大坝实测性态模糊积分评判模型的研究

在分析了大坝实测性态评价体系的基础上,将模糊积分评判模型引入到大坝实测性态评价中来,为客观定量地研究大坝实测性态评价方法提供了一条新的途径。示例表明,所提出的大坝实测性态模糊积分评判模型是合理、可行的。     

Sommerfeld积分的截断技术

提出了一种截断Ｓｏｍｍｅｒｆｅｌｄ积分的计算技术．利用该技术，将Ｓｏｍｍｅｒｆｅｌｄ积分中的近场信息提取出来并解析求解，从而将无穷积分的问题化成为定积分的数值计算问题．该方法不受物性条件的限制，具有适用范围广、计算速度快、精度高的特点．     

An unconditionally stable time-stepping procedure with algorithmic damping: a weighted integral approach using two general weight functions

An accurate algorithm for the integration of the equations of motion arising in structural dynamics is presented. The algorithm is an unconditionally stable single-step implicit algorithm incorporating algorithmic damping. The displacement for a Single-Degree-of-Freedom system is approximated within a time step by a function which is cubic in time. The four coefficients of the cubic are chosen to satisfy the two initial conditions and two weighted integral equations. By considering general weight functions, eight additional coefficients arise. These coefficients are selected to (i) minimize the difference between exact and approximate solutions for small time steps, (ii) incorporate specified algorithmic damping for large time steps, (iii) ensure unconditional stability and (iv) minimize numerical operations in forming the amplification matrix. The accuracy of the procedure is discussed, and the solution time is compared with a widely used algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical integration during Fourier integral analysis

Numerical integration required during Fourier integral analysis is discussed. For the case of a long and prismatic elastic medium subject to three-dimensional loads applied at the surface (e.g. live load response of buried structures), the complexity of inverse integrals depends on the relative magnitude of the load width and the distance from the load in the longitudinal direction, as well as the longitudinal spacing of the loads. The inverse integrand of the applied surface loading is more difficult to evaluate compared to those for stresses and displacements. Selection of integration schemes based on successful inversion of the applied load provides accurate solutions of stress and displacement throughout the elastic body. The use of superposition when considering complex loading cases is beneficial. Copyright © 1999 John Wiley & Sons, Ltd.     

Local integrals and the plane motion of a point in rotating systems

This paper deals with the plane motion of a star in the gravitational field of a system which is in a steady state and rotates with a constant angular velocity. For these systems a class of potentials permitting a local integral, linear with respect to the velocity components, has been found. The concept of the local integral itself was introduced by one of the authors of the present paper (Antonov, 1981). A detailed model has been constructed. The corresponding domain of the particle motion and the form of the trajectory coils have been determined. The result is compared with the motion in a more realistic potential.     

均匀半空间导体的并矢格林函数解析式

导出了低频时谐电磁场中均匀半空间导体的并矢格林函数解析式,它由初等函数和修正贝塞尔函数的有限形状所表示．该解析式可用Kelvin函数的近似多项式计算,可显著提高并矢格林函数的计算速度．用"电磁分析方法验证模型"的第15号问题作为验证模型,结果表明,计算值和测量值吻合良好．     

On some exceptional cases in the integrability of the three-body problem

We consider the Newtonian planar three-body problem with positive masses m ₁, m ₂, m ₃. We prove that it does not have an additional first integral meromorphic in the complex neighborhood of the parabolic Lagrangian orbit besides three exceptional cases ∑m _i m _j /(∑m _k )² = 1/3, 2³/3³, 2/3² where the linearized equations are shown to be partially integrable. This result completes the non-integrability analysis of the three-body problem started in papers [Tsygvintsev, A.: Journal für die reine und angewandte Mathematik N 537, 127–149 (2001a); Celest. Mech. Dyn. Astron. 86(3), 237–247 (2003)] and based on the Morales–Ramis–Ziglin approach.     

Solution of a Green’s function for a saturated porous medium in a half-space subjected to a torsional force

Based on the solutions of the Green’s function for a saturated porous medium obtained by the authors,and using transformation of axisymmetric coordinates,Sommerfeld integrals and superposition of the influence field on a free surface,the authors have obtained displacement solutions of a saturated porous medium subjected to a torsional force in a half-space.The relationship curves of the displacement solutions and various parameters(permeability,frequency,etc.)under action of a unit of torque are also given in this paper.The results are consistent with previous Reissner’s solutions,where a two-phase medium decays to a single-phase medium.The solution is useful in solving relevant dynamic problems of a twophase saturated medium in engineering.     

Fabric-diagram contour precision and size of counting element related to sample size by approximation theory methods

Density estimation on the unit sphere by kernel methods may be conceived as a process of approximation by singular integrals. This concept aids in the solution of the main problems concerning the contouring of fabric diagrams. The optimal size of the counting element in Schmidt's method with respect to the mean integrated square error (MISE)of the density estimation is given. It proved that the optimal size is not only a function of the sample size but seriously depends on the smoothness of the density of directions on the sphere. In the light of approximation theory the Schmidt method of contouring is qualified as a moving average process; an example of a more refined density estimator is given.