Acta Mechanica Sinica

, Volume 34, Issue 2, pp 371–380 | Cite as

Generalized mixed finite element method for 3D elasticity problems

  • Guanghui Qing
  • Junhui Mao
  • Yanhong Liu
Research Paper


Without applying any stable element techniques in the mixed methods, two simple generalized mixed element (GME) formulations were derived by combining the minimum potential energy principle and Hellinger–Reissner (H–R) variational principle. The main features of the GME formulations are that the common \(C_{0}\)-continuous polynomial shape functions for displacement methods are used to express both displacement and stress variables, and the coefficient matrix of these formulations is not only automatically symmetric but also invertible. Hence, the numerical results of the generalized mixed methods based on the GME formulations are stable. Displacement as well as stress results can be obtained directly from the algebraic system for finite element analysis after introducing stress and displacement boundary conditions simultaneously. Numerical examples show that displacement and stress results retain the same accuracy. The results of the noncompatible generalized mixed method proposed herein are more accurate than those of the standard noncompatible displacement method. The noncompatible generalized mixed element is less sensitive to element geometric distortions.


Minimum potential energy principle Hellinger–Reissner (H–R) variational principle Generalized variational principle Generalized mixed element (GME) Elasticity problem Noncompatible mode 



This work was supported by the National Natural Science Foundation of China (Grant 11502286).


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.College of Aeronautical EngineeringCivil Aviation University of ChinaTianjinChina

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