平面无限弹性介质中裂纹在同一直线上时复应力函数简单解法.pdf

平面无限弹性介质中裂纹在同一直线 上时复应力函数的简单解法 摘要 复变函数在断裂力学中应用较广，而工程上的金属断裂 弹性断裂 给人 类带来的损失是巨大的，为此研究裂纹上的复应力函数精确解，以讨论裂纹 扩展规律在工程上占有很重要的地位．很多学者致力于这方面研究，做出了很 大贡献，也获得不少成果．目前对复应力函数的求解方法多半用保形映射、 解析开拓或化为积分方程，但这些方法专业性太强且求解过程相当繁琐．随 着计算机飞速发展，现今很时兴复应力函数数值解法，这对于实际工程中的 复杂性贡献也很大，但对于研究解的性质有很大的局限性． 为此，本文在前人工作的基础上利用复解析应力函数在裂纹两侧取不同 值的特点及开平方函数也在裂纹两侧取相反值的特点，给出了平面无限弹性 介质中裂纹在同一直线上时复应力函数的另一简单解法．本文还证明了平面 无限弹性介质中裂纹在同一直线上具有反对称载荷时在裂纹端点处应力具有 对数阶奇异性．文章中求解过程简单易懂，所得结果还是有现实意义的． 关键词：复应力函数裂纹边界值反对称载荷对数奇异性 THE SIMPLESOLUTl0NTOCOMPLEXSTRESSFUNCTIONOFCRACKS THESAMELINEIN INFINITE WHICHAREON PLANE ABSTRACT functionis usedinfracture Complex widely in a losstohuman projectsbringgreat beings．So metal elasticcracks in ofthesolutionof functionon theresearches stress complex cracks，which areinordertodiscusscrack’S an role expandedregularity,playsimportant in ofscholarswho totheseresearcheshavemade projects．Lots devoting contributionsandachieved results．At great major respectable present，the methodsthatareusedtodealwith stressfunctionincludecon- complex formal continuationor aretoo function，which mapping，analytic integral and the of professionalcomplicated．Withrapiddevelopmentcomputer numericalsolutionof stressfunctionisvery technology,the complex pop- ular doesindeedcontributealottothe ofactual nowadays．It complexity whileitslimitationin of ofsolutionis projects researchingproperty huge． will another show understood isinterms So，myPaper solution，which ofboththe stressfunctioncharacterizationthatisdifI．er- complexanalytic entand functioncharacterizationthatis onthetwosides squared contrary of whenthecrackswhichareonthesamelinein infinite fracture，to plane whose stressfunctionbasedon elasticitycomplex previousstudy．Besides， this hasstill thosecrackswith of paper proved propertyanti—symmetric loadtobe ofstressOiltheendofcracks．Not logarithmicsingularity only isthesolution butalsotheresultshaverealistic proceduresimple signifio Ca．nCe． KEY stress WORDS：complexfunction；crack；boundaryvalue； singularity anti-symmetriclo