Received: 27 February 2019 Revised: 19 May 2019 Accepted: 17 June 2019 DOI: 10.1002/nme.6149 RESEARCH ARTICLE An unsymmetric 8-node hexahedral solid-shell element with high distortion tolerance: Geometric nonlinear formulations Zhi Li 1,3 Junbin Huang 1,2 Song Cen 1,4 Chen-Feng Li 3 1 Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing, China 2 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 3 Zienkiewicz Centre for Computational Engineering, College of Engineering, Swansea University, Swansea, UK 4 AML, School of Aerospace Engineering, Tsinghua University, Beijing, China Correspondence Song Cen, Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China; or AML, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China. Email: [email protected] Funding information National Natural Science Foundation of China, Grant/Award Number: 11872229; China Scholarships Council fellowship, Grant/Award Number: 201806210280 Summary A recent distortion-tolerant unsymmetric 8-node hexahedral solid-shell element US-ATFHS8, which takes the analytical solutions of linear elasticity as the trial functions, is successfully extended to geometric nonlinear analysis. This exten- sion is based on the corotational (CR) approach due to its simplicity and high efficiency, especially for geometric nonlinear analysis where the strain is still small. Based on the assumption that the analytical trial functions can prop- erly work in each increment during the nonlinear analysis, the incremental corotational formulations of the nonlinear solid-shell element US-ATFHS8 are derived within the updated Lagrangian (UL) framework, in which an appropri- ate updated strategy for linear analytical trial functions is proposed. Numerical examples show that the present nonlinear element US-ATFHS8 possesses excel- lent performance for various rigorous tests no matter whether regular or dis- torted mesh is used. Especially, it even performs well in some situations that other conventional elements cannot work. KEYWORDS analytical trial function, corotational approach, finite element methods, geometric nonlinear analysis, mesh distortion, unsymmetric solid-shell elements 1 INTRODUCTION To date, the finite element method is still considered as the most efficient tool to simulate the complicated behaviors of shell, one kind of the most important and complex structures in engineering, where the dimension in thickness direction is far smaller than those in the other two orthotropic directions. Generally, shell finite elements can be classified into three categories: the classical shell elements that are based on the conventional theories of shells, 1 the degenerated elements in which the 3D continuum is modified by some assumptions resulting in a midsurface description in analogy to standard shell theory, 2-4 and the solid-shell elements formulated by directly introducing some shell features into 3D solid element formulations. 5,6 Actually, more and more researchers and users prefer to use solid-shell elements in practical simulations because such models have no rotational degrees of freedom (DOFs) and can be easily applied with general 3D constitutive laws, ie, they can seamlessly and easily connect 3D solid elements in the mesh for a complicated structure composed of both 3D solid and shell parts. Int J Numer Methods Eng. 2019;1–27. wileyonlinelibrary.com/journal/nme © 2019 John Wiley & Sons, Ltd. 1
An unsymmetric 8-node hexahedral solid-shell element with high distortion tolerance: Geometric nonlinear formulations
Jun 14, 2023
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