Transient Analysis Of Cracks Using Double-regional Boundary Element Method

The boundary element method has become a powerfull method for mechanical analysis as well as other methods, for instance, the finite element method. It has played more and more importance especially in some speciall problems as infinite district problem and cracking problem. In pratical engineering projects, many structures are working under dynamic loading. This means the significance of dynamic analysis so as to evaluate the stress intensity and predict the structrues' service life. Firstly, in this work, the basic theories of boundary element method for elastostatics was introduced. And the discreting for linear element and relavant formulas were deduced. Herein, these basic theories and formulas in elastostatics were introduced to the boundary element method in elastodynamics. The method of Nardin-Brebbia solving the transient dynamic problems was used in elastodynamics here. This method was generalized to the solution of double-regional problems, which can not be resolved using single-regional boundary element method. Moreover, the appliance of it in solving cracking problems was interpreted. The most importance is that a special element was used at the tip of the crack when solving the transient problems of bodies with cracks, that is double-mapping singular element. After all, the calculating program was compiled based on the above theories. Some examples were analyzed using this program and the ANSYS software package individually and successively. The results obtained were compared to certify the validity of our program. The good compatibilities were observed with them. This implied that the method used in this work can effectively solve the transient problems of bodies with cracks. In this work, the precise solutions can be obtained even less elements were adopted in the local area near the crack. Otherwise, this method used in this work can lower the dimension of the problem, facilitate the preparation of data and solve the stress concentrating problems. However, more elements have to be meshed when using the finite element method.