Acta Mechanica Solida Sinica

, Volume 27, Issue 6, pp 612–625 | Cite as

A Rectangular Shell Element Formulation with a New Multi-Resolution Analysis

  • Yiming Xia
  • Yuanxue Liu
  • Shaolin Chen
  • Gan Tang


A multi-resolution rectangular shell element with membrane-bending based on the Kirchhoff-Love theory is proposed. The multi-resolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape functions. The basic node shape functions are constructed from shifting to other three quadrants around a specific node of a basic element in one quadrant and joining the corresponding node shape functions of four elements at the specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. The node shape functions of Kronecker delta property make the treatment of element boundary condition quite convenient and enable the stiffness matrix and the loading column vectors of the proposed element to be automatically acquired through quadraturing around nodes in RL adjusting. As a result, the traditional 4-node rectangular shell element is a mono-resolution one and also a special case of the proposed element. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The simplicity and clarity of node shape function formulation with the Kronecker delta property, and the rational MRA enable the proposed element method to be implemented more rationally, easily and efficiently than the conventional mono-resolution rectangular shell element method or other corresponding MRA methods.

Key Words

rectangular shell element multi-resolution analysis (MRA) resolution level (RL) basic node shape function mutually nesting displacement subspace sequence scaling and shifting 


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  1. 1.
    Zienkiewicz, O.C. and Taylor, R.L., The Finite Element Method (6th Edition). London: Butterworth-Heinemann, 2006.zbMATHGoogle Scholar
  2. 2.
    Artioli, E., Auricchio, F. and Veiga, L.B., Second-order accurate integration algorithms for von-Mises plasticity within nonlinear kinematic hardening mechanism. Computer Methods in Applied Mechanics and Engineering, 2007, 196(9–12): 1827–1846.MathSciNetCrossRefGoogle Scholar
  3. 3.
    Feng, X.T. and Yang, C.X., Genetic evolution of nonlinear material constitutive models. Computer Methods in Applied Mechanics and Engineering, 2001, 190(45): 5957–5973.CrossRefGoogle Scholar
  4. 4.
    Jäger, P., Steinmann, P. and Kuhl, E., Modeling three-dimensional crack propagation—A comparison of crack path tracking strategies. International Journal of Numerical Methods in Engineering, 2006, 66: 911–948.CrossRefGoogle Scholar
  5. 5.
    Fagerström, M. and Larsson, R., Theory and numerics for finite deformation fracture modelling using strong discontinuities. International Journal of Numerical Methods in Engineering, 2006, 76: 1328–1352.MathSciNetzbMATHGoogle Scholar
  6. 6.
    Luccioni, B.M., Ambrosini, R.D. and Danesi, R.F., Analysis of building collapse under blast loads. Engineering Structure, 2004, 26: 63–71.CrossRefGoogle Scholar
  7. 7.
    Wang, Z.Q., Lu, Y. and Hao, H., Numerical investigation of effects of water saturation on blast wave propagation in soil mass. ASCE-Journal of Engineering Mechanics, 2004, 130: 51–561.Google Scholar
  8. 8.
    Xiang, J.W., Chen, X.F., He, Y.M. and He, Z.J., The construction of plane elastomechanics and Mindlin plate elements of B-spline wavelet on the interval. Finite Elements in Analysis and Design, 2006, 42: 1269–1280.CrossRefGoogle Scholar
  9. 9.
    He, Z.J., Chen, X.F. and Li, B., Theory and Engineering Application of Wavelet Finite Element Method. Beijing: Science Press, 2006.Google Scholar
  10. 10.
    Yin, Y., Yao, L.Q. and Cao, Y., A 3-D shell-like approach using element-free Galerkin method for analysis of thin and hick plate structures. Acta Mechanica Sinica, 2013, 29: 85–98.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Liu, H.S. and Fu, M.W., Adaptive reproducing kernel particle method using gradient indicator for elasto-plastic deformation. Engineering Analysis with Boundary elements, 2013, 37: 280–292.MathSciNetCrossRefGoogle Scholar
  12. 12.
    Sukumar, N., Moran, B. and Belytschko, T., The natural elements method in solid mechanics. International Journal of Numerical Methods in Engineering, 1998, 43: 839–887.MathSciNetCrossRefGoogle Scholar
  13. 13.
    Sukumar, N., Moran, B. and Semenov, A.Y., Natural neighbor Galerkin methods. International Journal of Numerical Methods in Engineering, 2001, 50: 1–27.CrossRefGoogle Scholar
  14. 14.
    Cohen, A., Numerical Analysis of Wavelet Method. Amsterdam: Elsevier Press, 2003.zbMATHGoogle Scholar
  15. 15.
    Long, Y.Q., Cen, S. and Long, Z.F., Advanced Finite Element Method in Structural Engineering. Berlin, Heidelberg: Springer-Verlag, Beijing: Tsinghua University Press, 2009.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2014

Authors and Affiliations

  • Yiming Xia
    • 1
    • 2
  • Yuanxue Liu
    • 1
  • Shaolin Chen
    • 2
  • Gan Tang
    • 2
  1. 1.Chongqing Key Laboratory of Geomechanics and Geoenvironmental Protection, Department of Civil EngineeringLogistical Engineering UniversityChongqingChina
  2. 2.Civil Engineering DepartmentNanjing University of Aeronautics and AstronauticsNanjingChina

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