عنوان مقاله [English]
A novel approach is developed for computing the upper bound limit load of soil mechanic problems in cohesive soils under plane strain condition. In this regard, the cohesive soil is considered as a rigid-plastic material which obeys the Von-Mises failure criterion. By implementation of the associated flow rule and the normality law, the stress at the yield state is related to the plastic strain increment. A mesh-free technique, called the radial point interpolation method, is adopted to express the strain increment field in terms of nodal velocities. Hence, both stress and plastic strain increment can be attributed to the nodal velocities, as well as the rate of internal energy dissipation. The discretized internal energy dissipation power, in conjunction with the incompressibility condition for the Von-Mises yield criterion and the conditions related to external loads, leads to a mathematical optimization problem which should be solved by an iterative technique. The technique consists of the establishment of the Lagrange functional and the formation of a linear system of equations by differentiation, with respect to the unknown nodal velocities and the Lagrange multipliers. By solution of the system of equations, the unknown nodal velocities and the Lagrange ultipliers can be found. The deficiency of the proposed technique is that there is no guarantee regarding the differentiability of the Lagrange functional at all points, due to the rigidity of some regions. Hence, an iterative ethod s sed o ndividuate the plastic and rigid regions in successive steps, thereby, solving the optimization problem. Indeed, the combination of a mesh-free technique with the limit analysis principles leads to a stable upper bound solution for the cohesive soil problem under plane strain condition, in which there is no need for mesh in the traditional sense. Based on the derived formulation, a computer code has been developed, and the accuracy and efficiency of the proposed method is demonstrated by solving some examples at the end of the paper.