C1 natural element method for plastic limit analyses of thin plates

ZHOU Shutao; MA Binjie; HOU Chuantao; TONG Jun; JU Yatang; LIU Yinghua

doi:10.16511/j.cnki.qhdxxb.2020.25.041

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Journal of Tsinghua University(Science and Technology) ›› 2021, Vol. 61 ›› Issue (6) : 626-635. DOI: 10.16511/j.cnki.qhdxxb.2020.25.041

ENGINEERING MECHANICS

C¹ natural element method for plastic limit analyses of thin plates

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Abstract

The C¹ natural element method (C¹ NEM) was used to study the limiting loads of circular, rhombic, and equilateral polygon thin plates subjected to various loading conditions. An iterative solution for the upper load limits of the thin plates made the generalized stress fields satisfy the equilibrium equations and the boundary conditions. Iterative solutions were also used to calculate the lower limits of the load multipliers of thin plates using the lower bound theorem to obtain the generalized stress fields. This numerical method overcomes the difficulties introduced by the strong nonlinearity of the constraint condition in the lower bound theorem and reduces the calculations for the lower bound analysis in an easily implemented algorithm. This numerical approach can also be incorporated into upper bound analyses to estimate the limiting loads of thin plates. Numerical examples show that this numerical method can accurately and quickly predict the upper and lower load limits of thin plates.

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limit analysis / upper bound theorem / lower bound theorem / C¹ natural element method (C¹ NEM) / direct iteration algorithm

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ZHOU Shutao, MA Binjie, HOU Chuantao, TONG Jun, JU Yatang, LIU Yinghua. C¹ natural element method for plastic limit analyses of thin plates[J]. Journal of Tsinghua University(Science and Technology). 2021, 61(6): 626-635 https://doi.org/10.16511/j.cnki.qhdxxb.2020.25.041

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