Yongtao Yang

Four-Node Quadrilateral Element with Continuous Nodal Stress for Geometrical Nonlinear Analysis

In this paper, the performance of a hybrid ‘FE-Meshfree’ quadrilateral element with continuous nodal stress (Quad4-CNS) is investigated for geometrical nonlinear solid mechanic problems. By combining finite element method (FEM) and meshfree method, this Quad4-CNS synergizes the individual strengths of these two methods, which leads to higher accuracy, better convergence rate, as well as high tolerance to mesh distortion. Therefore, Quad4-CNS is attractive for geometrical nonlinear solid mechanic problems where excessive distorted meshes occur. For geometrical nonlinear analysis, numerical results show that the results of Quad4-CNS element are much better than those of four-node isoparametric quadrilateral element (Quad4), and are comparable to quadratic quadrilateral element (Quad8) and other hybrid ‘FE- Meshfree’ elements.

A Simplified Solution for Calculating the Phreatic Line and Slope Stability during a Sudden Drawdown of the Reservoir Water Level

On the basis of the Boussinesq unsteady seepage differential equation, a new simplified formula for the phreatic line of slopes under the condition of decreasing reservoir water level is derived by means of the Laplacian matrix and its inverse transform. In this context, the expression of normal stress on the slip surface under seepage forces is deduced, and a procedure for obtaining the safety factors under hydrodynamic forces is proposed. A case study of the Three Gorges Reservoir is used to analyze the influences of the water level, decreasing velocity and the permeability coefficient on slope stability.

A Three-Node Triangular Element with Continuous Nodal Stress (Trig3-CNS) for Geometry Nonlinear Solid Mechanics Problems

This paper investigates the performance of the three-node triangular element with continuous nodal stress (Trig3-CNS) for geometry nonlinear solid mechanic problems. This Trig3-CNS element was recently proposed to improve accuracy of the finite element method (FEM). By synergizing the individual strengths of meshfree method and FEM, the Trig3-CNS element achieves higher accuracy and convergence rate. Furthermore, Trig3-CNS presents high tolerance to mesh distortion. Therefore, it is potentially useful for geometry nonlinear solid mechanics problems in which mesh distortion takes place. Compared with the traditional hybrid “FE-Meshfree” elements, Trig3-CNS naturally processes CNS without requiring any extra operation in post-processing. Numerical tests in the present work show that for geometry nonlinear analysis, the results of the Trig3-CNS element are better than the 3-node triangular element (Trig3) and 4-node isoparametric quadrilateral element (Quad4). In addition, the performance of Trig3-CNS is com...