滑移线场理论中不同流动法则的极限分析有限元解

广义塑性理论表明,关联流动法则是非关联流动法则中的一种特殊情况.从理论上证明了在非关联流动法则条件下,速度矢量方向与破坏面夹角为φ,而不是目前通常采用的φ/2,澄清了传统滑移线场理论中对于这两种流动法则的模糊认识.通过极限分析有限元法,再次证明了滑移线场理论中用关联流动法则与非关联流动法则可得到相同的应力滑移线、极限荷载及速度滑移线,只是速度矢量方向不同.说明极限分析有限元法不仅可以精确地解决求地基极限荷载问题,而且有助于搞清滑移线场理论中采用非关联与关联流动法则的区别.

FEM Analysis of Associated and Non-associated Flow Rules in Theory of Slip Line Field

As shown in the theory of generalized plastic mechanics, the associated flow rule is just a particular case of non-associated flow rule. It is proved theoretically that in respect of non-associated flow rule the angle included by velocity vector and failure plane is ψ instead of ψ/2 that is usually used now, thus clarifying the misunderstanding on the two different flow rules in the theory of slip line field. Furthermore, the FEM limit analysis also proves that the stress slip line, ultimate load and velocity slip line are all the same if they are obtained by either associated or non-associated flow rule, but only the velocity vector shows difference. The result indicates that FEM limit analysis is available to not only solve accurately the geotechnical problem of ultimate load on foundation but also support the clarification of the difference between associated and non-associated flow rules used in the theory of slip line field.