Guiming Rong

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.

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.