多裂纹问题积分方程方法及相关问题

Thecontentofthisreviewconsistsofrecentdevelopmentscoveringanadvancedtreatmentofmultiplecrackproblemsinplaneelasticity.Severalelementarysolutionsarehighlighted,whicharethefundamentalsfortheformulationoftheintegralequations.Theelementarysolutionsincludethoseinitiatedbypointsourcesorbyadistributedtractionalongthecrackface.Twokindsofsingularintegralequations,threekindsofFredholmintegralequations,andonekindofhypersingularintegralequationaresuggestedforthemultiplecrackproblemsinplaneelasticity.Regularizationproceduresarealsoinvestigated.Forthesolutionoftheintegralequations,therelevantquadraturerulesareaddressed.Avarietyofmethodsforsolvingthemultiplecrackproblemsisintroduced.Applicationsforthesolutionofthemultiplecrackproblemsarealsoaddressed.Theconceptofthemodifiedcomplexpotential(MCP)isemphasized,whichwillextendthesolutionrange,forexample,fromthemultiplecrackprobleminaninfiniteplatetothatinacircularplate.Manymultiplecrackproblemsareaddressed.Thoseproblemsinclude(i)multiplesemi-infinitecrackproblem,(ii)multiplecrackproblemwithageneralloading,(iii)multiplecrackproblemforthebondedhalf-planes,(iv)multiplecrackproblemforafiniteregion,(v)multiplecrackproblemforacircularregion,(vi)multiplecrackprobleminantiplaneelasticity,(vii)T-stressinthemultiplecrackproblem,and(viii)periodiccrackproblemandmanyothers.Thisreviewarticlecites187references.