A symplectic expansion for stress/thermal/electric/magnetic intensity factors

Prof. Andrew Leung (City University, Hong Kong)

Thursday 20th October, 2011 14:00-15:00 325


A new analytical method to determine the stress/thermal/electric/magnetic intensity factors is introduced. The singularities near the crack-tip are represented in terms of exponential series that can show the boundary layer effects effectively. The governing PDEs are rewritten in Hamiltonian form. The analytical solutions of the Hamiltonian equations have the symplectic property that ensures convergence and are called the symplectic eigenfunctions. The coefficients of the symplectic series are determined from the lateral boundary conditions along the crack faces and the outer boundary conditions along the exterior geometric domain. The intensity factors are determined by the first two coefficients of the non-zero eigenvalue solutions. Numerical examples for various boundary conditions are given.

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