含孔边裂纹有限大单块板的解析变分解法.pdfVIP

第l3巷 第1l期 航 空 学 报 Vo1 ．13No．11 ACTA AERONAUTICA ET 1992年 11月 ASTR0NAUTICA SIN [CA 含孔边裂纹有限大单块板的 解析变分解法 V2／j 傅东 山 张 行 (北京航空航天大学，北京，100083) ANALYTICAL—VARIAT10NAL ME|TH0D oF S0LUT10N FOR FINITE M0N0LITHIC PLATE W ITH H0LE—EDGE CRACKS Fu D0ng—sha．n， Zh~．ug X g (．~．ijlngUmgarsify A舯一。％A t{csB Astro4““璐，BB{iig·100083) 摘 要 本文利用复变函数方法导出含孔边双侧直线裂纹有限大板应力与位移的垒场表达 式， 满足所有基本方程式、裂纹表面边界条件与复连通域位移单值条件。应用变分原理满足其 余边 界条件并求解应力强度困子。变分方程中只有线积分。故本方法计算效率较高。 ． 关键词!兰墼 位移递推公式，位移单值条件，变 、： 岐 ，11机。 j A~ baat Total field expressions o1 stress and dlsplacem ent components in a finite monolith／e 。】ate with double linear hole edge crack afe derived by means 0f m ethod offu~ onsofcomplex variables，and aIIofthe basic equations，ba undary coM itions of crack surfaces and single—。valued condition ofdisplac ements about multi—。connected rogion are satisfied exactly．Tho srtessiatensity fav orsare solvedby m ea丑8ofvariationalmethod to s~tlsfy theotherboundary condtiion8．In thevariationalequation~htere are only llne 2 integrals and no area iategrals-The convergency isvery rapid na d the m ethod is tim e— saving．Then，system aticalresults arepreced ed b， ellr~,e$o1nondimenslonM ~tress intensity factor ver辄 5 nondimensional crac k lengths with nondimensional hole radii na d aspect ratios asparam efer~．Finally．the analytical—vra iational method is ~xtended to e ．==a∞ t ， 、 ■● withoutcrac ks．the ocnvergency is nice also and sys~em atieal results are provided by