相对于三角形单元的下限分析,基于四边形单元的下限分析具有更高的精度和求解效率。该文利用格林公式把平衡方程的弱形式化为边界积分,从而得到简洁的线性方程,取代了以往的数值积分方案,克服了高斯积分中坐标变换等复杂的求解过程。此外还对应力连续性方程进行了简化。该积分方案不仅大大简化了计算,而且更易于编程实现。算例表明该文方法具有较高的精度。 Compared with the lower bound analysis of triangular elements, lower bound analysis based on quadrilateral elements has higher accuracy and solving efficiency. In this paper, Green’s formula is used to formalize the weakness of the equilibrium equation as the boundary integral, so as to obtain a concise linear equation, which replaces the previous numerical integration scheme and overcomes the complicated solution process such as coordinate transformation in Gaussian integral. In addition, the stress continuity equation is simplified. The integration scheme not only greatly simplifies the calculation, but also easier to program. The example shows that this method has higher accuracy.