Integration of localized surface geometry in fully parameterized ANCF finite elements

Abstract

This paper introduces a new method for the integration of localized surface geometry with fully parameterized absolute nodal coordinate formulation (ANCF) finite elements. In this investigation, ANCF finite elements are used to create the global geometry and perform the finite element (FE)/multibody system (MBS) analysis of deformable bodies. The localized surface geometry details can be described on ANCF element surfaces without the need for mesh refinement. The localized surface is represented using a standard computational geometry method, Non-uniform rational B-spline surface (NURBS), which can describe both conic surface and freeform surface efficiently and accurately. The basic idea of the integration of localized surface geometry with ANCF elements lies in the inclusion of such detail in the element mass matrix and forces. The integration can be implemented by overlapping the localized surface geometry on the original ANCF element or by directly trimming the ANCF element domain to fit the required shape. During the integration process, a mapping between ANCF local coordinates and NURBS localized geometric parameters is used for a consistent implementation of the overlapping and trimming methods. Additionally, two numerical integration methods are compared for the rate of convergence. The results show that the proposed subdomain integration method is better, since it is optimized for dealing with complex geometry. The proposed subdomain method can be used with any fully parameterized ANCF element. In order to analyze the accuracy of the proposed method, a cantilever plate example with localized surface geometry is used, and the simulation results with the proposed method are compared with the simulation results obtained using a commercial FE code. Two other examples that include contact with ground and localized surface geometry are also provided. These examples are a simple plate structure with surface geometry and a tire with tread details. The incompressible hyperelastic Mooney–Rivlin material model is used to describe the material used in the tire tread. It is shown through the tire contact patch that the proposed method can successfully capture the effect of the tread grooves. The rate of convergence and locking of fully parameterized ANCF elements are also discussed in this paper.