An isogeometric Reissner-Mindlin shell element for dynamic analysis considering geometric and material nonlinearities

10th International Conference and Workshop on Numerical Simulation of 3D Sheet Metal Forming Processes

Sobota, Paul^1 ; Dornisch, Wolfgang^2 ; Klinkel, Sven^1

Lehrstuhl für Baustatik und Baudynamik, RWTH-Aachen University, Mies-van-der-Rohe-Str. 1, Aachen

52074, Germany^1

Lehrstuhl für Technische Mechanik, Technische Universität Kaiserslautern, Gottlieb-Daimler-Str., Kaiserslautern

67663, Germany^2

关键词: Continuous interpolations;    Current configuration;    Discrete interpolation;    Geometric and material nonlinearities;    Implicit time integration;    Interpolation method;    Non-linear material law;    Nonlinear material behavior;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/734/3/032063/pdf
DOI  :  10.1088/1742-6596/734/3/032063

来源: IOP

【 摘 要 】

The present approach deals with the dynamical analysis of thin structures using an isogeometric Reissner-Mindlin shell formulation. Here, a consistent and a lumped mass matrix are employed for the implicit time integration method. The formulation allows for large displacements and finite rotations. The Rodrigues formula, which incorporates the axial vector is used for the rotational description. It necessitates an interpolation of the director vector in the current configuration. Two concept for the interpolation of the director vector are presented. They are denoted as continuous interpolation method and discrete interpolation method. The shell formulation is based on the assumption of zero stress in thickness direction. In the present formulation an interface to 3D nonlinear material laws is used. It leads to an iterative procedure at each integration point. Here, a J2 plasticity material law is implemented. The suitability of the developed shell formulation for natural frequency analysis is demonstrated in numerical examples. Transient problems undergoing large deformations in combination with nonlinear material behavior are analyzed. The effectiveness, robustness and superior accuracy of the two interpolation methods of the shell director vector are investigated and are compared to numerical reference solutions.