Articles written in Sadhana

    • A monolithic finite-element formulation for magnetohydrodynamics


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      This work develops a new monolithic strategy for magnetohydrodynamics based on a continuous velocity–pressure formulation. The magnetic field is interpolated in the same way as the velocity field, and the entire formulation is within a nodal finite-element framework. The velocity and pressure interpolations are chosen so that they satisfy the Babuska–Brezzi (BB) conditions. In most of the existing formulations, a stabilized formulation is used that requires a stabilization term, and some associated mesh-dependent parameters that need to be adjusted. In contrast, no such parameters need to be adjusted in the current formulation, making it more user-friendly and robust. Both transient and steady-state formulations are developed for two- and three dimensional geometries. An exact linearization of the monolithic strategy ensures that rapid (quadratic) convergenceis achieved within each time (or load) step, while the stable nature of the interpolations used ensures that no instabilities arise in the solution. An existing analytical solution is corrected. The coarse mesh accuracy is shown to be better compared with other existing strategies in several benchmark problems, showing that the developed formulation is both robust and efficient.

    • A novel hybrid isogeometric element based on two-field Hellinger– Reissner principle to alleviate different types of locking


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      In the present work, novel hybrid elements are proposed to alleviate the locking anomaly in non-uniform rational B-spline-based isogeometric analysis (IGA) using a two-field Hellinger–Reissner variational principle. The proposed hybrid elements are derived by adopting the independent interpolation schemes for displacement and stress fields. The key highlight of the present study is the choice and evaluation of higher-order terms for the stress interpolation function to provide a locking-free solution. Furthermore, the present study demonstrates the efficacy of the proposed elements with the treatment of several two-dimensional linear-elastic benchmark problems alongside the conventional single-field IGA, Lagrangian-based finite element analysis (FEA), and hybrid FEA formulation. It is shown that the proposed class of hybrid elements performs effectively for analyzing the nearly incompressible problem domains thatare severely affected by volumetric locking along with the thin plate and shell problems where the shear locking is dominant. A better coarse mesh accuracy of the proposed method in comparison with the conventional formulation is demonstrated through various numerical examples. Moreover, the formulation isnot restricted to the locking-dominated problem domains but can also be implemented to solve the problems of general form without any special treatment. Thus, the proposed method is robust, most efficient, and highly effective against both shear and volumetric locking.

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