Abstract: Expressing the total potential energy of the system of a cracked body П by Williams’ infinite series solution of stress and displacement components containing coefficients A_n(n = 1,2,...), we obtain a set of simultaneous linear equations of unknown coefficients A_n by using the principle of minimum potential energy. When the set of equations is solved, the stress intensity factor K₁ can be easily determined. It is equal to √2πaA₁ Take a sample plate as an example. A single-edgc-cracked plate under tension, with the ratio of crack length to the width of the plate being 0.5 and the ratio of half plate height to the width of the plate being 2.0 and 2. 5, has been calculated. Only 20 - 30 coefficients are taken, and the errors in stress intensity factors are within 5%.

Key words: general Brusselator system, Hopf bifurcation, diffusion, stability