A two-node spatial beam element with the Euler-Bernoulli assumption is developed for the nonlinear dynamic analysis of slender beams undergoing arbitrary rigid motions and large deformations. During the analysis, the global displacement and rotation vectors with six degrees of freedom are selected as the nodal coordinates. In addition, the “shear locking” problem is avoided successfully since the beam cross-sections are always perpendicular to the current neutral axes by employing a special coupled interpolation of the centroid position and the cross-section orientation. Then a scheme is presented where the original transient strains representing the nodal forces are replaced by proposed average strains over a small time interval. Thus all the high frequencies can be filtered out and a corresponding equivalent internal damping will be produced in this new formulation, which can improve the computation performance of the proposed element for solving the stiff problem and evaluate the governing equations even by using the nonstiff ordinary differential equation solver. Finally, several numerical examples are carried out to verify the validation and efficiency of this proposed formulation by comparison with the analytical solutions and other research works.

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In this paper, a new unified kinematic description, obtained from Bezier geometry using linear mapping and position vector gradients associated with three independent parameters, is used to develop large displacement plate/shell finite elements (FE). Contrary to the conventional FE method, in the approach developed in this paper based on the absolute nodal coordinate formulation (ANCF), no distinction is made between plate and shell structures. The proposed ANCF triangular plate/shell elements have twelve coordinates per node: three position coordinates and nine position gradient coordinates that define vector tangent to coordinate lines at the nodes. The fundamental differences between the conventional FE and the new ANCF parameterizations are highlighted. In this investigation, two different parameterizations, each of which employs independent coordinates, are used. In the first parameterization, called volume parameterization, coordinate lines along the sides of the triangular element in the straight (un-deformed) configuration are used in order to facilitate the development of closed-form cubic shape functions. In the second parameterization, called Cartesian parameterization, coordinate lines along the global axes of the structure (body) coordinate system are used to facilitate the element assembly. The element transformation between the volume and the Cartesian parameterizations is developed and used to define the structure inertia and elastic forces. Three new fully-parameterized ANCF triangular plate/shell elements are developed in this investigation; a four-node mixed-coordinate (FNMC) element and two three-node elements (TN1 and TN2). All the elements developed in this investigation lead to a constant mass matrix and zero Coriolis and centrifugal forces. A non-incremental total-Lagrangian procedure is used for the numerical solution of the nonlinear equations of motion. The performance of the proposed ANCF triangular plate/shell elements is analyzed by comparison with the ANCF rectangular plate element, and conventional three-node linear (TNL) and six-node quadratic (SNQ) triangular plate elements.

There is an intense desire for the substitution of the consumable carbon anode by inert anode (also called non-consumable or oxygen-evolving anode) in the Hall-Héroult process, which would drastically reduce the substantial emission of greenhouse gases such as CO 2 and perfluorocarbons. 1−3 The upgrading of suitable non-carbon anode is highly challenged on account of the numerous restrictive requirements for inert anode materials in the rugged environment of Al electrolytic cell. 2 The basic requirements for an inert anode are as follows: prominent oxidation resistance at high temperature, remarkable corrosion resistance to electrolyte molten salt, high electric conductivity, excellent thermal shock resistance, mechanical robustness, and so on. Up to now, despite major research efforts from Al producers and academic laboratories, no acceptable inert anode material has yet been found for long-term use in industrial Al electrolytic cell.Among the possible inert anode materials (namely, metal, ceramic, and cermet) that have been explored, NiFe 2 O 4based cermet is ranked as the most appropriate candidate, largely owing to the accredited combination of the features of NiFe 2 O 4 ceramics and metals, namely, excellent oxidation resistance at high temperature and high corrosion resistance

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