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基于将塑性上限分析等效为弹性迭代计算的总量虚拟加载上限分析理论,在商业化有限元软件ABAQUS中实现了弹性有限元虚拟加载上限方法(弹性有限元T-EMSD)。应用弹性有限元T-EMSD法分析了不排水黏土中的二维水平受荷桩,其获得的荷载-位移曲线与弹塑性有限元分析结果一致,其极限承载力与塑性解相近。在极限位移加载量下弹性有限元T-EMSD法对应的上限机构从弹性始速度场开始随迭代逐渐演化,迭代收敛后的速度场和解析塑性破坏机构相似。与其他基于可变强度概念(MSD)的方法相比,弹性有限元T-EMSD法对水平受荷桩桩身的分析具有更高的精度。弹性有限元T-EMSD法最大的优势在于可在计算中自然地获得塑性机构,因而可被用于研究一些塑性机构难以构造的复杂问题,并对弹塑性数值方法进行验证。
Based on the theory of upper bound of virtual loading estimated by plastic upper bound analysis as elastic iteration, the finite element virtual loading upper bound method (elastic finite element T-EMSD) is implemented in commercial finite element software ABAQUS. The elastic-finite element method T-EMSD was used to analyze the two-dimensional horizontal piles in undrained clay. The obtained load-displacement curve was consistent with the results of elasto-plastic finite element analysis. The ultimate bearing capacity and plastic solution were similar. The upper bound mechanism of elastic finite element T-EMSD method evolves gradually with iteration from the elastic initial velocity field under the limit displacement loading. The velocity field after iterative convergence is similar to the analytic plastic failure mechanism. Compared with other methods based on variable intensity concept (MSD), the elastic finite element T-EMSD method has higher accuracy for the analysis of horizontally loaded pile. The biggest advantage of the elastic finite element T-EMSD method is that the plastic mechanism can be obtained naturally in the calculation. Therefore, it can be used to study the complex problems that some plastic mechanisms are difficult to construct and to verify the elastoplastic numerical method.