A New Triangular Thin Shell Element Based on the Absolute Nodal Coordinate Formulation for Complex Surfaces

Abstract This work proposed a new Hermite triangular thin shell element based on the absolute nodal coordinate formulation to model thin shells with complex curved surfaces. Three techniques are adopted to enhance its universality and efficiency. First, local numerical curvilinear coordinates are used on each node for those curved surfaces whose global curvilinear coordinates cannot be obtained analytically, and the Lie group interpolation is used for obtaining the curvilinear coordinates on the non-nodal domain. Second, the slope vector of the element is obtained by cross-producing the two gradient vectors only on each node; but interpolated inside the element to ensure its continuity. Additionally, this processing maintains the linear relationships between the shape functions and nodal coordinates, resulting in constant elastic tensors. Third, the enhanced assumed strains (EAS) and the assumed natural strains (ANS) methods are adopted respectively to accelerate the convergence speed and avoid locking problems of the element. Several numerical examples show that this new element is universal for irregularly curved surfaces without locking problems. In addition, the efficiency is much higher than the traditional triangular shell element.