C1 natural element method for plastic limit analyses of thin plates
ZHOU Shutao1, MA Binjie1, HOU Chuantao1, TONG Jun1, JU Yatang1, LIU Yinghua2
1. Beijing Institute of Structure & Environment Engineering, Beijing 100076, China; 2. Department of Engineering Mechanics, School of Aerospace, Tsinghua University, Beijing 100084, China
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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2021, Vol. 61 
