Study On The Theory And Application Of Spline Fictitious Boundary Element Method For Fracture Dynamics

Crack defects often occur in engineering structures,and the influence of this kind of defect on the dynamic characteristics and dynamic response of the structure can not be neglected.In addition,dynamic loads are essentially uncertain due to the influence of many complex factors,so it is more reasonable to use random vibration method to analyze the dynamic behavior of cracked structures.In this paper,a spline fictitious boundary element method for linear elastic fracture dynamics is proposed based on Erdogan fundamental solution.Combining with the explicit time-domain method of random vibration,the statistical moment solutions of dynamic stress intensity factor under random vibration and the dynamic reliability of initial crack propagation are realized.The main work of this paper includes:(1)The research significance and the research progress of linear elastic fracture dynamics are introduced.The commonly used numerical methods for linear elastic fracture dynamics analysis are reviewed.The research progress of spline fictitious boundary element method and its application in fracture mechanics are described.(2)The spline fictitious boundary element method for dynamic characteristics analysis of multi-crack problems is studied.A complete set of formulas for free vibration of multi-crack problems is established.The solving process of structural frequency,displacement mode,stress mode and strain mode is given.The numerical stability of the method is studied,and the method is further applied to the damage identification analysis of cracked structures.(3)The spline fictitious boundary element method for dynamic response analysis of multicrack problems is studied.A complete set of formulas for forced vibration of multi-crack problems is established.The formulas for calculating displacement,stress,strain and dynamic stress intensity factor of cracked structure under dynamic loads are derived.The effectiveness of the method is verified by numerical examples,and the influence of moving loads on dynamic stress intensity factors and impact coefficients of cracked structures is further studied.(4)The spline fictitious boundary element method for random vibration analysis of multicrack problems is studied.The explicit expression of dynamic response for multi-crack problem is established by spline fictitious boundary element method.Then the statistical characteristics of dynamic response and dynamic stress intensity factor of cracked structure are obtained by using statistical moment operation rule or random simulation method.The explicit time domain direct method and explicit time domain stochastic simulation method for stochastic vibration analysis of multi-crack problem are proposed.The effectiveness of the method is verified by numerical examples,and the method is further applied to the reliability analysis of crack dynamic initial propagation of 2024-T3 aluminum alloy wing girder components.The results show that the spline fictitious boundary element method for for fracture dynamics presented in this paper can avoid complex crack tip treatment process,and the results of dynamic stress intensity factor can be directly solved,therefore,this method has good calculation accuracy and high calculation efficiency.Combining with the explicit time domain method of random vibration,the problem of random vibration of cracked structures can be solved efficiently and the statistical characteristics of dynamic stress intensity factors can be obtained.The application in the damage identification analysis of cracked structures,dynamic response analysis of cracked structures under moving loads and the dynamic reliability of initial crack propagation of 2024-T3 aluminium alloy wing girder components fully verifies the effectiveness of the proposed method.