A Domain Decomposition Algorithm With Finite Element-Boundary Element Coupling And Its Application In Metallic Cracked Structure Repairs With Composite Patch

Repairs of cracked components in aerospace structures are becoming more and moreimportant due to the requirement of operation safety. The repair methods based onadhesively bonded composite patches have been demonstrated to be very promising tothese cracked structures. Fatigue crack growth behavior of cracked panels after beingrepaired decides the extension of fatigue life or service life of the repaired structures.Therefore, the evaluation of fatigue crack growth behavior of cracked panels repairedwith a FRP composite patch becomes a focus in this research area.An improved algorithm coupling finite element-boundary element based on aniterative method is presented in this paper. An advantage of the algorithm proposed isthat the positions of the nodes on the interface of the two sub-domains can beinconsistent. It will be more efficient in some situations such as the simulation of crackpropagation. Based on the facts that the boundary element method (BEM) is moreaccurate to determine stress intensity factors and the FEM is more powerful to analyzeFRP composite laminates, this algorithm essentially involves subdivision of theanalyzed domain into sub-regions being independently modeled by the two methods.The original problem is restored with continuity and equilibrium conditions beingsatisfied on the interface of the two sub-regions. It is noted that the governing equationof the FE sub-domain involves nodal displacements and forces, and the primaryunknowns in the BE sub-domain are nodal displacements and tractions. The basic ideahere is to use the virtual work principle to set up this relation between the nodaltractions and nodal forces. To speed up the convergence rate of the iterative algorithm, adynamically changing relaxation parameter during iteration is introduced.This decomposition algorithm with finite element-boundary element (FE-BE)coupling is programmed. The validity of the proposed algorithm is demonstrated by theconsistence of the results of two numerical examples obtained by the proposed methodand those by the FEM, the BEM and another FE-BE coupling method. Finally, acracked aluminum panel repaired with a composite repairing patch is analyzed by theproposed algorithm, and the distribution of stress intensity factor (SIF) along crack frontis obtained. Because the position of the nodes on the interface of the FE and BEsub-domains can be completely independent, there is no need to modify the FE meshand the stiffness matrix of FE sub-domain in each increment step during the simulationof crack propagation of cracked panel.