采用C1自然单元法研究了不同工况下圆形、菱形、等边多边形薄板的极限承载力。根据薄板极限上限分析的迭代求解格式，构造出了满足平衡方程和边界条件的广义应力场，并由极限下限定理和得到的广义应力场，建立了求解薄板结构极限下限载荷乘子的迭代格式。提出的数值方法克服了极限下限定理中约束条件的强非线性，降低了下限分析的计算规模，具有易于程序实现的优点。该数值方法与极限上限分析方法相结合可以有效估算出薄板结构极限载荷的范围。数值算例表明，提出的求解薄板结构上、下限载荷的方法是有效的，具有较高的计算精度和较快的收敛性。
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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