Two new triangular thin plate/shell elements based on the absolute nodal coordinate formulation

摘要

In this paper, two three-node triangular thin plate/shell elements are proposed based on the absolute nodal coordinate formulation. As the gradient deficient element, the thin plate/shell element does not possess a full Jacobian matrix for the mapping between different configurations. Thus, the formulation cannot be derived in the conventional method directly based on the continuum mechanics. The independent area coordinate gradients with obvious geometrical interpretation are introduced to simplify the derivation of the shape function. To account for the initially curved reference configuration, the curvilinear coordinate system is used as the global structure coordinate system to calculate the Green-Lagrange strain and formulate the elastic force. The tangent plane is built node-wise to transform the global curvilinear structural gradients to the local area gradients. In this way, the problem of the slope discontinuity associated with the area gradient is circumvented and the continuity of the structural gradient is guaranteed by the standard element assembly procedure. The generalized transformation between the vectors of the Bezier triangle control points and the nodal vectors of the triangular element is presented. Thus, the elements can be used for the integration of computer-aided design and analysis. Finally, the accuracy and convergence property of the new ANCF triangular plate/shell elements are verified by both static and dynamic numerical examples.