Transient Finite Element Simulations Research Articles

Topology optimization and experimental validation of mass-reduced aircraft wing designs

Development and evaluation of a novel design of mass reduced aircraft wing ribs through topology optimization is reported herein. For comparison, the same examination is performed on ribs with normal internal geometry. The wing rib design is based on the Gulfstream G650 transonic jet. The rib is divided into three segments for analysis based around the positions of the two spars. Only the center section of the rib is mass optimized, while the leading and trailing edges of the ribs are kept solid. Methodology in this study includes the k-Ω shear stress transport turbulence model computational fluid dynamic simulation as well as static and transient finite element simulations. The optimized wing rib is found to be between 8% and 15% lighter than traditional wing ribs depending on configuration. Simulation of the wing showed a tip deflection of 13.8 cm upward at an angle of 1.1°. An experimental scaled model of the optimized wing subjected to near identical bending loads as identified in the FEA simulation is applied to validate stress concentrations and performance. It is found that in the simulations, average stress never exceeded the factor of safety prescribed by the FAA. While the average factor of safety on the full computational model was 2.649, the average factor of safety on the experimental model was 9.185. Four strain gauges attached to the experimental model are used to compare the strains at similar locations on the computational model. The experimental results validate the CFD simulation results with acceptable tolerances.

Solution of nonlinear Lamb waves in plates with discontinuous thickness.

Nonlinear Lamb waves can propagate over long distances in plate and shell structures and are sensitive to the early fatigue damage of materials. Therefore, they offer unique advantages in the fields of nondestructive testing and material health monitoring. Plate and shell structures with discontinuous thicknesses (e.g., ribs, stiffeners, or joints) will cause nonlinear Lamb wave scattering, and it is necessary to study the scattering processes of nonlinear Lamb waves at discontinuities and how these processes impact the resulting signal characteristics. Thus, nonlinear Lamb waves can be used to identify the structural characteristics and defect characteristics of signals in practical applications. In this paper, the propagating and scattering processes of the second harmonic of a Lamb wave in a discontinuous plate are studied, including the contributions of the evanescent Lamb modes near the discontinuity and the nonlinear boundary effect at the discontinuity. The scattering characteristics of the second harmonics with respect to the frequency and geometry of the plate are analyzed. In addition, the integral formula is adjusted to improve the computational stability under different numbers of Lamb wave modes. Transient finite element simulation is used to validate the proposed method.

Investigating noise radiation pattern of railway bridges for urban rail transit

Noise from elevated railway bridges in urban areas has been causing severe environmental issues. To find the peak frequency of sound energy and thus develop targeted countermeasures for noise mitigation, policymakers need a better understanding of the noise characteristics of urban railway bridges during train passage. This study approaches this issue by combining transient dynamic analyses and acoustic finite element simulation. Our frequency characteristic analysis focused on two primary noise sources: wheel-rail noise and bridge-borne noise. We built a spatial noise model that predicts the radiated noise of urban railway bridges in both the active and planning stages. The results show that the wheel-rail noise peaked at 800 Hz, 1600 Hz, and 3150 Hz, while the bridge-borne noise peaked at 40 Hz, 50 Hz, 80 Hz, and 125 Hz. The validation results demonstrated that the developed noise spatial prediction model extended well to similar urban railway bridges.

Mechanism of slow-wave generation and tuning in a perforation-modulated sonic black hole structure

A sonic black hole (SBH) in a retarding duct can be used to manipulate sound waves and achieve sound absorption. The SBH incorporates two indispensable physical processes: wave speed reduction and energy dissipation. In this study, a perforation-modulated SBH (PMSBH) retarding structure is proposed, in which the two physical phenomena can be balanced to enhance the black hole effects by modulating the perforation parameters. To fully investigate the mechanism of slow-wave generation and the effect of perforation parameters, an analytic model is established based on the Wentzel–Kramers–Brillouin (WKB) solutions to the linear acoustic wave equation. By examining the analytical solutions and comparing them with the numerical results obtained from transient finite element simulations, the effect of several important parameters on reducing the sound speed and enhancing sound absorption performance is revealed, offering a set of criteria and physical insights for modulating the parameters to design an optimal slow-sound absorber. Finally, an experiment is conducted to confirm the theoretical studies and demonstrate the performance of PMSBH. This study brings forward the concept of tunable design to improve the performance of SBH structures, which can benefit the design of sound wave manipulation and noise control devices.

On quantifying uncertainty in lightning strike damage of composite laminates: A hybrid stochastic framework of coupled transient thermal-electrical simulations

Lightning strike damage can severely affect the thermo-mechanical performance of composite laminates. It is essential to quantify the effect of lightning strikes considering the inevitable influence of material and geometric uncertainties for ensuring the operational safety of aircraft. This paper presents an efficient support vector machine (SVM)-based surrogate approach coupled with computationally intensive transient thermal-electrical finite element simulations to quantify the uncertainty in lightning strike damage. The uncertainty in epoxy matrix thermal damage and electrical responses of unprotected carbon/epoxy composite laminates is probabilistically quantified considering the stochasticity in temperature-dependent multi-physical material properties and ply orientations. Further, the SVM models are exploited for variance-based global sensitivity analysis to investigate the input parameters' relative influence on the lightning strike-induced damage behavior. Due to the adoption of a coupled SVM-based simulation approach here, it has become possible to carry out a comprehensive uncertainty quantification leading to complete probabilistic descriptions of the electrical and lightning damage parameters despite the requirement of performing a large number of computationally intensive function evaluations. The results reveal that source-uncertainty of the unprotected laminates significantly influences the epoxy matrix decomposition, electrical current density and electric potential, wherein longitudinal electrical conductivity is most sensitive to stochastic variations followed by other electrical, thermal and geometric parameters.

Heat transfer characterization with alternative heating element layout in electric ‘Injera’ baking technology

The quantitative understanding of the heat transfer mechanism of injera baking technology is critical to evaluate energy consumption, cooking time, and thermal loss of the technology. However, the impact of the heating element layout on the heat transfer process has not been studied. Here, this paper studies four heating element layout arrangements consisting of a fixed power input with a varying power density as a function of layout design to investigate wiring layout impact on product performance. The conduction heat transfer of each heating element layout modelled using transient finite element simulation. Results indicate that higher power density bear a strong, positive correlation with startup time, which showed a 13% better performance when compared with the benchmark. The temperature distribution, however, incurs a 32% higher deviation. Whereas the model with the least favourable startup time shows a threefold higher performance than the benchmark. The results show wiring layout has influence over the key performance parameter of the technology.

Simulation of Wire Arc Additive Manufacturing in the Reinforcement of a Half-Cylinder Shell Geometry.

Wire arc additive manufacturing (WAAM) is an additive manufacturing process based on gas metal arc welding. It allows the fabrication of large-volume metal components by the controlled deposition and stacking of weld beads. Next to the near-net-shape manufacturing of metal components, WAAM is also applied in the local reinforcement of structural parts, such as shell geometries. However, this procedure can lead to undesired thermally induced distortions. In this work, the distortion caused by the WAAM reinforcement of half-cylinder shell geometries was investigated through experiments and transient thermo-mechanical finite element simulations. In the experiments, the weld beads were applied to the specimen, while its thermal history was measured using thermocouples. The developing distortions were registered using displacement transducers. The experimental data were used to calibrate and validate the simulation. Using the validated model, the temperature field and the distortions of the specimens could be predicted. Subsequently, the simulation was used to assess different deposition patterns and shell thicknesses with regard to the resulting part distortions. The investigations revealed a non-linear relation between shell thickness and distortion. Moreover, the orientation and the sequence of the weld beads had a significant impact on the formation of distortion. However, those effects diminished with an increasing shell thickness.

Structure-borne noise of steel and concrete box girders in an urban metro system: A hybrid evaluation and parametric study

Metro systems provide an efficient, convenient, and expeditious way to travel around crowded routes. Because these systems are established in cities, residential buildings close to metro viaducts are significantly affected by structure-borne noise (SBN). Although most previous studies developed SBN prediction with a focus on the accuracy and computational efficiency of a specific bridge type, only limited studies on parameters for the SBN on bridges were carried out. Thus, eliminating SBN is still a challenging task for both the design and operation phases of bridge design. Therefore, this study integrates simplified experiments with numerical analyses to evaluate the influential parameters on the structure-borne noise level (SBNL) for two types of bridge girders, that is, the double-box pre-stressed concrete girder and the double-box steel girder. The present study also proposes an optimization method for reducing the SBNL in the bridge design and operation phases and identifies the sources of SBN for these two types of bridges. In this paper, the solutions to mitigating SBN are first reviewed and briefly introduced. Theories associated with SBN are then derived and experimentally verified using a concrete or steel plate with a unit area. A hybrid evaluation method is developed to integrate transient finite-element simulation with experimental results, and the main sources (e.g., plate thickness, train speed, fastener stiffness, and track irregularity) that induce SBN are examined by this hybrid method. Consequently, the approach to resolving the SBN problem can be optimally determined. As demonstrated in the results from the hybrid evaluation method, the track condition dominates the SBNL for both types of bridges, and the relationship between train speed and plate eigenfrequency should be carefully investigated to avoid the effect of plate resonance. The pre-stressed concrete box girder is the recommended bridge type for use in urban areas from the viewpoint of minimizing the SBNL.

Numerical simulation of the thermal wave induced by a moving interfacial heat source with respect to Christov–Cattaneo's equation

AbstractThe hyperbolic wave equation of heat conduction with respect to Christov's formulation is utilized with the Streamline‐ Upwind‐Petrov‐Galerkin method in space and the Θ, Houbolt, linear acceleration, Wilson‐Θ and Newmark methods in time. The derivation of this equation and its matrix formulation are shown. A 2D transient finite element simulation of a generic asperity with an infinite line heat source in an interface, either as a heat flux density q̇ or temperature distribution T, is performed for Math = [0.5; 1.0]. A sensitivity study is presented for the mentioned numerical schemes. The temperature jump in the solution is interpreted as an indicator for a thermal shock.

Multi-Physical Field Simulation of Cracking during Crystal Growth by Bridgman Method.

Crystal materials are prone to cracking during growth, which is a key problem leading to slow growth and difficulty in forming large-size crystals. In this study, based on the commercial finite element software COMSOL Multiphysics, the transient finite element simulation of the multi-physical field, including fluid heat transfer-phase transition-solid equilibrium-damage coupling behaviors, is performed. The phase-transition material properties and maximum tensile strain damage variables are customized. Using the re-meshing technique, the crystal growth and damage are captured. The results show the following: The convection channel at the bottom of the Bridgman furnace greatly influences the temperature field inside the furnace, and the temperature gradient field significantly influences the solidification and cracking behaviors during crystal growth. The crystal solidifies faster when it enters the higher-temperature gradient region and is prone to cracking. The temperature field inside the furnace needs to be properly adjusted so that the crystal temperature decreases relatively uniformly and slowly during the growth process to avoid crack formation. In addition, the crystal growth orientation also significantly affects the nucleation and growth direction of cracks. Crystals grown along the a-axis tend to form long cracks starting from the bottom and growing vertically, while crystals grown along the c-axis induce the laminar cracks from the bottom in a horizontal direction. The numerical simulation framework of the damage during crystal growth, which can accurately simulate the process of crystal growth and crack evolution and can be used to optimize the temperature field and crystal growth orientation in the Bridgman furnace cavity, is a reliable method to solve the crystal cracking problem.

Development of a Transient Synchronization Analysis Tool for Line-Start PM Motors

With more stringent IEC energy efficiency standards, electrical machine industry increasingly focuses on new motor technologies. Amongst others, the line-start permanent magnet synchronous machine (LSPMSM) is considered as an attractive alternative to induction machine, especially for low power and fixed-speed applications. However, the design of LSPMSMs is rather complex as both steady-state and transient synchronization performances need to be considered. The synchronization capability determination of a LSPMSM design usually relies on time-consuming transient finite-element simulations, which is impractical for use in an iterative design optimization process. This paper compares and evaluates various existing analytical synchronization analysis methods in an attempt to identify most suitable equations and methods for fast synchronization analysis. Using the selected methods, a software tool is developed that can seamlessly work with ANSYS Electronics Desktop to perform rapid transient synchronization analysis. Given its ability to quickly determine the critical inertia factor of a LSPMSM design, the software tool is further adapted for use in a highly iterative, multi-objective design optimization procedure. It shows that the developed software tool can be successfully used in the design of LSPMSMs.

Scattering of the Fundamental Lamb Modes in Bent Metallic Plates

Abstract Guided elastic waves, propagating through curved waveguides, have attracted significant attention in the recent past, both from the perspectives of assessment of structural integrity and generating novel designs of acoustic waveguides. This article presents investigation of the interaction of the fundamental Lamb modes with a cylindrical bend in thin metallic plates. A hybrid numerical method is exposited, which combines the computational efficacy of the semi-analytical finite element method in modeling the long straight portions of the plate and the versatility of the conventional finite element method in modeling the bent portion. The predictive capabilities of the proposed method are validated using transient finite element simulations. Appropriate modifications to the hybrid method, needed for simulating the multimodal incidence resulting from the point-force actuation, are discussed. Using the hybrid method, the scattering and mode-conversion behavior, imparted by the cylindrical bend, is studied when the two fundamental Lamb modes are used as the incident interrogation signals. The extents of equi-modal and cross-modal contributions in both the reflected as well as transmitted waveforms are quantified in terms of the respective modal energy ratios. Explicable contour charts are presented for comprehending the scattering behavior over a wide range of frequencies and bend angles that span from 0 deg to 180 deg. For two representative cases, the modal displacement patterns inside the bend region are presented and discussed. The present investigation can find its potential use in the analysis of geometrically irregular structures leading to the design of novel acoustic waveguides.

Large-Signal Equivalent-Circuit Model of Asymmetric Electrostatic Transducers

This article presents a circuit model that is able to capture the full nonlinear behavior of an asymmetric electrostatic transducer whose dynamics are governed by a single degree of freedom. Effects such as stress-stiffening and pull-in are accounted for. The simulation of a displacement-dependent capacitor and a nonlinear spring is accomplished with arbitrary behavioral sources, which are a standard component of circuit simulators. As an application example, the parameters of the model were fitted to emulate the behavior of an electrostatic MEMS loudspeaker whose finite-element (FEM) simulations and acoustic characterisation where already reported in the literature. The obtained waveforms show good agreement with the amplitude and distortion that was reported both in the transient FEM simulations and in the experimental measurements. This model is also used to predict the performance of this device as a microphone, coupling it to a two-stage charge amplifier. Additional complex behaviors can be introduced to this network model if it is required.

Winding Function Model for Predicting Performance of 2-DOF Wound Rotor Resolver

Two-degree-of-freedom (2-DOF) electrical machines require position sensors for their motion control. In comparison with using two independent sensors, using a 2-DOF sensor enhances the closed-loop control system’s performance. However, due to the 3-D structure of the 2-DOF sensor, its performance evaluation needs 3-D analysis. Also, due to helical motion the accuracy deterioration of the sensor, under mechanical faults needs more attention. Although the finite element method (FEM) is the best way to simulate such sensors, most of the commercial packages for transient finite element simulations are not able to consider two separate motions simultaneously. Furthermore, FEM has a high computational burden that limits its usage in iterative design and optimization process or under mechanical faults. Therefore, developing a fast, and comprehensive analytical model to be used for performance evaluation of helical motion resolvers under mechanical faults is appreciate. Consequently, in this article, an analytical model based on the winding function method (WFM) is developed for a helical motion resolver. The model can predict the performance of the sensor in a healthy condition, as well as that under eccentricity fault. The success of the model is verified using 3-D FEM and the experimental measurements on the prototype sensor.

Thermal characterization of direct wafer bonded Si-on-SiC

Direct bonded Si-on-SiC is an interesting alternative to silicon-on-insulator (SOI) for improved thermal management in power conversion and radio frequency applications in space. We have used transient thermoreflectance and finite element simulations to characterize the thermal properties of direct bonded Si-on-4H–SiC samples, utilizing a hydrophobic and hydrophilic bonding process. In both instances, the interface has good thermal properties resulting in TBReff values of 6 + 4/−2 m2 K GW−1 (hydrophobic) and 9 + 3/−2 m2 K GW−1 (hydrophilic). Two-dimensional finite element simulations for an equivalent MOSFET showed the significant thermal benefit of using Si-on-SiC over SOI. In these simulations, a MOSFET with a 200 nm thick, 42 μm wide Si drift region was recreated on a SOI structure (2 μm buried oxide) and on the Si-on-SiC material characterized here. At 5 W mm−1 power dissipation, the Si-on-SiC was shown to result in a >60% decrease in temperature rise compared to the SOI structure.

Thermomechanical simulations of the transient coupled effect of thermal cycling and oxidation on residual stresses in thermal barrier coatings

Failures in thermal barrier coatings (TBCs) are associated with the build-up of residual stresses that result from thermal cycling, growth strain, and stress relaxation associated with high temperatures. To address these highly coupled processes, three aspects were examined. The first was concerned with the effect of thermal cycling and thermal gradients on the resulting residual stress fields. The second with the dynamic growth of thermally grown oxide (TGO) layer using novel finite volume-finite element algorithms. In the third, we examined the effect of stress relaxation on the (TC/TGO) interface. We modelled these highly coupled processes using transient thermomechanical finite element simulations. The temperature profile and state of oxidation variation with time were imported as a predefined field and solved in ANSYS nonlinear platform. Our results revealed that stress relaxation of the TGO stresses at high temperatures leads to a reduction in the TC/TGO interfacial stresses. They also revealed that the use of the isotropic hardening rule limits the increase in plastic deformation of the bond coat (BC), while the use of kinematic hardening rule leads to ratcheting. Furthermore, we highlighted the importance of considering uneven growth of TGO on the resulting stress field.

Electromagnetic Force and Mechanical Response of Turbo-Generator End Winding under Electromechanical Faults

This paper comparatively studies the electromagnetic force and mechanical response of the end winding before and after 3 kinds of typical electromechanical faults in turbo-generator. The analytical expression of electromagnetic force of end winding is derived under the composite fault of static eccentricity and rotor interturn short circuit. Meanwhile, the three-dimensional transient finite element simulation is carried on, and the frequency composition and amplitude variation characteristics of the radial, axial, and tangential electromagnetic force are analyzed for the end windings under static eccentricity, rotor interturn short circuit, and composite fault. Therefore, it provides a reference for the vibration wear detection and electromagnetic force control of the end winding. Moreover, the maximum stress and deformation of different positions on the end involute are obtained. And the three-directional vibration acceleration characteristics of the end winding are further analyzed. Finally, the distribution law of winding fatigue failure and vibration wear is acquired, which lays a foundation for the reverse suppression of end winding fatigue failure and insulation wear.

Effect of Pole Number on Generator End Winding Electromagnetic Force and Mechanical Response before and after RISC

This paper comparatively studies on the end winding electromagnetic force and mechanical response for generators with different numbers of poles. The analytical expression of the end winding electromagnetic force is derived under the rotor winding interturn short circuit (RISC) considering the pole number. Meanwhile, the three-dimensional transient finite element simulation is carried on two generators with one-pair poles and three-pair poles. Then, the frequency composition and amplitude variation characteristics of the radial, axial, and tangential electromagnetic forces are analyzed. Further, the maximum stress and deformation on the end winding are calculated and the similarity and difference of the coil failure law are obtained for two kinds of generators. It is found that RISC will bring odd harmonics to electromagnetic force for one-pair pole generators but it will bring odd and fraction harmonics for multipair pole generators. Moreover, the max mechanical response under RISC will decrease for one-pair pole generators but it will increase for multipair pole generators.

A metamaterial ultrasound mode convertor for complete transformation of Lamb waves into shear horizontal waves

This article reports a new mechanism involving a non-perforated resonant elastic metamaterial to achieve the complete conversion of Lamb waves (A0 and S0) into the fundamental shear horizontal (SH0) wave. The proposed metamaterial ultrasound mode convertor is studied via the observation of the special resonant shear motion of its unit cells, initiating with a conventional additive stub design. Thereafter, such a stubbed structure is further modified to fully couple the Lamb modes with the shear horizontal stub motion. By investigating the band structure of the metamaterial unit cell through modal analysis and tuning the shear resonant motions, a complete SH0 mode generation band within the simultaneous Lamb modes bandgap can be established in a wide frequency range. Such a special bandgap situation enables the complete mode conversion from Lamb waves into shear horizontal waves. The transformation capability of the proposed ultrasound mode convertor is further substantiated via the harmonic analysis of metamaterial chain model, showcasing the frequency spectrum of the transmitted wave modes. The optimal configuration is determined by conducting a parametric study to identify the most effective mode conversion performance. Finally, a coupled-field transient finite element simulation is carried out to acquire the dynamic response of the structure. The frequency-wavenumber analysis of the transmitted wave field illuminates the successful realization of the mode conversion behavior. Experimental demonstrations are presented to validate the numerical predictions. The proposed complete mode conversion capability may possess great potential for wave control and manipulation.

Leaf Vein-Inspired Bionic Design Method for Heat Exchanger Infilled with Graded Lattice Structure

Due to its excellent performance and high design freedom, the lattice structure has shown excellent capabilities and considerable potential in aerospace and other fields. This paper proposes a method to map the biometric model to the lattice structure. Taking leaf veins as bionic objects, they are used to generate a bionic design with a gradient lattice structure to improve the performance of a heat exchanger. In order to achieve the above goals, this article also proposes a leaf vein model and a mapping method that combine the leaf vein model with the lattice structure. A series of transient thermal finite element simulations was conducted to evaluate and compare the heat dissipation performance of different designs. The analysis results show that the combination of the bionic design and the lattice structure effectively improves the heat dissipation performance of the lattice structure heat exchanger. The results indicate that the application of bionic design in lattice structure design has feasibility and predictable potential.