A scaled boundary shell element formulation using Neumann expansion

被引:0
作者
Jianghuai Li
机构
[1] Ningbo University,School of Civil and Environmental Engineering
来源
Computational Mechanics | 2022年 / 70卷
关键词
Shell element; Scaled boundary finite element method; Neumann expansion; Spectral element; Poisson thickness locking;
D O I
暂无
中图分类号
学科分类号
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 ξ, 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 ξ. After introducing the boundary conditions on the top and bottom surfaces and evaluating the resulting matrix exponential via Padé 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:23
相关论文
共 142 条
[1]  
Ahmad S(1970)Analysis of thick and thin shell structures by curved finite elements Int J Numer Methods Eng 2 419-451
[2]  
Irons BM(1985)Stress projection for membrane and shear locking in shell finite elements Comput Methods Appl Mech Eng 51 221-258
[3]  
Zienkiewicz OC(1986)A formulation of general shell elements—the use of mixed interpolation of tensorial components Int J Numer Methods Eng 22 697-722
[4]  
Belytschko T(1989)Assumed strain stabilization procedure for the 9-node Lagrange shell element Int J Numer Methods Eng 28 385-414
[5]  
Stolarski H(2000)An evaluation of the MITC shell elements Comput Struct 75 1-30
[6]  
Liu WK(2000)A unified approach for shear-locking-free triangular and rectangular shell finite elements Comput Struct 75 321-334
[7]  
Carpenter N(2005)The discrete strain gap method and membrane locking Comput Methods Appl Mech Eng 194 2444-2463
[8]  
Ong JSJ(2017)A new 4-node MITC element for analysis of two-dimensional solids and its formulation in a shell element Comput Struct 192 34-49
[9]  
Bathe KJ(2017)Performance of the MITC3+ and MITC4+ shell elements in widely-used benchmark problems Comput Struct 193 187-206
[10]  
Dvorkin EN(2017)Isogeometric collocation for the Reissner-Mindlin shell problem Comput Methods Appl Mech Eng 325 645-665