Modified multiplying-factor integration method for solving exponential function dual integrals in crack problems.

Crack problems are often reduced to dual integral equations, which can be solved by expanding the displacement integral equation as a series in the form of Chebyshev-like or Jacobi polynomials. Schmidt's multiplying-factor integration method has been one of the most favorable techniques for determining the expansion coefficients by constructing a well-posed system of linear algebraic equations. However, Schmidt's method is less efficient for numerical computation because the matrix elements of the linear equations are evaluated from dual integrals. In this study, we propose a modified method to construct linear equations to efficiently determine the expansion coefficients. The modified technique is developed upon the application of certain multiplying factors to the traction integral equation and then integrating the resulting equation over "source" regions. Such manipulations simplify the matrix elements as single integrals. By carrying out numerical examples, we demonstrate that the technique is not only accurate but also very efficient. In particular, the method only needs approximately 1/5 of the computation time of Schmidt's method. Therefore, this method can be used to replace Schmidt's method and is expected to be very useful in solving crack problems. [ABSTRACT FROM AUTHOR]