دانلود رایگان مقاله روش لاگرانژی برآورد خطا و مشینگ تطبیقی برای مشکلات کشش تغییر شکل

Abstract

Solving large deformation problems of hyperelastic materials by the finite element method is still a challenging problem due to the severe mesh distortion that occurs during the computation. In Leger et al. (2014), it was shown that combining an updated Lagrangian method with an efficient adaptive remeshing algorithm, an accurate transfer method for the deformation gradient tensor as well as an efficient continuation method leads to a very stable, efficient and accurate algorithm to solve two-dimensional very large deformation problems. In this paper, we show that this method can also be generalized to solve three-dimensional problems. A number of static problems will be presented and analyzed.

5. Conclusion

In this work, we have presented a complete updated Lagrangian algorithm to solve three-dimensional large deformation elasticity problems. This algorithm is a generalization of the algorithm presented in [6] and includes key ingredients for its good performance, such as error estimation and adaptive remeshing, an accurate transfer method for the deformation gradient tensor as well as an efficient continuation method. Our adaptive remeshing not only leads to optimal meshes when the Hessian of the solution is indefinite, but also improves the accuracy of the numerical results. The numerical examples presented in this paper not only show the good accuracy of this method, but also its robustness in the case of complex large deformation problems. In practical applications, where accuracy and robustness is of utmost importance, this complete method has been very performant and has lead to better results. We also note that remeshing the initial configuration, which does not necessitate any transfer of variables (meaning that no loss of information results from this), has also shown to enhance the performance of the updated Lagrangian method.