Thermoelastic and thermomechanical contact analysis using polyhedral smoothed finite elements

Abstract

A node-to-node contact method using the polyhedral smoothed finite elements for thermomechanical analysis is developed. Polyhedral elements are not limited to the number of nodes and faces constituting the element unlike four noded tetrahedral or eight noded hexahedral elements used in conventional FEM. Due to its high geometric adaptability, polyhedral elements are suitable for rendering complex geometry and connecting dissimilar mesh. Since the smoothed finite element method (S-FEM) utilizes the strain smoothing technique and implicit shape function based on the linear point interpolation, it has an advantage that the polyhedral elements can be implemented without further treatments.

First of all, thermoelastic analysis using polyhedral smoothed elements is studied. By introducing the gradient smoothing technique, smoothed finite element formulation of the conduction equation are achieved. The temperature increase of the domain is applied to the equilibrium equation as the thermal strain calculated in the smoothing domain. The S-FEM is categorized into the cell-based S-FEM (CS-FEM), the edge-based S-FEM (ES-FEM) and the node-based S-FEM (NS-FEM) by the way of constructing the smoothing domains, and they have own characteristics of their numerical solution. The smoothing domain is composed of tetrahedral smoothing subdomains. In this study, thermal strain calculation method based on these smoothing subdomains is suggested. The proposed method passes the patch test by reproducing constant temperature gradient field and constant thermal stress field. The CS-FEM and the ES-FEM using polyhedral elements provides better performance than the conventional FEM using four noded tetrahedral elements and even eight noded hexahedral elements. They show good geometric adaptability for the complex geometry in practical application and better convergence than the conventional FEM using tetrahedral elements. The NS-FEM produces zigzag deformed shape and temperature distribution, because it causes the non-zero spurious modes. Thus, the NS-FEM with polyhedral elements is not applicable to the thermoelastic analysis.

Subsequently, a node-to-node contact scheme using the polyhedral smoothed finite element method for the thermomechanical contact analysis is studied. The polyhedral elements with added nodes play an important role in connecting the dissimilar hexahedral interface and implementing the node-to-node contact scheme. The CS-FEM is used to implement the node added polyhedral elements. The proposed method guarantees that the patch test is passed, while the conventional FEM with node-to-surface or surface-to-surface contact scheme do not in a strict sense. Contact pressure dependency of the constitutive law for the heat transfer is well covered in the proposed method, which is verified by comparing with the analytical solution. Numerical solution of the contact pressure obtained from the proposed method is more accurate than conventional FEM with the surface-to-surface scheme, even the mesh density is low. For the high mesh density case, there is no significant difference from the reference solution like the conventional FEM.

Finally, a node-to-node contact method using the polyhedral smoothed finite elements for the thermomechanical contact analysis including relative motion between two bodies in contact is developed. If there is relative motion between two contact bodies, the nonmatching interfaces occur continuously as a body moves. Accordingly, a matching mesh construction method for converting the nonmatching mesh into the matching one is implemented, and a state variable update method for assigning state values that reflect the current deformation field and temperature field to the newly generated nodes on the contact interface is suggested. Furthermore, the node correction method based on the Nagata patch is developed. The node correction method relocates the added node on the contact interface to the surface defined by four vertices of a quadrilateral if the hexahedral element. Introducing this method, unintentional element distortion generated by the matching mesh algorithm is eliminated, and numerical solutions of the contact interface are improved. The proposed method successfully converts the nonmatching mesh that occurs continuously into the matching mesh, and the variables assigned by the variable update method generate small errors. The temperature increment due to friction is demonstrated by the analytic solution and the numerical examples. Numerical solutions obtained by the proposed method show better result in the aspect of the contact pressure and temperature than the conventional FEM with the surface-to-surface scheme.