Quadrilateral scaled boundary spectral (QSBS) shell elements are a new class of shell finite elements that require only the shell midsurface to be discretized, contain no rotational degree of freedom and adopt the full three-dimensional constitutive law. In this paper, improved QSBS shell elements are developed. The quadratic Lagrange interpolation with three arbitrarily selected sampling points is adopted to assume the displacement field along the nodal normal and three specific sampling schemes are considered. A scheme of scaling the coefficients of the quadratic Lagrange shape functions is proposed to treat ill-conditioning of the global stiffness matrix. The inverse Jacobian matrix is approximated as a quadratic matrix polynomial of the thickness coordinate to enhance the accuracy of the shell elements in modeling thick curved shells. A modified nodal normal calculation scheme is designed to guarantee the accuracy of the shell elements in simulating folded shells. Numerical examples show that the improved shell elements are applicable to thick to extremely thin general shells. The present work will facilitate the extension and practical application of the QSBS shell elements.

中文翻译：

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改进的四边形缩放边界谱壳单元

四边形尺度边界谱（QSBS）壳单元是一类新型壳有限元，只需将​​壳中面离散化，不包含旋转自由度，采用全三维本构律。本文开发了改进的 QSBS 壳单元。采用任意选择三个采样点的二次拉格朗日插值来假设沿节点法向的位移场，并考虑了三种具体的采样方案。提出了一种缩放二次拉格朗日形函数系数的方案来处理全局刚度矩阵的病态。将逆雅可比矩阵近似为厚度坐标的二次矩阵多项式，以提高厚曲面壳建模中壳单元的精度。为了保证模拟折叠壳时壳单元的精度，设计了改进的节点法线计算方案。数值算例表明，改进的壳单元适用于厚壳到极薄的一般壳。目前的工作将有助于QSBS壳单元的扩展和实际应用。