Based on the weight integration to obtain the closed solution of cohesive crack problem, a method is proposed to obtain the stress function of a simply supported beam under uniform distributed forces in this paper. The key technique is to determine the weight of several solutions of elastic mechanics problems to satisfy the given crack traction within the cohesive crack surfaces and the boundary conditions. The error degree of the function to satisfy the boundary conditions mainly depends on the number and the location of the selected points. In the formed fracture process zone, there is both the finite magnitude of stress concentration and the smooth closed- crack opening displacement. The FE numerical simulation is also carried out; its results are in good agreement with the present theoretical calculation results.
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