A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

Finite Element Modelling Approach for Progressive Crushing of Composite Tubular Absorbers in LS-DYNA: Review and Findings

Robust finite element models are utilised for their ability to predict simple to complex mechanical behaviour under certain conditions at a very low cost compared to experimental studies, as this reduces the need for physical prototypes while allowing for the optimisation of components. In this paper, various parameters in finite element techniques were reviewed to simulate the crushing behaviour of glass/epoxy tubes with different material models, mesh sizes, failure trigger mechanisms, element formulation, contact definitions, single and various numbers of shells and delamination modelling. Six different modelling approaches, namely, a single-layer approach and a multi-layer approach, were employed with 2, 3, 4, 6, and 12 shells. In experimental studies, 12 plies were used to fabricate a 3 mm wall thickness GFRP specimen, and the numerical results were compared with experimental data. This was achieved by carefully calibrating the values of certain parameters used in defining the above parameters to predict the behaviour and energy absorption response of the finite element model against initial failure peak load (stiffness) and the mean crushing force. In each case, the results were compared with each other, including experimental and computational costs. The decision was made from an engineering point of view, which means compromising accuracy for computational efficiency. The aim is to develop an FEM that can predict energy absorption capability with a higher level of accuracy, around 5% error, than the experimental studies.

An Alternative Electro-Mechanical Finite Formulation for Functionally Graded Graphene-Reinforced Composite Beams with Macro-Fiber Composite Actuator

With its extraordinary physical properties, graphene is regarded as one of the most attractive reinforcements to enhance the mechanical characteristics of composite materials. However, the existing models in the literature might meet severe challenges in the interlaminar-stress prediction of thick, functionally graded, graphene-reinforced-composite (FG-GRC)-laminated beams that have been integrated with piezoelectric macro-fiber-composite (MFC) actuators under electro-mechanical loadings. If the transverse shear deformations cannot be accurately described, then the mechanical performance of the FG-GRC-laminated beams with MFC actuators will be significantly impacted by the electro-mechanical coupling effect and the sudden change of the material characteristics at the interfaces. Therefore, a new electro-mechanical coupled-beam model with only four independent displacement variables is proposed in this paper. Employing the Hu–Washizu (HW) variational principle, the precision of the transverse shear stresses in regard to the electro-mechanical coupling effect can be improved. Moreover, the second-order derivatives of the in-plane displacement parameters have been removed from the transverse-shear-stress components, which can greatly simplify the finite-element implementation. Thus, based on the proposed electro-mechanical coupled model, a simple C0-type finite-element formulation is developed for the interlaminar shear-stress analysis of thick FG-GRC-laminated beams with MFC actuators. The 3D elasticity solutions and the results obtained from other models are used to assess the performance of the proposed finite-element formulation. Additionally, comprehensive parametric studies are performed on the influences of the graphene volume fraction, distribution pattern, electro-mechanical loading, boundary conditions, lamination scheme and geometrical parameters of the beams on the deformations and stresses of the FG-GRC-laminated beams with MFC actuators.