A wrinkling model for pneumatic membranes and the complementarity computational framework

  • Liang ZhangEmail author
  • Kaijun Dong
  • Mengkai LuEmail author
  • Hongwu Zhang
Original Paper


The paper proposes a complementarity computational framework for the wrinkling analysis of pneumatic membranes under follower loads. Geometric and material nonlinearities are separated by using the co-rotational finite element method. A reasonable wrinkling model is proposed based on the constitutive law of bi-modulus materials in the principal stress space. To improve the convergence, a linear complementarity framework is constructed in the local frame and embedded into the global Newton–Raphson iteration. The proposed method requires no extra solution techniques to ensure convergence, compared with other solution strategies, such as a pseudo-dynamic method and a penalty stabilization method. Three benchmark tests are employed to verify the proposed model and method. The numerical results have a good agreement with the existing numerical and experimental data. Importantly, the proposed computational method can even make a more accurate prediction on the displacement response and wrinkling regions than the post-buckling analysis of thin shells in some situation.


Pneumatic membranes Wrinkling model The co-rotational FEM Complementarity 



Supports from National Natural Science Foundation of China (No. 11872133), SAST Funding (No. SAST2017-022), Chongqing Research Program of Basic Research and Frontier Technology (No. cstc2016jcyjA0058), Fundamental Research Funds for the Central Universities (No. 2019CDQYHK039) at Chongqing University and Research Foundation (No. GZ18110) of State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology are gratefully acknowledged.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Aerospace EngineeringChongqing UniversityChongqingPeople’s Republic of China
  2. 2.State Key Laboratory for Strength and Vibration of Mechanical StructuresXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  3. 3.State Key Laboratory of Structural Analysis for Industrial EquipmentDalian University of TechnologyDalianPeople’s Republic of China
  4. 4.Department of Mechanical Engineering and MechanicsNingbo UniversityNingboPeople’s Republic of China

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