Multibody dinamikaren ekuazioen integrazioa metodo estrukturalak erabiliz

Résumé

The main contribution of this document lies on the development of a new algorithm to integrate the equations of multibody dynamics using Newmark. This method takes advantage of the use of fundamental nullspace basis to integrate the equations in the manifold, so unconditionally stable behaviorwithout the introduction of numerical damping can be achieved. This is quite similar to the concept of using minimal coordinates but, in this case, instead of using the same coordinates for an interval, the same nullspace used to solve a step is used to define the coordinate set at a moderate cost.Along with this main contribution, other contributions have also been achieved:¿ A method for the general linearization of the equations (including equilibrium and constraints) regardless of the chosen orientation representation. This method simplifies the use of different systems of representation when this is required.¿ A new set of conditionally explicit methods of general use based on the classical structural central difference method. They allow for a higher degree of convergence at a very limited computational cost.¿ A preliminary study of the applicability of structural methods for the resolution of Discrete Element problems. // The main contribution of this document lies on the development of a new algorithm to integrate the equations of multibody dynamics using Newmark. This method takes advantage of the use of fundamental nullspace basis to integrate the equations in the manifold, so unconditionally stable behaviorwithout the introduction of numerical damping can be achieved. This is quite similar to the concept of using minimal coordinates but, in this case, instead of using the same coordinates for an interval, the same nullspace used to solve a step is used to define the coordinate set at a moderate cost.Along with this main contribution, other contributions have also been achieved:¿ A method for the general linearization of the equations (including equilibrium and constraints) regardless of the chosen orientation representation. This method simplifies the use of different systems of representation when this is required.¿ A new set of conditionally explicit methods of general use based on the classical structural central difference method. They allow for a higher degree of convergence at a very limited computational cost.¿ A preliminary study of the applicability of structural methods for the resolution of Discrete Element problems.