A scaled boundary shell element formulation using Neumann expansion

被引:5
作者
Li, Jianghuai [1 ]
机构
[1] Ningbo Univ, Sch Civil & Environm Engn, Ningbo 315211, Peoples R China
关键词
Shell element; Scaled boundary finite element method; Neumann expansion; Spectral element; Poisson thickness locking; UNBOUNDED-DOMAINS; FINITE-ELEMENTS; SHAPE FUNCTIONS; SHEAR-LOCKING; PROPAGATION; MEMBRANE;
D O I
10.1007/s00466-022-02184-9
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper proposes a new shell element formulation using the scaled boundary finite element (SBFE) method. A shell element is treated as a three-dimensional continuum. Its bottom surface is approximated with a quadrilateral spectral element and the shell geometry is represented through normal scaling of the bottom surface. Neumann expansion is applied to approximate the inversions of the matrix polynomials of the thickness coordinate xi, including the Jacobian matrix and the coefficient of the second-order term in the SBFE equation. This permits the solution along the thickness to be expressed as a matrix exponential function whose exponent is a high-order matrix polynomial of xi. After introducing the boundary conditions on the top and bottom surfaces and evaluating the resulting matrix exponential via Pade expansion, we derive the element stiffness and mass matrices. Poisson thickness locking is avoided fundamentally. Numerical examples demonstrate the applicability and efficiency of the formulation.
引用
收藏
页码:679 / 702
页数:24
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