A new curved gradient deficient shell element of absolute nodal coordinate formulation for modeling thin shell structures

作者：Yan D; Liu C; Tian Q; Zhang K; Liu X N^*; Hu G K

来源：Nonlinear Dynamics, 2013, 74(1-2): 153-164.

DOI：10.1007/s11071-013-0955-z

• Absolute nodal coordinate formulation (ANCF)
• Gradient deficient element
• Shell element
• Slope discontinuity

A curved gradient deficient shell element for the Absolute Nodal Coordinate Formulation (ANCF) is proposed for modeling initially thin curved structures. Unlike the fully parameterized elements of ANCF, a full mapping of the gradient vectors between different configurations is not available for gradient deficient elements, therefore it is cumbersome to work in a rectangular coordinate system for an initially curved element. In this study, a curvilinear coordinate system is adopted as the undeformed Lagrangian coordinates, and the Green-Lagrange strain tensor with respect to the curvilinear frame is utilized to characterize the deformation energy of the shell element. As a result, the strain due to the initially curved element shape is eliminated naturally, and the element formulation is obtained in a concise mathematical form with a clear physical interpretation. For thin structures, the simplified formulations for the evaluation of elastic forces are also given. Moreover, an approach to deal with the on-surface slope discontinuity is also proposed for modeling general curved shell structures. Finally, the developed element of ANCF is validated by several numerical examples.

• 出版日期2013-10
• 单位北京理工大学