DYNAMIC ANALYSIS OF VARIABLE MESH ISOGEOMETRIC THIN PLATE BASED ON T-SPLINE

Abstract

The local strain of a thin plate with large displacement and large deformation will change dramatically under contact and collision working conditions. In order to ensure the accuracy and computational efficiency of flexible thin plate system’s dynamic analysis, this investigation integrates computer aided design (CAD) and computer aided engineering (CAE) systems, and proposes an isogeometric analysis (IGA) method for variable mesh flexible multibody system based on T-spline surface elements. Firstly, the kinematic description of a Kirchhoff thin plate based on T-spline surface elements is modeled, and the elastic model of a thin plate discretized by T-spline surface elements is established according to the nonlinear Green−Lagrange strain. Secondly, the goal of updating mesh of T-spline surface locally is achieved by inserting knots into the local region of the corresponding T-mesh. The transformation matrix, which is used to calculate the new generalized coordinates, generalized velocities and generalized accelerations of the refined system, is obtained by using the T-spline blending function refinement algorithm. The calculating solution algorithm for the dynamic equation of the system with variable degrees of freedom is created by combining the generalized α method with geometry update routine, and thus the local mesh refinement algorithm for the surface which is modeled by T-spline is formed. Finally, statics examples and flexible pendulum model verify the correctness for the elastic model of Kirchhoff thin plate based on T-spline surface, as well as computation precision and convergence for the proposed method in the dynamics analysis respectively. The dynamic analysis of the impacted flexible thin plate shows that the T-spline element and local refinement algorithm proposed in this paper can realize local mesh update only in the area where the strain changes violently, such as contact and collision, so as to control the degree of freedom of the system and improve the computational efficiency.