Abstract：Three nodal triangular elements，of which velocity variables vary linearly，are often used in limit analysis of finite element upper bound solution. However，this low-order element has deficiency in simulating the shear and plastic zones occurred in failure mechanism of rock and soil masses. Based on predecessors? research，the six nodal triangular elements which have quadric changes of variables were introduced into finite element upper bound solution；and velocity discontinuities were also set between adjacent elements. The formulated model with this quadric element was a linear programming and can be used to analyze stability problems of the soil which obeys Mohr-Coulomb yield criterion. The formula of finite element upper bound theory was deduced and its calculating program was compiled. Using two typical calculating examples，the influences of linearization of yield criterion and velocity discontinuities additional variables on calculation results were investigated. The results obtained by six nodal triangular elements were compared to those of three nodal triangular elements. It was indicated that the calculation precision of results were improved by using six nodal triangular elements with equivalent number of elements. However，for the problems that failure zones were not remarkably constrained and velocity discontinuities line playing an key role，the favorable results can also obtained by using three nodal triangular elements.
杨 峰，阳军生，李昌友，张 箭. 基于六节点三角形单元和线性规划模型的上限有限元研究[J]. 岩石力学与工程学报, 2012, 31(12): 2556-2563.
YANG Feng，YANG Junsheng，LI Changyou，ZHANG Jian. INVESTIGATION OF FINITE ELEMENT UPPER BOUND SOLUTION BASED ON SIX NODAL TRIANGULAR ELEMENTS AND LINEAR PROGRAMMING MODEL. , 2012, 31(12): 2556-2563.
2012, Vol. 31 
