A hybrid/finite element is proposed to calculate stresses or stress intensity factors at notches, fillets, cutouts, or other geometric discontinuities in plane-loaded anisotropic materials. Stress and displacement fields assumed in the element satisfy all governing elasticity equations. Furthermore, the shape and stress-free conditions of the discontinuity are modeled exactly using conformal mapping and analytic continuation. Continuity of analytic and finite element displacement fields on the remaining element boundary are enforced in an approximate manner with a variational principle. Numerical results are presented for both elliptical void and circular fillet hybrid elements. Comparisons are made to analytic solutions. Results indicate that structural models using a hybrid element with a coarse conventional element mesh yield efficient and accurate calculations of critical stresses.

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