Analysis of newly-defined stress intensity factors for angular corners using singular integral equations of the body force method

Abstract

In this study, numerical solutions of singular integral equations are discussed in the analysis of angular corners. The problems are formulated as a system of singular integral equations on the basis of the body force method. In the numerical solutions, two types of fundamental density functions are chosen to express the symmetric type stress singularity of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaamOCamaaCaaaleqajqwaacqaaiaaigdacqGHsislcqaH% 7oaBdaWgaaqcKjaGaeaacaaIXaaabeaaaaaaaaaa!3CE1!\[{1 \mathord{\left/ {\vphantom {1 {r^{1 - \lambda _1 } }}} \right. \kern-\nulldelimiterspace} {r^{1 - \lambda _1 } }}\] and the skew-symmetric type stress singularity of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGGipm0dc9vqaqpepu0xbbG8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSGbaeaaca% aIXaaabaGaamOCamaaCaaaleqajqwaacqaaiaaigdacqGHsislcqaH% 7oaBdaWgaaqcKjaGaeaacaaIYaaabeaaaaaaaaaa!3CE2!\[{1 \mathord{\left/ {\vphantom {1 {r^{1 - \lambda _2 } }}} \right. \kern-\nulldelimiterspace} {r^{1 - \lambda _2 } }}\] then the unknown functions are expressed as a linear combination of the fundamental density functions and power series. The calculation shows that the present method gives rapidly converging numerical results for angular corners as well as ordinary cracks in homogeneous materials. The stress intensity factors of angular corners are calculated for various geometrical and loading conditions.