中文摘要：

对于含裂纹的板,有时裂纹尺寸与板的宽度相比并不很小,必须按有限宽板来计算。针对含尖角裂纹的有限宽板,建立基于弹性断裂理论的计算模型。通过所求得的复变应力函数,给出裂纹周围应力场的解析计算公式。根据保角变换原理,得到不同裂纹形状所对应的映射函数。对两端受弯矩作用含尖角裂纹的有限宽板,在具有不同的裂纹张开角情况下,对裂纹周围应力分布进行较为详细的仿真分析。另外,对不同的板宽对裂纹周围应力场的影响进行分析,并对不同裂纹张开角的情况进行了计算、比较。

英文摘要：

Sometimes the crack＇s size of a plank is not much smaller than the plank＇s width,thusly a plank with crack must be treated as a finite-width plank.Calculation models are founded by elastic failure theory.According to the complex stress function obtained,the analytic formulae of the stress field around the crack are given.Mapping functions with different crack forms are developed by mapping transformation.Detailed simulation of the stress distribution around the sharp crack of a finite-width plank is made in bending moment.Moreover,the influence of different plank＇s widths and crack opening angles on the stress field around the crack is analyzed.