración implícita del tiempo aplicado a problemas lineales de la dinámica estructural.
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In the present work a new implicit method of numerical integration will be exposed step by step in the time developed in the year of 2007 by the professor of mechanical engineering and of finite elements of the Technological Institute of Massachusetts, Klaus-Jürgen Bathe. This numerical procedure is based on determining the dynamic response by dividing those time steps into two parts, where the first one is analyzed by the numerical method of the trapeze rule, and the second one by Euler's numerical method, which is why it is called a method composed of implicit integration of time.
This composite numerical method will be referred to as the Bathe method and is compared against the commonly studied methods such as: the Newmark, Wilson-Theta method and the central difference, this in order to analyze and compare its properties of precision and stability when Problems of structural dynamics are studied in bodies subjected to deformations and long vibration times.