The recently emerged idea of incorporating higher-order strain or displacement discontinuities into standard finite element interpolations has triggered the development of robust techniques, which allow efficient modeling of large deflections and rotations. A number of studies on efficient elements with embedded high-order discontinuities, including mixed interpolation tensorial components (MITC) and assumed natural strain (ANS) elements, were published during the past decade. It was verified that local enrichments of the displacement and/or strain interpolation can enhance the responses of displacements and stresses by efficient models. The multitude of methods proposed in the literature calls for a comparative study that would present the diverse approaches in a unified framework, point out their common features and differences, and find their limits of applicability. In this regard, by proposing two robust triangular elements based on the higher-order strain field, mixed and strain-based approaches are compared. The strengths and weaknesses of individual formulations are elucidated by analyzing the convergence behavior. After determining the optimal condition, the nonlinear theoretical analysis of functionally graded (FG) shells has been performed by employing the weighted arc-length method. The equilibrium path for load-bearing factor versus post-buckling capacity, the error rate path and the residual force norm are also presented in different material and boundary conditions.

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