Limit analysis of strip footing using mesh-free equilibrium method

In this paper, a novel numerical approach is proposed for determination of a lower bound solution for the bearing capacity of strip footings. In this method, the geometry of problem is constructed by nodes and, there is no need for mesh in the traditional sense. The gradient of stress is smoothed piecemeal by the aid of the stabilized nodal integration technique and, the equilibrium and boundary conditions are fully satisfied at the entire domain consequently. The stress field is discretized by a mesh-free technique called Shepard's method. Due to the individual properties of Shepard's shape functions, the non-yielding condition is just controlled at the nodes. Putting the objective function and the related constraints together forms a mathematical optimization problem which is solved by a linear programming technique. At the end, the accuracy and efficiency of the proposed method is investigated by solving some examples for the cohesive soils with uniform and depth dependent shear strength, and the cohesive-frictional soil.