Abstract A corotational finite-element formulation is developed for piezoelectric plane frames subject to small strains but large deformations. In the corotating (local) system, the element is linear and superconvergent, with no electrical degrees of freedom. The formulation is derived from a piezoelectric beam theory that incorporates the Timoshenko displacement assumption and assumes a quadratic variation of the electric potential through the thickness of each piezoelectric patch. All linearizations required by the Newton–Raphson solution procedure, including those related to certain induced follower loadings, are explicitly and consistently derived. The proposed formulation (a) avoids membrane, transverse shear, and piezoelectric lockings; (b) yields assembled stiffness matrices that are not affected by the high condition numbers, typically found in piezoelectric finite-element models; (c) requires no special corotational algorithm; and (d) effectively handles large deformations, as demonstrated through numerical examples, including shape control applications.
Pack cementation is an established route for producing protective aluminide layers on nickel-based superalloys, yet the first adsorption and incorporation events are difficult to resolve experimentally. Here, ab initio molecular dynamics (AIMD) and climbing-image nudged elastic band calculations were used to examine Al motion at a simplified Ni(111)/Ti(0001) interface at 593 K. Five independent 0.5 ps AIMD trajectories were considered. Al adatoms relaxed rapidly from atop toward three-fold hollow environments and subsequently sampled lateral hollow-bridge-hollow paths. A short-time two-dimensional mobility estimate obtained from the ensemble meansquare displacement was (1.3 +/- 0.2) & times; 10-4 cm2 s- 1; because the fitting interval was only 0.15 ps, this value is not interpreted as an equilibrium macroscopic diffusivity. In the trajectories, thermally assisted fluctuations enabled occupation of near-surface octahedral environments, whereas no Al atom crossed into the Ti region. The local Al coordination increased from approximately three to six Ni neighbors, producing Al-centered motifs compatible with the nearest-neighbor geometry of L12-Ni3Al. These motifs indicate short-range chemical ordering, not phase nucleation. The results therefore describe ultrafast local relaxation pathways within the limits of a thin-slab, sub-picosecond model and do not represent long-range coating growth.
This work presents an efficient analytical method for spur gear modelling based on the interpolation of precomputed power-law parameters to calculate contact forces. The motivation arises from the fact that, when a nonlinear contact expression is combined with the linear deformations of the tooth body, the resulting force must be obtained through an iterative procedure to ensure deformation compatibility, which increases computational cost. To overcome this, a preprocessing stage is introduced together with the assumption that, for a meshing situation, the force-penetration relation can be represented by a power-law combining the linear stiffnesses of the tooth bodies with the nonlinear contribution of local contact. In this stage, a database is generated by fitting the power-law parameters for all combinations of contacting points between the teeth. Then, during simulation, the position and rotation of the gears directly provide the penetration and active contact points, from which the corresponding parameters are interpolated within the database, and the force is evaluated through the power-law. This strategy eliminates the iterative compatibility procedure required in the traditional approach when nonlinear contacts are included, inherently reducing the computational time while preserving accuracy.
Closed-form analytical solutions for displacement, strain, and stress serve as essential benchmarks for validating numerical methods. This work constructs complete function sets that generate two classes of strong solutions to the governing partial differential equations of two-dimensional beams. The boundary conditions are of Neumann type, prescribing displacement derivatives (strains) or equivalently stresses along all surfaces. The proposed framework is demonstrated on orthotropic and isotropic beams, effectively reproducing continuous and discontinuous surface stresses. The results provide a versatile set of benchmark solutions for assessing beam mechanics models.
This article presents the development and implementation of incremental nonlinear dynamic inversion (INDI), integrated with a proportional-derivative (PD) controller, to enhance stability and reference tracking during the takeoff, hover, and landing phases of an eVTOL (electric vertical takeoff and landing) vehicle. Simulation results indicate that INDI, combined with a PD controller tuned with natural frequencies between 0.1 and 3.0 rad/s and damping ratios near 1.0 , yields an overshoot below 20% . The steady-state time is less than 2 s for the attitude variables and less than 10 s for altitude. The rise time (10–90 ± 10% variations), maintaining bounded tracking errors within the vertical-flight envelope considered. The study further includes hardware-in-the-loop experiments to evaluate the behavior of the control law implemented on an STM32F4 microcontroller. Finally, a simulation-based stability and robustness analysis confirms that the closed-loop system remains stable provided that model uncertainties remain moderate.
