Papers by Keyword: Bending Problem

Abstract: A differentiation matrix method based on barycentric Lagrange interpolation for numerical analysis of bending problem for elliptical plate is presented. Embedded the elliptical domain into a rectangular, the barycentric Lagrange interpolation in tensor form is used to approximate unknown function. The governing equation of bending plate is discretized by the differentiation matrix derived from barycentric Lagrange interpolation to form a system of algebraic equations. The boundary conditions on curved boundary are directly discretized using barycentric Lagrange interpolation. Combining discrete algebraic equations of governing equation and boundary conditions to form an over-constraints system of equations, the numerical solutions on rectangular can be obtained by solving it. Then, the numerical solutions on elliptical domain are obtained by interpolating the data on rectangular. Numerical results of elliptical plate with uniform load illustrate the effectiveness and accuracy of the proposed method.

Abstract: The shape function of the meshless local radial point interpolation method is constructed by using the radial basis functions and possesses Kronecker delta function properties. Therefore, the essential boundary conditions can be easily imposed. Causation of shear locking occur in plate bending is analyzed. Bending problems for plate with two sides simply supported, the other two sides clamped boundary conditions, are analyzed by the meshless local radial point interpolation method. The shear locking is easier avoided in the meshless method than in the finite element method, and the measure of avoiding the shear locking are presented.

Abstract: The Green quasifunction method(GQM) is employed to solve the bending problem of clamped orthotropic thin plates with trapezoidal boundary shape. Firstly the governing differential equation of the problem is reduced to the boundary value problem of the biharmonic operator, and then it is reduced to the Fredholm integral equation of the second kind by Green’s formula. A Green quasifunction is established by using the fundamental solution and the boundary equation of the problem. This function satisfies the homogeneous boundary condition of the problem. The irregularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. A numerical example demonstrates the feasibility and efficiency of the proposed method, and it is a novel mathematical method.

Abstract: We developed the 3-D local hybrid method to evaluate the 3-D stress field inside the specimen from displacement data on the free surface obtained from the 2-D intelligent hybrid method. When a uniform load was applied to the structure with a surface crack, high accuracy was already acquired in stress analyses. The 3-D local hybrid method was newly applied to structure with a surface crack which is subjected to bending load. It is expected that the accuracy depends on local model size. In this study, the width, the thickness and the height of the local model were changed widely, and analyses were carried out. Then the size of the local model necessary for the analyses was examined. Assessment of analyses was performed by comparing J integral value of a full model and the local model.