On the Application of the Mixed Finite Element Methods to the Stress Concentration Problems of Cylindrical Shells with a Circular Cutout or a Crack

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The present paper describes an application of Hellinger-Reissner's variational principle to the finite element formulation for general shells. The authors derived three types of stiffness matrices, two of which depend on Novozhilov and Mushtari-Vlasov's strain-displacement relations respectively, and the last one is represented for flat elements. Some simple examples for cylindrical shells show that a flat element gives more exact values than curved ones. As applications of above methods, stress concentration problems of cylindrical shells with a circular cutout or curved plates with a central through-wall crack were solved. Finite element solution for the stress distributions along a circular cutout of the cylindrical shell under internal pressure is found to agree with Durelli's experimental value for a photo-elastic model. Solution for the curved plate with a central through-wall crack was compared with Ishida's theoretical value of a rectangular flat plate with a central crack and the curvature effect was found to be significant.
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