Contact problem modelling using the cartesian grid finite element method
- Autores: Jose Manuel Navarro Jimenez
- Directores de la Tesis: Manuel Tur Valiente (dir. tes.), Juan José Ródenas García (dir. tes.)
- Lectura: En la Universitat Politècnica de València ( España ) en 2019
- Idioma: español
- Tribunal Calificador de la Tesis: Ernst Josef Rank (presid.), Francisco David Denia Guzmán (secret.), Riccardo Rossi (voc.)
- Programa de doctorado: Programa de Doctorado en Ingeniería y Producción Industrial por la Universitat Politècnica de València
- Materias:
- Enlaces
- Tesis en acceso abierto en: RiuNet
- Resumen
The contact interaction between elastic solids is one of the most complex phenomena in the computational mechanics research field. The solution of such problem requires robust algorithms to treat the geometrical non-linearities characteristic of the contact constrains. The Finite Element Method (FE) has become one of the most popular options for the mechanical components design, including the solution of contact problems. In this method the computational cost of the generation of the discretization (mesh generation) is directly related to the complexity of the analysis domain, namely its boundary. This complicates the introduction in the numerical simulations of complex surfaces (for example NURBS), which are being increasingly used in the CAD industry.
This thesis is grounded on the Cartesian grid Finite Element Method (cgFEM). In this methodology, which belongs to the family of Immersed Boundary methods, the problem at hand is extended to an approximation domain which completely embeds the analysis domain, and its meshing is straightforward. The decoupling of the boundary definition and the discretization mesh results in a great reduction of the mesh generation's computational cost. Is for this reason that the cgFEM is a suitable tool for the solution of problems that require multiple geometry modifications, such as shape optimization problems or wear simulations.
The cgFEM is also capable of automatically generating FE models from medical images without the intermediate step of generating CAD entities. The introduction of the contact interaction would open the possibility to consider different states of the union between implant and living tissue for the design of optimized implants, even in a patient-specific process.
Hence, in this thesis a formulation for solving 3D contact problems with the cgFEM is presented, considering both frictionless and Coulomb's friction problems. The absence of nodes along the boundary in cgFEM prevents the enforcement of the contact constrains using the standard procedures. Thus, we develop a stabilized formulation that makes use of a recovered stress field, which ensures the stability of the method. The analytical definition of the contact surfaces (by means of NURBS) has been included in the proposed formulation in order to increase the accuracy of the solution.
In addition, the robustness of the cgFEM methodology is increased in this thesis in two different aspects: the control of the numerical problem's ill-conditioning by means of a stabilized method, and the enhancement of the stress recovered field, which is used in the error estimation procedure.
The proposed methodology has been validated through several numerical examples, showing the great potential of the cgFEM in these type of problems.
