Investigation Of Crack Propagationandfluid-structure Interaction Basedonnumerical Manifoldmethod

Crack propagation problem is one of the hot issues in the mechanics of material,with wide applications in civil engineering,water conservancy and mechanical engineering.In these applications,fluid-structure interaction(FSI)problems are also often encountered.It is desirable to develop versertile numerical method to solve these problems.Using two cover systems,the numerical manifolf method(NMM)can be used to solve both the continuous and discontinuous problems within the idential theoretical framework.It is therefore advantageous to solve fracture propagations problem.There is however no general algorithm for crack propagation under arbitrary finite cover in NMM.In addition although the stochastic finite element method has been developed and the finite element method can be considered as a special case of NMM,the discontinuous deformation analysis of randomly distributed joints has not yet been investigated.There is also a need to consider the random distribution of material properties in NMM.The Smoothed Particle Hydrodynamics(SPH)has many advantages in dealing with the problem of fluid-solid coupling,especially for large deformation of water.Although SPH has been coupled with the finite element method to solve fluid-solid coupling problems,the finite element is not as powerful as NMM in handling large deformation and non-continuous problems.To overcome the above limitations,NMM and SPH are coupled for the first time to simulation the fluid-solid coupling problems for the first time.The solid is simulated using NMM while the fulid is simulated using SPH.The coupling method takes full advantages of the two methods and it provides an effectivenumerical tool for FSI problems.This thesis completed the following tasks:(1)A new algorithm suitable for arbitrary limited coverage system is proposed.Based on the geometrical relative between the crack tip and the NMM nodes,this algorithm determines elements to cut and physical covers to update.This algorithm exhibits good robustness even at the intersection of complex cracks.(2)This thesis proposes a crack propagation criterion combining the Mohr-Coulomb failure criterion and the maximum circumferential tensile stresscriterion.The Mohr-Coulomb criterion is used to calculate the possible fracturepropagation direction and the maximum tensile stress is used to determine the final propagation direction.The improved model is easy and friendly to use.The simulations results for the semi-circular bending and four-point bilateral shear beam tests match well withthe experimental results.It is also used for the gravity dam cracking and slope sliding simulation,achieving results consistent with field observations.(3)By introducing the random number generation algorithm,the NMM is modified to simulate weak discontinuous problems with randomly distributed material properties for the first time.The simulation result of the uniaxial compression test is consistent with the existing experimental ones.This modified NMM with weak discontinuous analysis is also adopted for the slope safety problem,validating its effectivenss.(4)In the NMM preprocessing,a random crack generation algorithm is introduced to generate specific types of distribution,such as Gaussian distribution,Weibull distribution,logarithmic distribution,exponential distribution,Rayleigh distribution and chi-square distribution.The efficiency of the algorithm is qualified through a tensile test.The preprocessing algorithm is combined with the random number generation algorithm to realize the unified simulation of stochastic strong and weak discontinuities,and is proved effective by the analysis of tunnel excavation.(5)The coupling NMM-SPH method is proposed for the first time to simulate FSI problems.In order to take full advangtage of the merits of these two algorithms,the NMM is adopted to simulate the solid material,while SPH is used for the fluid.A contact regulation is developed to realize the coupling.The validity and accuracy of the proposed algorithm is verified by an example of the hydrostatic pressure problem.The proposed method is then adopted to simulate the cracking of gravity damns.The resuls demonstrates the advantages of the coupled NMM-SPH method in problemes featuring dynamic boundary and large deformation.