Tesis doctoral de Yolanda Vidal Segui
This thesis makes two noteworthy contributions in the are of mesh-free methods: a pseudo-divergence-free (pdf) element free galerkin (efg) method which alleviates the volumetric locking and a stabilized updated lagrangian formulation which allows to solve fast-transient dynamic problems involving large distortions. The thesis is organized in the following way. first of all, this thesis dedicates one chapter to the state of the art of mesh-free methods. The main reason is because there are many mesh-free methods that can be found in the literature which can be based on different ideas and with different properties. There is a real need of classifying, ordering and comparing these methods: in fact, the same or almost the same method can be found with different names in the literature. secondly, a novel improved formulation of the (efg) method is proposed in order to alleviate volumetric locking. It is based on a pseudo-divergence-free interpolation. Using the concept of diffuse derivatives an a convergence theorem of these derivatives to the ones of the exact solution, the new approximation proposed is obtained imposing a zero diffuse divergence. in this way is guaranteed that the method verifies asymptotically the incompressibility condition and in addition the imposition can be done a priori. This means that the main difference between standard efg and the improved method is how is chosen the interpolation basis. Modal analysis and numerical results for two classical benchmark tests in solids corroborate that, as expected, diffuse derivatives converge to the derivatives of the exact solution when the discretization is refined (for a fixed dilation parameter) and, of course, that diffuse divergence converges to the exact divergence with the expected theoretical rate. For standard efg the typical convergence rate is degrade as the incompressible limit is approached but with the improved method good results are obtained even for a nearly
Datos académicos de la tesis doctoral «Mesh-free methods for dynamic problems incompressibility and large strains.«
- Título de la tesis: Mesh-free methods for dynamic problems incompressibility and large strains.
- Autor: Yolanda Vidal Segui
- Universidad: Politécnica de catalunya
- Fecha de lectura de la tesis: 17/01/2005
Dirección y tribunal
- Director de la tesis
- Antonio Huerta Cerezuela
- Tribunal
- Presidente del tribunal: javier Bonet
- philippe Boulliard (vocal)
- niikica Petrinic (vocal)
- marino Arroyo balaguer (vocal)