Analysis of Uniformly Distributed Limit Load for Circular Plate by TSS Criterion

  • Siwei Gao
  • Shunhu Zhang
  • Guijing Wu
  • Jian Cao
Conference paper


In order to analyze the uniformly distributed limit load for circular plate, a trial function of deflection with cosine form is investigated by the variational method. With the specific plastic work of the Twin Sheer Stress (called TSS for short) criterion, the internal deformation power is deduced. ATn analytical solution of limit load based on the TSS criterion is obtained as a function of circular plate radius a, thickness h and yield stress \( \sigma_{s} \). Compared with the available solutions based on Tresca and Mises criteria, it is shown that the present result is the highest, but the relative error between the present one and the Mises result is only 0.77%. The deflection increases with the decrease of plate thickness or the increase of the ratio of r/a, and the limit load decreases with the increase of plate radius.


Variational method Trial function Twin sheer stress criterion Simply supported circular plate Limit load 


  1. 1.
    ZHOU S, Liu Y, Chen S. Upper bound limit analysis of plates utilizing the C1 natural element method[J]. Computational Mechanics, 50(5) (2012) 543–561.Google Scholar
  2. 2.
    Lu M W, Shou B N, Yang G Y. Plastic analysis methods for design by analysis of pressure vessels[J]. Pressure Vessel Technology, 28(1) (2011) 33–39. (in Chinese).Google Scholar
  3. 3.
    MA G W, HAO H, LWASAKI S. Unified plastic limit analyses of circular plates under arbitrary load[J]. Journal of Applied Mechanics, 66(2) (1999) 568–570.Google Scholar
  4. 4.
    MA G W, LWASAKI S. Plastic analysis of circular plates with respect to unified yield criterion[J]. Int J Mech Sci, 40(10) (1998) 963–976.Google Scholar
  5. 5.
    CHARROPADHYAY J. Limit load analysis and safety assessment of an elbow with circumferential crack under a bending moment [J]. Int. J. Ves. & Piping, 62(2) (1995) 109–116.Google Scholar
  6. 6.
    SAVE M A. Plastic analysis and design of plates, shells and disks[M]. Amsterdam: North-Holland, (1972) 5–94.Google Scholar
  7. 7.
    Yu M. Twin shear stress yield criterion[J]. International Journal of Mechanical Sciences, 25(1) (1983) 71–74.Google Scholar
  8. 8.
    ZHAO D W, LI J, LIU X H, et al. Deduction of plastic work rate per unit volume for unified yield criterion and its application [J]. Trans. Nonferrous Met. Soc. China, 19 (2009) 657–660.Google Scholar
  9. 9.
    XU Bing-ye, LIU Xin-sheng. Plastic limit analysis of structure [M]. BeiJing: China Architecture and Building Press, (1985) 129–173. (in Chinese).Google Scholar
  10. 10.
    LIU Shi-guang, ZHANG Tao. Basic theory of elasticity and plasticity[M]. Wuhan: HuaZhong University of Science and Technology, (2008) 236–237. (in Chinese).Google Scholar
  11. 11.
    WANG Guo-dong, ZHAO De-wen. Modern mechanics of materials forming[M]. Shenyang: Northeastern University Press, (2004) 9–10. (in Chinese).Google Scholar
  12. 12.
    HOPKINS H G, WANG A J. Load carring capacities for circular plates of perfectly-plastic material with arbitrary yield condition[J]. Journal of Mechanics and Physics of Solids. 3 (1954) 117–129.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Shagang School of Iron and SteelSoochow UniversitySuzhouChina

Personalised recommendations