Hiroyuki Kisu

A new algorithm for bending problems of continuous and inhomogeneous beam by the BEM

Abstract The conventional algorithms of BEM for the bending problems of continuous beam are inefficient and have several points to be improved upon. Although such defects may not become a serious problem as far as they are put to practical use for an individual calculation, once they are applied to a kind of optimal design with a certain optimization algorithm small disadvantages in the conventional algorithm are amplified greatly and the cost of design work becomes very high. It is because a great many repetitive calculations are required in such problems. From this point of view, we intend to develop a new algorithm. Main points of this study are: (1) to improve the composition of the simultaneous equations by introducing a new formulation process; (2) to establish a scheme without any variables at intermediate points; and (3) to establish a generalized solution scheme for an inhomogeneous beam. These new algorithms will greatly reduce the size of a matrix as well as the computing time and, therefore, will bring about high efficiency on the repetitive calculations. As a result, this will give a low cost for optimal design in daily work.

The usefulness and limit of the direct regular method in boundary element elastostatic analysis.

A Boundary Element Method(BEM) has been developed as a new efficient numerical analysis method, and is applied widely to various fields of engineering problems1,2 these days. The mainstream of them is the Direct (Singular) Method, in which a boundary integral equation is discretized directly. Very accurate results have come to be obtained by introducing the sophisticated discretization techniques of FEM3. In the Direct Method, a special care must be taken to carry out the singular integral, since both the load point and the object point of the fundamental solution are located on the boundary. Therefore much computation time is necessary for the numerical integration.

On the Improvement of the Boundary Element Analysis for the Crack Problems

The boundary element method has attracted special interest as a powerful method to analyze the crack problems. However, there still remain some problems to be improved for the accuracy and efficiency. In this study, it is attempted that some simple and accurate methods for determining the stress intensity factors are developed and introduced into the BEM analysis. In the three dimensional BEM analysis, Mindlin’s solution has been used as a fundamental solution for a point load acting within a semi- infinite medium instead of the ordinary Kelvin’s solution. It is expected that the accuracy of solution is improved and that the cost for computation is reduced because there is no necessity for dividing into elements on the surface where boundary conditions are satisfied by the fundamental solution.

Accuracy of triangulation method sensor with optical skid

To measure a profile on a machine accurately, it is necessary to remove influences caused by various disturbances such as vibration. Vibration between a workpiece and a sensor causes measurement error on machine measurements. Therefore, the authors proposed a sensor using triangulation with an optical skid to remove vibration error. It showed effectiveness against vibration. When the skid probe diameter is not much larger than the wavelength of the profile, the amplitude of the measured profile is smaller than the actual amplitude. This report presents reconstruction method for use with the profile surface of a workpiece with the optical skid sensor and describes effects obtained by simulations and experiments using reconstruction method.

Heat Transfer Analysis for FGMs Using SPH-CSPM

The solution of heat transfer problems for functional graded materials (FGMs) by smoothed particle hydrodynamics, in which the thermal conductivity is a function of the spatial coordinates and the temperature, is discussed for both steady and non-steady problems under various boundary conditions. The boundary is treated using the corrective smoothed particle method to heighten the accuracy. Several calculations are performed to test the validity of the formulation. As an example of practical application, the problem of FGM cylindrical plates subjected to thermal shock is calculated, in which the thermal conductivity is temperature dependent and the heat transfer coefficient is varied in radial direction.

Transient Heat Transfer Analysis for Brake Disks Using SPH

Smoothed particle hydrodynamics (SPH) is a mesh-free numerical approximation technique for simulating various physical problems. A calculation system for transient heat transfer problem by SPH has been improved to deal with various boundary conditions and several model calculations are performed to verify it. As a practical application, the transient temperature field of a brake disk under emergency braking is analyzed. Both solid and ventilated disks are modeled with a moving heat source on the sliding surface. The numerical results show that the temperature sharply fluctuates because of the cyclic loading. Improvement of the calculation model is also discussed.

Boundary element formulation using relative quantity for unsteady heat conduction problem

Abstract It has been found that the boundary integral equations for the field functions in the steady problems such as potential and displacement can be regularized by introduction of their relative quantities. This report describes that the same techniques are also applicable to the unsteady problems for regularization of the integral equations. Integral equations with relative quantity for potential are obtained by superposing a particular solution under the condition of time-independent uniform potential upon the usual integral equations. These new equations give accurate numerical results at any points in the whole domain. In addition, since the integral equations for boundary and inside become continuous, the integral equation for boundary temperature gradient, which is absent hitherto in the usual formulations, has been readily obtained. Through two- and three-dimensional examples, the present integral equations are verified to be valid and useful.

Boundary element formulation using relative quantity for viscous flow

Abstract The regularizing using relative quantity is applied to the problems of incompressible viscous flow in two dimensions. The regularized boundary integral equation for flow rate is obtained by superposing a particular solution of uniform flow rate upon the usual equation in the case of both finite and infinite region. The relative quantity is also introduced into the internal integral equations for flow rate and pressure. Since the integral equations for flow rate from inside to boundary become continuous, the integral equation for surface pressure is obtained, which has hitherto been absent in usual formulations. As a result, numerical results both of flow rate and pressure become very accurate all over the domain. Through two-dimensional examples of finite and infinite region, the new equations are verified to be correct.

Formulation of SPH for discretizing the fractional differentiation

This study is a basic research for introducing the SPH as a solution to the fractional differential equation, because the SPH method has the flexibility in the boundary representation. To begin with, the discretized form for the integration is presented in addition to the conventional one for differentiation by SPH, because both the integration and differentiation are needed in the fractional differentiation. Then the formulation for the fractional differentiation by SPH is proposed by combining these two formula. The discretization formulation is applied to several concrete functions and the accuracy of their derivatives and primitive functions is examined numerically. These results are compared with those from FDM and FEM. It is found that the presented formulation has the sufficient accuracy to calculate the fractional differential equation.

Study on Particle Inconsistency Problem in Smoothed Particle Hydrodynamics

In the smoothed particle hydrodynamics (SPH) method, the particle inconsistency problem significantly influences the calculation accuracy. In the present study, we investigate primarily the influence of the particle inconsistency on the first derivative of field functions and discuss the behavior of several methods of addressing this problem. In addition, we propose a new approach by which to compensate for this problem, especially for functions having a non-zero second derivative, that is less computational demanding, as compared to the finite particle method (FPM). A series of numerical studies have been carried out to verify the performance of the new approach.