Analysis Of Thermoelastic Crack Problem Based On Symplectic Analytic Singular Element

Stress analysis of thermoelastic cracks remains challenging due to the fact that both of heat flux field and stress field have singularity issue.Thermal conduction analysis should be conducted in prior to stress analysis to provide an accurate thermal state around the crack tip.In this study,the thermoelastic crack problem is led into the Hamiltonion system via the Hellinger-Reissner(H-R)variational principle and the governing symplectic dual equation is obtained.An analytic term is resulted in due to material thermal expansion,and the corresponding analytical form special solution is solved under the Hamilton system for the first time.With the obtained symplectic eigen solution and special solution,a symplectic analytical singular element(SASE)is proposed for thermoelastic crack.Both of thermal conduction and thermal stress analyses can be conducted with the proposed element.The formulations of the proposed element including stiffness matrix and equivalent nodal force vector are derived analytically.All of the fracture parameters,i.e.heat flux intensity factors(HFITs)and the mixed mode thermal stress intensity factor(TSIFs),can be solved accurately without any post-processing.Further,the SASE is combined with the precise time-domain expanding method and the precise integration method separately for the numerical analysis of heat transfer and thermal stress of cracks under thermal shock.Numerical results with high precision can be obtained with different SASE sizes,number of SASE nodes and mesh density.Results also indicate that the proposed method has the advantages of high accuracy and high stability.This work has extended the application of the SASE,and also provides a preliminary work of developing a new “Extended-SASE” to deal with the fatigue propagation of thermoelastic cracks.