Three-dimensional (3-D) solids containing corner configurations with straight corner fronts are considered. A super polygonal prismatic element containing a straight corner front is established by using the numerical eigen-solutions of singular stress fields and Hellinger-Reissner variational principle. Singular stresses near corner fronts for far-field boundary conditions can be obtained by incorporating the super singular element with the conventional three-dimensional (3-D) brick elements. The numerical studies are conducted to demonstrate the simplicity of the proposed technique in handling fracture problems of 3-D through-thickness cracks. The usage of the super singular element can avoid mesh refinement near the corner front domain, and the simulation results have high accuracy and fast convergence speed. Compared with the conventional finite element methods and existing analytical methods, the present method is more suitable for dealing with complicated problems of stress singularity in elasticity including multiple defects.

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