Papers by Keyword: Boundary Integral Equation

Abstract: Regarding the displacements and internal forces of Timoshenko beams as dual variables, Timoshenko beam problems were included into dual variables system. Corresponding to state transfer solution of Hamiltonian dual equation, transfer form solution of dual variables for Timoshenko beams was presented. Based on transfer form solution, element stiffness equation and the shape functions of Timoshenko beams were deduced, boundary integral equation and the fundamental solution function of Timoshenko beams were obtained, which reveal the intrinsic relationships among the finite element method, the boundary element method and dual variables system of Timoshenko beams. Based on the transfer form solution of Timoshenko beams, transfer matrix method for chain structure of Timoshenko beams was proposed. For chain beam structure problems, transfer matrix method is simple, intuitive, and has the advantages of good boundary adaptability and less calculation in solving the node variables of chain structures with recursive solution. The numerical results demonstrate the feasibility and accuracy of transfer matrix method in complex beam structure problems.

Abstract: By the potential theory, axisymmetric flow problem is converted into boundary integral equations (BIEs). The mechanical quadrature methods (MQMs) are presented to deal with the singularities in the integral kernels, which are simple without any singularity integral computation. In addition, the convergence rate of the MQMs can be improved by using the extrapolation methods (EMs). The efficiency of the algorithms is illustrated by examples.

Abstract: This paper presents a study for the square crack in a three-dimensional infinite transversely isotropic medium, which can model the fracture damage of rock that displays transversely isotropic behavior. The study is based on a newly derived boundary integral equation. To carry out the numerical simulation, the crack opening displacement is first expressed as the product of the weight functions and the characteristic terms, and the unknown weight is approximated with the moving least-square approximation. A boundary type numerical scheme is established, and the effect of the orientation of the principle axis on the stress intensity factor is studied. The interaction between two coplanar square cracks are also modeled and discussed.

Abstract: With the balance of elastic mechanics differential equation and basic solution(Kelvin solution) As the foundation introduced the boundary element method for calculating the stress and displacement of elastomer. With a numerical example of the algorithm proved. The results show that the method can be more accurate solving 2 D elastic stress and displacement problem.

Abstract: It is studied how to analyze the magnetostatic problems by employing the boundary integral equations. There have been reported a lot of papers about the magnetostatic analysis by these equations. When the permeability is low, most of the magnetostatic problems are solved adequately. However, as the permeability becomes higher, the computed results become poorer especially in the case of the problems without air-gap (multiple-connected problem) or the problem with small air-gap. In order to overcome these difficulties, we derive two new kinds of the boundary integral equations and check their adequacy and effectiveness by solving the multiple-connected problem. Further we investigate their capability to solve the problems concerning the magnetic core with small air-gap.

Abstract: This paper presents a boundary element-free computational method for the fracture analysis of 2-D anisotropic bodies. The study starts from a derived traction boundary integral equation (BIE) in which the boundary conditions of both upper and lower crack surfaces are incorporated into and only the Cauchy singular kernal is involved. The boundary element-free method is achieved by combining this new BIE and the moving least-squares (MLS) approximation. The new BIE introduces two new variables: the displace density and The dislocation density. For each crack, the dislocation density is first expressed as the product of the characteristic term and unknown weight function, and the unknown weight function is approximated with the MLS approximation. The stress intensity factors (SIFs) can be calculated from the the weight function. The examples of the straight and circular-arc cracks are computed, and the convergence and efficiency are discussed.