岩土工程加固分析的弹塑性力学基础

Elastoplastic basis of geotechnical engineering reinforcement analysis

研究了弹塑性计算中不平衡力的性质,揭示了它和加固力、结构稳定性的密切关系。弹塑性有限元分析迭代过程实质上就是一个逐步消除不平衡力的过程。可以采用弹塑性分析中的不平衡力来指导加固设计:只要施加和不平衡力大小相等、方向相反的加固力,结构就是平衡、稳定的。在所有加固方案里,弹塑性分析确定的加固力是最小的,并归结为应力转移的最小余能原理和加固力上限定理,弹塑性计算确定的加固力和真解相比偏于安全。拱坝计算实例表明,不平衡力分析对分析结构稳定性、指导加固设计是有助益的。

This paper focuses on properties of unbalanced forces in 3D elastoplastic calculation. The relationship among unbalanced forces, reinforced force and structural stability is established. In fact, the iteration procedure of elastoplastic calculation is a procedure of gradually elimination of unbalanced forces. It is revealed that a structure is stable if loading it with a reinforced force which is the same as the unbalanced force but with opposite direction; and therefore unbalanced forces can be used to guide reinforcement analysis. Furthermore, it was shown that the elastoplastic theory always minimizes unbalanced force or reinforced force in the sense of the minimum complementary energy principle of transferred force and superior limit theorem of reinforced force, and such a reinforced force is more safer than the actual one. Case study for an arch dam shows that the distribution of unbalanced force is helpful to evaluate the structural stability and reinforcement.