Finite Element Technique Research Articles

Heat Enhancement of Ethylene Glycol/Water Mixture in the Presence of Gyroid TPMS Structure: Experimental and Numerical Comparison

Cooling small components is becoming an attractive topic for researchers. In this paper, an attempt is made to use an ethylene glycol/water mixture as a cooling liquid. This liquid is a helpful application for when the fluid is in a harsh environment and should not freeze. The experiment uses an ethylene glycol/water mixture circulating through a triply periodic minimal surface structure (TPMS) made of aluminum and silver. A constant heat flux equal to 38,000 W/m2 is applied, and three different flow rates, 11.8 cm3/s, 15.5 cm3/s, and 19.6 cm3/s, are studied. The experimental setup is complemented with numerical modelling by solving the Navier–Stokes equation and the energy equation using the finite element technique. The flow is Newtonian, and a laminar regime is implemented. Results reveal that the performance of the ethylene glycol/water mixture did not enhance heat removal when compared to water. The average Nusselt number is similar regardless of the concentration of ethylene glycol in the mixture. This average Nusselt number, Nuaverage, in the presence of aluminum TPMS ranges between 60 and 80 (60 < Nuaverage < 80) and between 65 and 85 (65 < Nuaverage < 85) using silver TPMS. The increase in the mixture’s viscosity due to ethylene glycol increased the pressure drop. The performance evaluation criteria reach the maximum value of 90 when the mixture is composed of 5%vol ethylene glycol in water with aluminum TPMS. In the presence of silver TPMS, the maximum performance evaluation criterion is around 95 with a 5% ethylene glycol/water mixture. Finally, it is proven experimentally and confirmed numerically that the TPMS structure secures uniform heat extraction from the hot surface.

Deflection responses of damaged hybrid (carbon nanotubes – luffa) composite structure: An experimental verification

AbstractThe deflection responses of intact and damaged hybrid curved shell structures are investigated numerically and experimentally under mechanical loading conditions. The damaged hybrid composite is numerically modelled in MATLAB using higher‐order mid‐plane polynomials and finite element technique. The consistent characteristics and model accuracy have been established by comparing the consequences to those accessible in the existing article. Additionally, the study examined experimentally and computationally obtained elastic properties from the DIGIMAT tool, substantially boosting the extent and reliability of the analysis. Finally, numerous examples are provided to illustrate the impact of damage, considering various parametric input constraints, on the deflection characteristics of the hybrid composite.

Finite Element Modeling of RC Beams Produced with Low-Strength Concrete and Strengthened for Bending and Shear with CFRP and GFRP

In this study, the analysis of reinforced concrete (RC) beams strengthened with Fiber Reinforced Polymer (FRP) composites against bending and shear loads was carried out with the finite element technique, using ABAQUS software, which is widely used in simulating experimental circumstances in numerical studies. It has been reported that buildings in areas damaged by earthquakes are generally constructed using low-strength concrete and inadequate reinforcement. Additionally, construction errors also contribute to reducing the load-bearing capacity of structural elements. For this purpose, nine rectangular cross-section RC beams were experimentally constructed using low-strength concrete and inadequate bending and shear reinforcement. These beams were strengthened by wrapping them in different configurations with Carbon and Glass FRP (CFRP and GFRP) composites to resist shear and bending forces in both transverse and longitudinal directions, and their load-displacement curves were obtained. Subsequently, a three-dimensional Finite Element Model (FEM) was created to validate the experimental results. The FEM validation demonstrated high accuracy in replicating experimental outcomes, emphasizing the influence of mesh size, dilation angle, and concrete constitutive models on simulation fidelity. Parametric studies revealed that increasing longitudinal reinforcement diameters had minimal effect on load capacity but highlighted the critical role of transverse reinforcement, as reducing stirrup spacing significantly improved load-bearing capacity. GFRP-reinforced beams exhibited superior ductility and a 15% higher strength compared to CFRP, suggesting their suitability for applications demanding enhanced displacement capacity. Furthermore, the findings underline the need for refined FEM models to better capture inclined fiber orientations and optimize structural reinforcement strategies.

Subsidence and Effective Stresses Distribution Using Finite Element Techniques for an Iraqi Oilfield

Geomechanical problems are the most important problems that happen in the Zubair oil field; treating these problems requires a lot of time (Non-Productive Time) and thus increases the cost of drilling the well. Wellbore instability, subsidence, reservoir compaction, casing smash, pipe damage, and well kick is the main geomechanical problems facing the drilling process in the Mishrif formation, Zubair oilfield. The main goals of this study are to estimate the changes in stresses and subsequent subsidence values for this field during the production and injection periods. These estimation values, many problems can be avoided, thus increasing the drilling efficiency. This study is to introduce the one way coupling between the reservoir model and geomechanical model using the finite element method. The finite element technique in CMG 2018 program was used to estimate the stress states during the production or injection operations in this field of interest. The results of the 3D finite element model showed that the effective vertical stress rises by 32 psi during production while the effective horizontal stress increases by 16 psi. This may be explained by the fact that variations in pore pressure have little or no impact on the total vertical stress generated by weight. The results of this study demonstrated that the finite element method is a conservative method for coupling reservoir geomechanics and fluid flow. Subsidence values were 6.096 mm in the north part of the Al-Hammar dome, while at the center the subsidence was -5.1816 mm. Shuaiba dome has negative subsidence which is about -9.75 mm. It is important to note that the positive results subsidence signify the pore volume compacting, which may have an impact on the permeability and porosity of the reservoir petrophysics. As a result of a negative subsidence deformation, different failures including well casing damage, wellbore failure, and pipe smashing, are expected. Based on these results, production can cause an increase in the differential stress, which leads to rock shear failure and in injection cases, increasing pore pressure can cause a tensile rock failure.

Unsteady MHD Casson fluid flow past a vertical plate in the presence of viscid dissipation and Dufour effects

PurposeThis research investigates the impact of Dufour effects and viscous dissipation on unsteady magnetohydrodynamic (MHD) natural convection in an incompressible, viscous, and electrically conductive fluid over a vertically oscillating flat plate. The study highlights the significance of magnetic fields in influencing thermal and mass transfer, particularly in the context of thermal radiation. Computational fluid dynamics method including finite difference or finite element techniques can be used to crack the governing equations of the fluid flow. In this work, we used the finite element method (FEM) numerical technique to analyze the numerical behavior of unsteady boundary layer flow of Casson fluid with natural convection past an oscillating vertical plate. Key parameters such as skin friction, temperature, concentration, velocity and Sherwood numbers are derived and analyzed. The results demonstrate that viscous dissipation significantly elevates the fluid temperature, while an increase in the radiation parameter is associated with a decrease in internal friction at the plate. These findings provide critical insights into the interplay between thermal radiation and magnetic fields in MHD flows, with potential applications in engineering systems involving heat and mass transfer, such as cooling systems and material processing. This study underscores the importance of understanding these dynamics for optimizing the performance of MHD applications in various industrial settings.Design/methodology/approachThe mainly authorized and energetic FEM to explain the non-linear, dimensionless partial differential equations (11–13) via equation with boundary conditions (14) makes use of Bathe (36), Reddy (37), Connor (38) and Chung (39). Following are the key steps that make up the method: discretize the domain, derivation of element equation, assembly of element equation, imposition of boundary condition and solution of assembly equation.FindingsThis study examined the impact of viscid dissipative radiation and the Dufour effect on unsteady one-dimensional MHD natural convective flow of a viscous, incompressible, electrically conducting fluid past an infinite moving vertical flat plate with a chemical reaction. Numerically solving the governing equations using the FEM approach is efficient and precise, aiming to be applied to fluid mechanics and related problems. Along with their effects on temperature, concentration and velocity, the following parameters are included: the mass Grashof number, the Soret number, the Grashof number, the Prandtl number, chemical reaction, the Schmidt number, radiation and the Casson parameter. Both the Grashof numbers of thermal and mass rates (Gr, Gm) make an increment in the velocity region. The velocity decreases with an increase in the magnetic parameter. The velocity increases with an increase in the permeability of the porous medium parameter. The temperature flow rate is higher for both Dufour and Viscid dissipation, while a decrement is noted of both Prandtl number and radiation effects. The decrementing behavior of the concentration region is observed at supreme inputs of chemical reaction coefficient and Schmidt number.Originality/valueThis is an original paper and not submitted anywhere.

A low-cost space-time finite element for free-surface flows under total Lagrangian description

In this work, we propose a position-based space-time finite element formulation for incompressible Newtonian flows under a total Lagrangian description. This formulation is suggested within the context of finite strain free-surface flows and differs from the traditional finite element approach for fluid dynamics by utilizing current nodal positions as the main variables instead of nodal velocities. In contrast to time-marching methods, space-time formulations involve applying the finite element technique not only to the spatial domain but also to the temporal domain. The proposed approach employs a finite element discretization that can be unstructured or structured in space, but is always structured in time. Thus, the space-time shape functions are expressed as a tensor product of linear shape functions in the spatial direction and specially designed quadratic shape functions in the temporal direction. Consequently, the space-time domain is divided into time slabs that are solved progressively, with the final velocities and positions from the previous time slab serving as initial conditions for the current one, thereby reducing the dimension of the discrete system of equations. The proposed shape functions in the temporal direction yield a system of equations of the same size as standard time-marching methods, but with advantages stemming from the space-time discretization: different stability and high-frequency dissipation can be achieved based on the selection of the time test functions. To solve the incompressible problem stably, we employ mixed equal-order position-pressure finite elements with Petrov-Galerkin/pressure stabilization (PSPG). This formulation possesses several significant features that justify its development: 1) the space-time formulation facilitates dynamic re-meshing by permitting the spatial discretization at the end of one time slab to differ entirely from the spatial discretization at its beginning, thus extending its applicability to flows with undefined distortion and topological changes; 2) by considering positions as variational parameters, it becomes straightforward to couple with Lagrangian hyper-elastic solid solvers, which may also be formulated in terms of positions or displacements in a monolithic way. Numerical examples conducted to validate the formulation demonstrate its robustness and efficiency for finite strain free surface flows, including phenomena such as dam breaks with smooth surfaces and sloshing.

Application of Q4 Strain Gradient Notation Finite Element Method (SGN-FEM) in Level Set Optimization Using Radial Basis Functions

The Strain Gradient Notation Finite Element Method (SGN-FEM) employs physically interpretable polynomials in the development of finite elements, allowing for the precise identification and subsequent elimination of parasitic shear sources, which cause shear locking. The element is corrected a priori, during development, by simply removing the spurious terms from the shear strain polynomials.The Level Set Method (LVM) is an optimization technique widely employed in topology optimization to minimize the compliance of structures. This method consistently provides clear boundary and geometry information during the optimization process, giving it inherent advantages in solving boundary and geometry-related problems.While numerous studies investigate different approaches to calculate level set optimization, there are fewer studies evaluating how the finite element technique contributes to the analysis. Considering this, this paper presents the application of Q4 SGN-FEM in optimization studies using LVM to minimize the compliance of a two-dimensional linear elastic structure. The differences obtained when using the SGN-FEM model are investigated. The parametrized level set method, as defined in Wei et al. (2018), is utilized alongside SGN-FEM to conduct the study. The model is validated through comparison with other studies, demonstrating that SGN-FEM proves to be a viable alternative for conducting optimization studies using the level set method.

Compressive and Bending Properties of 3D-Printed Wood/PLA Composites with Re-Entrant Honeycomb Core

This study investigates the mechanical behavior of sandwich structures comprising a re-entrant honeycomb core structure created using wood/polylactic acid (PLA) filaments via fused deposition modeling (FDM) technology. The sandwich structures were manufactured with different face layer thicknesses (0 mm, 0.8 mm, and 1.6 mm) and various core topologies. Material characterizations included bending tests, compressive tests, and finite element analysis (FEA) to identify stress concentration areas. In-plane and out-of-plane re-entrant honeycomb core structure specimens were tested to examine the bending properties. In addition, flatwise and edgewise compressive tests were performed to investigate the structures' compressive properties. Furthermore, the modulus of elasticity for each specimen was determined using the finite element technique (FEM). The results reveal that increasing the thickness of the face layer significantly enhances the structure's resistance to bending forces. Furthermore, specimens with an in-plane orientation demonstrated better bending strength compared to those with an out-of-plane orientation due to increased material underloading. In flatwise compressive tests, specimens without a face layer exhibited the highest strength, attributed to their greater displacement. In contrast, edgewise compressive tests showed significant buckling behavior of the face sheet, the maximum stress increased proportionally with the thickness of the face layer, reaching its peak at a skin thickness of 1.6 mm. The findings are validated by ANSYS analysis, which closely mirrors the experimental results, providing insight into flexural modulus, modulus of elasticity, and stress concentration. These findings indicate that architected core structures could be efficiently utilized to improve bending/compressive characteristics and failure mechanisms, providing valuable insights into the mechanical response of sandwich structures for different industrial applications.

Analytical method for random seismic response of structures with tuned parallel inerter mass system and optimal parameters based on reliability

Tuned parallel inerter mass system (TPIMS) composed of tuned mass damper (TMD) and series parallel inerter-Ⅱ system has excellent damping performance. Earthquake action on structures has typical randomness, however the existing methods for outputs of structures with TPIMS only are numerical. In the work, an analytical method for calculating outputs and a globe method for optimizing TPIMS’s parameters was presented. Firstly, using dynamic finite element technique, the general dynamic equation of high-rise structures with TPIMS was established. Secondly, using quadratic decomposition method, the concise unified analytical solutions of zero-, first- and second-order spectral moments (ZFS-OSMs) of structural absolute and interlayer displacement, the inerter’s force and TMD’s displacement were deduced. Finally, three examples were carried out to verify the proposed method, to study influence of number of real vibration modes and to demonstrate the method for optimizing TPIMS’s parameters, respectively. The results show that the quantity of real vibration modes of uncontrolled structures with a participation weight of 100 % has the characteristics of both accuracy and efficiency in output analysis and the proposed optimal method is global.

The Role of Heater Size and Location in Modulating Natural Convection Behavior in Cu-Water Nanofluid-Loaded Square Enclosures

Enhancing the energy efficiency of thermal systems reduces their consumption, lowers costs, and reduces undesired environmental impact, thus making these systems more sustainable. The current work introduces a passive method for heat transfer enhancement that is carried out using natural convection by nanofluid. This work introduces a computational study of the process of natural convection within a square cavity containing Cu/H2O nanofluid. The cavity wall on the left side undergoes partial isothermal heating, while the opposing side is fully cooled isothermally, with all other boundaries maintained adiabatic. A mathematical model formulated based on a 2-D model was used to provide the solution for the system of governing equations of mass, momentum, and energy conservation, employing the finite element technique. A commercial CFD package is utilized to perform the computational simulation. The present investigation delves into the impact of the Rayleigh number, nanoparticle concentration, heater length, and heater location on the flow field and heat transfer characteristics. The model outcomes were displayed for a wide range of the pertinent parameters as 103 ≤ Ra ≤ 106, 0.25 ≤ lh ≤ 1.0, 0.125 ≤ hc ≤ 0.875, and 0.02 ≤ ϕ ≤ 0.10. Also, correlation equations relating the average Nusselt number to these crucial parameters are derived. These equations are simple and can be applied in practice easily in many fields, such as electric and electronic equipment cooling and thermal management of heat sources. Also, these equations gather all the parameters that affect the heat transfer process. They are shedding light on the intricate interplay between these parameters in the natural convection heat transfer process.

Numerical computations of MHD mixed convection flow of Bingham fluid in a porous square chamber with a wavy cylinder

This work examines the behavior of Bingham fluids in porous media under magnetohydrodynamic (MHD) conditions, addressing a significant issue in fluid dynamics and heat transport. The authors study mixed convection in a porous square chamber with twisted cylinders using COMSOL Multiphysics and finite element techniques. Compared to other research, this one offers a more complicated and realistic model since it integrates Bingham fluid flow and MHD effects in a porous chamber with wavy cylinders. Plotting of streamlines, isotherms, and Nusselt numbers is done for several parameters: Numbers Reynolds (1, 5, 10, 50), Hartmann (0, 25, 50, 100), Bingham (0, 1, 5, 10), Darcy (10−4, 10−3, 10−2, 10−1), and Grashof (102,103,104,105) are among those assigned numbers. According to findings, larger Bn values promote thermal stratification and decrease flow mobility, which results in dominating conductive heat transmission. The nusselt number falls with Ha and Bn but rises with Re, Da, and Gr. The study aims to provide useful insights into several industrial disciplines, such as nuclear power plant architecture and petroleum engineering, by enhancing heat transfer in non-Newtonian fluids under magnetic fields. It also boosts the efficiency of chemical reactors and filters. Based on our findings, for lower Re = 1, the lowest value of Numean is 2.602, while at Re = 50, its values rise to 6.425.

Determination and Application of Stress States Based on Finite Element Techniques: A Case Study of the Longmaxi Formation in the Luzhou Block, Sichuan Basin.

Knowledge of the present-day in situ stress field (PIS) has important theoretical and practical significance for shale gas exploration and development. The Wufeng-Longmaxi Formation in the Luzhou Block serves as the main reservoir of marine shale production in southern China. However, there is no clear understanding of PIS in the Luzhou area, which leads to a series of production problems. To investigate the PIS of deep shale reservoirs in Luzhou, experimental and finite element methods (FEMs) were used. Data obtained from imaging logging data, well deviation data, multipole array acoustic logging (XMAC), and world stress map were used to determine the orientation of the horizontal maximum principal stress (S Hmax). Additionally, acoustic emission experiments were employed to determine the magnitude of three principal stresses. Based on FEM, with the stress of a single well as a constraint, a three-dimensional (3D) stress field model was developed. The results show that the orientation of S Hmax varies from 90 to 120 °E. Further, there are significant differences in stress regimes across the region, with strike-slip/reverse faulting stress regime (S Hmax > S v ≈ S hmin) in the northern region and strike-slip stress regime in the southern region (S Hmax > S v > S hmin). In addition, geomechanical evaluations of wellbore stability and natural activation of fractures were performed. The Luzhou Block mainly develops two groups of natural fractures (NE-SW trending and NW-SE trending), with NW-SE trending being the dominant fracture development orientation. During the fracturing operation, a pore pressure increment larger than 50 MPa is conducive to maintaining a high opening ratio of the reservoir and improving the gas production efficiency. Horizontal wells drilled in the direction of maximum horizontal principal stress in the Wufeng-Longmaxi Formation reduce the probability of wellbore instability. The research results provide a reference for the effective development of deep shale gas reservoirs in southern Sichuan.

A Galerkin finite element technique with Iweobodo-Mamadu-Njoseh wavelet (IMNW) basis function for the solution of time-fractional advection–diffusion problems

In this paper, the authors used wavelet-based Galerkin finite element technique constructed with Iweobodo-Mamadu-Njoseh wavelet as the basis function, for the numerical solution of time-fractional advection–diffusion equations. To achieve this, the authors used the Iweobodo-Mamadu-Njoseh wavelet as well as fractional calculus, wavelet and wavelet transform, and the Galerkin finite element technique. Also, time and space discretization in relation to the finite element technique were considered, followed by the steps in implementing numerical solutions to TFADE with the new technique. The new technique was considered in seeking numerical solutions of some Caputo type TFADE test problems, and the resulting numerical evidence displayed the effectiveness and accuracy of the method as the results obtained with the new method converged at a good pace to the exact solutions. The results obtained at different fractional order were also compared and the resulting evidence showed that at certain fractional value the convergence behavior displayed slight differences. Every numerical computation was done with the use of MAPLE 18 software.

Heat transfer in a non-uniformly heated enclosure filled by NEPCM water nanofluid

PurposeThis paper aims to focuses on by investigate the heat transmission and free convective flow of a suspension of nano encapsulated phase change materials (NEPCMs) within an enclosure. Particles of NEPCM have a core-shell structure, with phase change material (PCM) serving as the core.Design/methodology/approachThe enclosure consists of a square chamber with an insulated wall on top and bottom and vertical walls that are differently heated. The governing equations are investigated using the finite element technique. A grid inspection and validation test are done to confirm the precision of the results.FindingsThe effects of fusion temperature (varying from 0.1 to 0.9), Stefan number (changing from 0.2 to 0.7), Rayleigh number (varying from 103 to 106) and volume fraction of NEPCM nanoparticles (changing from 0 to 0.05) on the streamlines, isotherms, heat capacity ratio and average Nusselt number are investigated using graphs and tables. From this investigation, it is found that using a NEPCM nano suspension results in a significant enhancement in heat transfer compared to pure fluid. This augmentation becomes more important for the low Stefan number, which is around 16.57% approximately at 0.2. Secondary recirculation is formed near the upper left corner as a result of non-uniform heating of the left vertical border. This eddy expands notably as the Rayleigh number rises. The study findings indicate that the NEPCM nanosuspension has the potential to act as a smart working fluid, significantly enhancing average Nusselt numbers in enclosed chambers.Research limitations/implicationsThe NEPCM particle consists of a core (n-octadecane, a phase-change material) and a shell (PMMA, an encapsulation material). The host fluid water and the NEPCM particles are considered to form a dilute suspension.Practical implicationsUsing NEPCMs in energy storage thermal systems show potential for improving heat transfer efficiency in several engineering applications. NEPCMs merge the beneficial characteristics of PCMs with the enhanced thermal conductivity of nanoparticles, providing a flexible alternative for effective thermal energy storage and control.Originality/valueThis paper aims to explore the free convective flow and heat transmission of NEPCM water-type nanofluid in a square chamber with an insulated top boundary, a uniformly heated bottom boundary, a cooled right boundary and a non-uniformly heated left boundary.

Robust and accurate numerical framework for multi-dimensional fractional-order telegraph equations using Jacobi/Jacobi-Romanovski spectral technique

This paper presents a novel spectral algorithm for the numerical solution of multi-dimensional fractional-order telegraph equations, a critical model used to capture the combined effects of diffusion and wave propagation. The core innovation of this work is the application of Jacobi-Romanovski polynomials as the basis functions for spectral discretization. These polynomials offer unique advantages, including the ability to handle nonstandard domains and boundary conditions, making them particularly suitable for partial differential equation (PDE) applications. A comprehensive error analysis is conducted, providing deep insights into the convergence rates and factors affecting the accuracy of the numerical solutions. Extensive numerical experiments further demonstrate the superior performance of the proposed spectral algorithm in solving a wide range of multi-dimensional fractional-order telegraph equation models. The results show a significant improvement in accuracy and computational efficiency compared to traditional numerical methods, such as finite difference or finite element techniques. This research advances the field of computational science by offering a robust, efficient, and versatile numerical framework for the precise solution of complex multi-dimensional PDEs.

Heat transfer characteristics of mixed convection inside a differentially heated square cavity containing an oscillating porous cylinder

The current study presents mixed convective flow inside a square chamber holding a centrally placed and thermally conductive oscillating porous circular cylinder. The left boundary's temperature is kept larger than that of the right edge, and the horizontal edges are preserved at adiabatic settings. The circumferential speed of the cylinder is sinusoidal and oscillating in nature. The fluid region within the chamber is modeled employing 2D Navier-Stokes and heat energy equations. Furthermore, the fluid circulation and heat transmission within the porous cylinder are modeled using the Darcy-Brinkman-Forchheimer formulation. The leading equations are discretized utilizing the Galerkin finite element technique. The parametric study is undertaken considering three distinct diameters of the porous cylinder and three distinct oscillation frequencies. The instant Nusselt number is evaluated along the heated wall, which varies in an oscillatory pattern owing to the repeated contraction and enlargement of the thermal boundary layer. The Nusselt number is averaged over time once the value becomes statistically stationary. The study is conducted within a mixed convection region with Reynolds (Re = 100), Richardson (0.1 ≤ Ri ≤ 10), and Grashof (103 ≤ Gr ≤ 105) numbers. Upon thorough examination, it becomes clear that the system's thermal performance shows promising improvement with the largest cylinder diameter and the lowest oscillation frequency. Specifically, the average Nusselt number shows a maximum improvement of 21.50 % at the largest cylinder diameter.

Concepts for Frequency Sweeps and Efficient Repeated Analysis in the Context of Vibroacoustic Optimization and Uncertainty Quantification

This paper aims at passive noise control for vibroacoustic problems, which are analyzed by finite and boundary element techniques. The author distinguishes interior and exterior problems mainly because of the quantities used as the objective function to assess the acoustic quality. For interior problems, it is common to use local quantities such as the sound pressure at a field point or, in rare cases, energy density at a field point. The situation is different for exterior problems where the radiated sound power accounts for a suitable and global quantity to assess the emission from a vibrating structure. For most engineering purposes, the assessment requires frequency sweeps in which the problem needs to be solved at many discrete frequencies. In vibroacoustic optimization and in sampling based uncertainty quantification, it is very common that structural parameters are varied, while the acoustic field remains the same throughout the entire process. We will review concepts and recent developments of efficient frequency sweeps and repeated analysis with unmodified fluid domain. For many practical cases, the situation for interior problems is rather simple to survey. Either the authors have applied a modal analysis and used a modal superposition for the frequency sweep and repeated analysis, or the concept of unmodified acoustic transfer vectors is applied. Both concepts are quite successful as long as certain conditions are fulfilled. For exterior problems, a modal superposition is possible but, so far, only for a limited number of cases practically applicable as discussed herein. The concept of using acoustic transfer vectors becomes inefficient since the evaluation of the radiated sound power asanintegral over a closed enveloping surface would require an excessively high amount of storage capacity. Therefore, other concepts are being followed. For frequency sweeps, a number of methods are using a frequency interpolation based on a limited number of discrete sample frequencies. Often, these techniques are used together with Krylov–subspace model order reduction techniques. Further recently published approaches investigate low-rank approximations, greedy algorithms, and deflated Krylov subspace techniques. A completely different kind of approach is based on multi–fidelity models and Gaussian processes. The field of efficient repeated analysis shows some interesting developments, which can be easily applied to sampling based uncertainty quantification but do not seem to be easily and generally applied to optimization.

An optimum structural design method for a torque sensor measuring the control moment of the micro flapping-wing robot

Abstract This paper presents an optimum structural design method for a sensor capable of measuring the control torque of the micro flapping-wing robot. Torque measurement in flapping-wing robots has special demands on the sensor bandwidth. The method in this paper focuses on the development of a multi-objective optimization method based on the surrogate model to solve the sensor indicator design issues, for example, increasing sensitivity while meeting bandwidth requirements. Initially, Latin hypercube sampling was applied to the choice of the characteristic parameters of the sensor. Based on finite element techniques, the surrogate models describing displacement and eigenfrequency were established to characterize the sensor indicators, and a multi-objective optimization was conducted. According to the optimization results, the sensor structure was manufactured, and a torque measurement platform was set up. Calibration experiments and frequency response experiments demonstrated a high level of consistency between the surrogate model and the experimental data. With the assistance of the eddy current displacement sensor, the actual displacement sensitivity coefficient of the torque sensor is determined to be 0.4325 mm mNm−1, consistent with the calculation of the surrogate model. The characteristic frequency is 488.5 Hz, with a relative error of 7.47% compared to the surrogate model. This indicates that the optimum structural design method can be utilized for the rapid design of torque sensors for special requirements, thus laying the foundation for the control torque measurement of micro flapping-wing robots.

Dislocation-based finite element method for homogenized limit domain characterization of structured metamaterials

PurposeHeterogeneous and micro-structured materials have been the object of multiscale and homogenization techniques aimed at recognizing the elastic properties of the equivalent continuum. The proposed investigation deals with the mechanical characterization of the heterogeneous material structured metamaterials through analyzing the ultimate strength using the limit analysis of the Representative Volume Element (RVE). To get the desired material strength, a novel finite element formulation based on the derivation of self-equilibrated solutions through the finite elements devoted to calculating the lower bound theorem has been implemented together with the limit analysis in Melàn’s formulation.Design/methodology/approachThe finite element formulation is based on discrete mapping of Volterra dislocations in the structure using isoparametric representation. Using standard finite element techniques, the linear operator V, which relates the self-equilibrated internal solicitation to displacement-like nodal parameters, has been built through finite element discretization of displacement and strain.FindingsThe proposed work presented an elastic homogenization of the mechanical properties of an elementary cell with a geometry known in the literature, the isotropic truss. The matrix of elastic constants was calculated by subjecting the RVE to numerical load tests, simulated with a commercial FEM calculation code. This step showed the dependence of the isotropy properties, verified with Zener theory, on the density of the RVE. The isotropy condition of the material is only achieved for certain section ratios between body-centered cubic (BCC) and face-centered cubic (FCC), neglecting flexural effects at the nodes. The density that satisfies Zener’s conditions represents the isotropic geomatics of the isotropic truss.Originality/valueFor the isotropic case, the VFEM procedure was used to evaluate the isotropy of the limit domain and was compared with the Mises–Schleicher limit domain. The evaluation of residual ductility and dissipation energy allowed a measurement parameter for the limit anisotropy to be defined. The novelty of the proposal consisted in the formulation of both the linearized and the nonlinear limit locus of the material; hence, it furnished the starting point for further limit analysis of the structures whose elementary volume has been described through the proposed approach.

Maximizing the notional area in single tip field emitters

One of the critical aspects in advancing high-brightness field emitter devices is determining the conditions under which single-tip emitters should be constructed to optimize their emission area. Recent experiments have explored varying the axis ratio ξ of the cap of a single-tip emitter, ranging from an oblate semi-spheroid to a prolate shape, mounted on a nearly cylindrical conducting body. In this work, we present a strategy, based on high-accuracy computer simulations using the finite element technique, to maximize the emission area of those single-tip emitters. Importantly, our findings indicate that the notional emission area achieves its maximum when the emitter’s cap is adjusted to an oblate semi-spheroid with a characteristic axis ratio ξC≈0.85. We do a comparison of notional emission area as a function of ξ for an ellipsoidal emitter on a post and compare these results from other emitter configurations, which are feasible to fabricate.