摘要
在各类薄板弯曲问题,加权残值法和摄动法是经常使用的两种方法。把它们结合起来以求得在全区域一致有效的数值解,可供选择的作法很多,思路不尽相同。为了求解薄板非对称弯曲问题,本文只讨论小参数在微分方程最高阶项上的一类奇异摄动问题;为了充分利用外部解提供的现成结果,考虑用样条函数构造边界层解的方法,简称为样条边界层方法。这种方法使用起来简单,便于上机计算,而且还同时得到外部解的解析表达式,如果需要,不必借助复杂的匹配原则,也能很容易得到边界层解的解析式,因此可以拓广奇异摄动方法在工程计算中的应用。
In this paper, the author presents a mixed method in which the technique of singular perturbation is coupled with the method of weighted residuals to analyse the unsymmetrical bending of thin plates. However, in order to solve the unsymmetrical bending of thin plates and to give a variety, the author only discuss the singular perturbation in which the small parameters in the differential equations of higher derivatives are eonsidered; and in order to ultilize the results offered by the exterior solution, the author suggests the use of the spline function to construct the solution of the boundary layers which may be called the method of boundary layers. This method is simple and convenient for computations on the computer, and the expression of the exterior solution is given simultaneously. If necessary, the expression, of the boundary layer solution may also be obtained without the complicated matching principle. Thus, the technique of singular perturbation in the applieatio, in engineering problems has been extended.
出处
《上海力学》
CSCD
1990年第2期42-50,共9页
Chinese Quarterly Mechanics
