复变函数与数值法相结合计算复合材料层合板的应力场

 在各向异性数学弹性理论的基础上,把复应力函数φ_1(z-1)和φ_2(z_2)分别在z_1和z_2平面的域内展开成复Taylor级数,并用边界配点最小二乘法确定级数系数,从而计算受面内载荷作用单连通复合材料层合板的应力场。文中进行了算例分析,给出了应力随级数项数和边界所配点数的变化曲线。结臬表明,本方法具有形式简单、原始数据准备工作量小、计算精度高、所需计算机容量小和计算时间短等特点。

STRESS CALCULATION IN A COMPOSITE PLATE BY COMPLEX FUNCTION AND NUMERICAL METHOD

On the basis of anisotropic mathematical and elastic theory, the complex stress functions (z1) and 2(z2) are respectively expanded into Taylor series in the regions of z1 and z2 planes. The boundary collocation method is used to determine the coefficients of the series. Then, the stress field of a single-connected composite plate loaded by inplane loads can be calculated. Two examples are given, the effects of the number of stress function terms and the boundary points on calculating results are discussed. It is shown that this method is very convenient and precise to handle single-connected linear-elastic plane problems.