采用精确化理论求解厚板任意形开孔动应力集中

论文基于复变函数与保角映射法,采用平板弯曲振动精确化方程[1],对含任意形开孔平板中弹性波散射与动应力集中问题进行了研究.利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解.作为算例,计算了自由边界条件下圆孔和椭圆孔的动弯矩集中系数的数值结果,并对板厚与孔径比对动弯矩分布的影响做了分析研究.结果表明:入射波数、平板厚度和椭圆偏心率等参数对动弯矩的分布都有很大的影响.在较低频率和平板较薄的情况下,基于文献[1]的方程与基于Mindlin板的动弯矩结果在数值分布上是基本一致的;在较高频率和平板较厚的情况下,基于文献[1]的方程与基于Mindlin板的动弯矩结果在数值分布计算结果相差较大.由于文献[1]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此本文的分析计算结果更精确一些.

DYNAMIC STRESS CONCENTRATIONS IN THICK PLATES WITH AN ARBITRARY CUTOUT BY USING THE REFINED THEORY

Abstract: In this paper, based on complex variables and conformal mapping methods, using the refined dynamic equation of plates[9], elastic wave scattering and dynamic stress concentrations in plates with an arbitrary cutout were studied. Applying the orthogonal function expansion method, the problem to be solved can be reduced into the solution of a set of infinite algebraic equations. As examples, under free boundary conditions, numerical results of dynamic moment concentration factors in thick plates with a circular, elliptic cutout were computed, and then, the influences of the thickness ratio to the cutout radius on dynamic moment distributions were also analyzed. The results indicate that the parameters such as incident wave number, thickness of plates and elliptic eccentricity ratio have a great effect on dynamic moment distributions. It is shown that at a higher frequency, the numerical results, which are from the Mindlin theory and the refined theory, respectively, are different. The results are more accurate because the refined equation is derivative without using any engineering hypotheses.