Search Results (38)

Homogenization researches for corrugated cardboard are predominantly based on plate theories assuming constant thickness, such as the Reissner–Mindlin plate. However, corrugated cardboard is prone to significant deformation in the thickness direction. To address this limitation, the present work proposes an improved plate element designed by expanding the deflection function to the quadratic term of the thickness coordinate, enabling a linearly varied transverse normal strain. Furthermore, an extension of the established homogenization method is developed to derive the constitutive matrix. The element is implemented via the Abaqus user subroutine UEL. Validation demonstrates that the proposed element effectively characterizes a linearly varied transverse normal strain and stress. Simulation results from the homogenized model applying the proposed element and extended homogenization method are compared with those from detailed models. The comparisons confirm the efficiency and accuracy of the proposed approach. Full article

Caragana korshinskii Kom. (CKB), widely cultivated in Inner Mongolia, China, has potential for silage feed development due to its favorable nutritional characteristics, including a crude protein content of 14.2% and a neutral detergent fiber content below 55%. However, its vascular bundle fiber structure limits the efficiency of lactic acid conversion and negatively impacts silage quality, which can be improved through mechanical crushing. Currently, conventional crushing equipment generally suffers from uneven particle size distribution, high energy consumption, and low processing efficiency. In this study, a layered aggregate model was constructed using the discrete element method (DEM), and the Hertz–Mindlin with Bonding contact model was employed to characterize the heterogeneous mechanical properties between the epidermis and the core. Model accuracy was enhanced through reverse engineering and a multi-particle-size filling strategy. Key parameters were optimized via a Box–Behnken experimental design, with a core normal stiffness of 7.37 × 10¹¹ N·m⁻¹, a core shear stiffness of 9.46 × 10¹⁰ N·m⁻¹, a core shear stress of 2.52 × 10⁸ Pa, and a skin normal stiffness of 4.01 × 10⁹ N·m⁻¹. The simulated values for bending, tensile, and compressive failure forces had relative errors of less than 10% compared to experimental results. The results showed that rectangular hammers, due to their larger contact area and more uniform stress distribution, reduced the number of residual bonded contacts by 28.9% and 26.5% compared to stepped and blade-type hammers, respectively. Optimized rotational speed improved dynamic crushing efficiency by 41.3%. The material exhibited spatial heterogeneity, with the mass proportion in the tooth plate impact area reaching 43.91%, which was 23.01% higher than that in the primary hammer crushing area. The relative error between the simulation and bench test results for the crushing rate was 6.18%, and the spatial distribution consistency reached 93.6%, verifying the reliability of the DEM parameter calibration method. This study provides a theoretical basis for the structural optimization of crushing equipment, suppression of circulation layer effects, and the realization of low-energy, high-efficiency processing. Full article

For relaxor ferroelectric single crystal (1 − x)Pb(Mg_1/3Nb_2/3)O₃ − xPbTiO₃ (PMN-PT), through reasonable component regulation and electric field polarization, an orthogonal mm² point group structure can be obtained, which has high piezoelectric constants and is, therefore, a desired substrate material for lateral-field-excited (LFE) bulk acoustic wave (BAW) devices. In this work, acoustic wave resonance characteristics of (zxt) 45° PMN-PT BAW devices with LFE are investigated. Firstly, Mindlin first-order plate theory is used to obtain vibration governing equations of orthorhombic crystals excited by a lateral electric field. By analyzing the electrically forced vibrations of the finite plate, the basic vibration characteristics, such as motional capacitance, resonant frequency, and mode shape are obtained, and influences of different electrode parameters on resonance characteristics of the device are investigated. In addition, the effects of the structure parameters on the mass sensitivity of the devices are analyzed and further verified by FEM simulations. The model presented in this study can be conveniently used to optimize the structural parameters of LFE bulk acoustic wave devices based on orthorhombic crystals, which is crucial to obtain good resonance characteristics. The results provide an important basis for the design of LFE bulk acoustic wave resonators and sensors by using PMN-PT orthorhombic crystals. Full article

Shells are significant structural components that are extensively utilized in numerous engineering fields, including architectural and infrastructural projects. These components are employed in the construction of domes, water tanks, stadiums and auditoriums, hangars, and cooling towers. Significant research efforts have been dedicated to the analysis of vibrations and dynamic behaviors of shells, due to their distinctive capacity to efficiently bear loads through their geometry rather than mass. Additionally, a vast array of shell theories and computational methods have been proposed and developed by researchers. This paper represents a continuation of research initiated begun in a 2009 paper by Elishakoff, wherein the suggestion was made to disregard an energetic term in the dynamic analysis of Timoshenko–Ehrenfest beams, wherein the suggestion was made to disregard an energetic term in the dynamic analysis of Timoshenko–Ehrenfest beams. The resulting reduced theory was found to be both more straightforward and more reliable than the complete, classical approach. While the original idea was heuristically justified, a more sound variationally consistent theory was proposed in the papers of De Rosa et al. concerning the dynamic analysis of the Timoshenko-Ehrenfest beams and later extended to the case of the Uflyand-Mindlin plates. In accordance with the proposal put forth in those works, we initially delineate the classical shell theory and subsequently propose two alternative hypotheses that give rise to two distinct aspects of the energy terms. By employing the variational approach, we derive two novel boundary problems, which are direct generalizations of those previously considered. Both theories can be readily specialized for beams and plates, and the theory can also be specialized for the case of cylindrical shells. Full article

This paper explores and discusses how wing structures vibrate by using the Mindlin–Reissner plate theory, which takes into consideration the effects of transverse shear deformation and rotary inertia. This theory works well for thicker structures, like aircraft wings, where it gives accuracy by detecting shear and rotation effects. FGMs, or functionally graded materials, are used in aviation to enhance structural patterns and reduce stress points by gradually changing material properties along the wing thickness based on the volume fraction index. Finite element method (FEM) simulations were conducted to compare the natural frequencies and mode shapes of tapered and interpolated wing geometries. The results indicate that interpolated meshes exhibit higher natural frequencies due to increased stiffness, whereas tapered meshes show lower frequencies due to their flexibility. Validation through ANSYS simulations confirms the accuracy of the FEM results, highlighting the influence of geometry and material gradation on vibrational behavior. The findings offer valuable insights for aerospace applications, supporting the development of lightweight and efficient wing designs. Full article

The primary objective of modal identification for variable thickness quartz plates is to ascertain their dominant operating mode, which is essential for examining the vibration of beveled quartz resonators. These beveled resonators are plate structures with varying thicknesses. While the beveling process mitigates some spurious modes, it still presents challenges for modal identification. In this work, we introduce a modal identification technique based on the energy method. When a plate with variable thickness is in a resonant state of thickness–shear vibration, the proportions of strain energy and kinetic energy associated with the thickness–shear mode in the total energy reach their peak values. Near this frequency, their proportions are the highest, aiding in identifying the dominant mode. Our research was based on the Mindlin plate theory, and appropriate modal truncation were conducted by retaining three modes for the coupled vibration analysis. The governing equation of the coupled vibration was solved for eigenvalue problem, and the modal energy proportions were calculated based on the determined modal displacement and frequency. Finally, we computed the eigenvalue problems at different beveling time, as well as the modal energies associated with each mode. By calculating the energy proportions, we could clearly identify the dominant mode at each frequency. Our proposed method can effectively assist engineers in identifying vibration modes, facilitating the design and optimization of variable thickness quartz resonators for sensing applications. Full article

Guided wave tomography is an effective non-destructive method for mapping corrosion damage in thin-walled metal structures. Its efficiency and accuracy depend on the choice of a suitable forward model and inversion method. Current techniques mainly use acoustic forward models that, while computationally efficient, are approximate and fail to accurately represent wave propagation in physical experiments, making them less suitable for inversion. This study investigates the performance of Mindlin plate theory, which accounts for through-thickness shear deformations, enabling the modeling of flexural modes in a two-dimensional (2-D) plane. The scattering of $A_0$ mode Lamb waves from defects of varying depth, width, and shape is analyzed using finite difference and pseudospectral simulations for 2-D and three-dimensional (3-D) defects, respectively. Results from the Mindlin model are compared to finite element model simulations. It is found that Mindlin plate theory accurately represents smooth defect scattering, but is less accurate for sharp-edged defects. Full article

An experimental study was undertaken to investigate the problem of the substantial variability in water content in unrotted sheep dung, which leads to a lack of universality and practicality in calibrating its discrete element simulation parameters. The stacking angle was used as the response value in these experiments. The objective of this study was to establish precise simulation parameters for the composting process. A model for water content-stacking angle was established using the cylinder-lifting technique, resulting in a correlation value of 0.997. Utilizing the Hertz–Mindlin with JKR bonding model, three EDEM particle models were developed, each with distinct particle sizes, based on the particle size distribution of sheep dung. The JKR surface energy was determined using the Plackett–Burman test, the steepest-climbing test, and the Box–Behnken test using a set of 10 parameters. A subsequent study was conducted on the JKR surface energy, rolling friction factor, and static friction factor utilizing the Plackett–Burman test and Box–Behnken test. A parameter model for stacking angle–discrete elements was developed that achieved a p-value below 0.0001 and a relative inaccuracy of 3.46% or less. The regression model for the water content–discrete element parameter was derived by combining the water content–stacking angle model with the stacking angle–discrete element parameter model. Validation of this model was conducted using both the pumping plate technique and the hopper approach, resulting in a relative error of 4.89% or less. The findings demonstrate that the specific characteristics of sheep manure may be accurately anticipated by considering its water content. This approach offers a valid and universally applicable way of predicting the specific characteristics of sheep dung in the simulation of composting equipment. Full article

In view of the large difference in moisture content of cotton stalk in autumn in Xinjiang, the existing process of obtaining discrete element simulation parameters of cotton stalk is low in accuracy and complicated in operation, leading to the problems of poor universality and low accuracy in regard to the discrete element simulation parameter-calibration method in the process of mechanized transportation, throwing and returning to the field. Therefore, the experimental study on cotton stalk with different moisture content was carried out with the accumulation angle as the response value, so as to construct a parameter model that can quickly and accurately calibrate cotton stalk with different levels of moisture content. The model has high applicability and flexibility, and it can be widely used in the simulation test of various cotton field-operation machinery, such as a residual film-recycling machine, cotton picker, crushing and returning machine and other equipment. The water content–accumulation angle model was established by the cylinder-lifting method, and the correlation coefficient of the model was 0.9993. Based on EDEM 2020 software, the Hertz–Mindlin model was used to simulate the stacking angle of cotton stalk, and the rolling friction coefficient, static friction coefficient and collision recovery coefficient between cotton stalk and cotton stalk–steel were obtained. Through the Plackett–Burman test, climbing test and Box–Behnken test, three significant parameters, namely the rolling friction coefficient, static friction coefficient and static friction coefficient between cotton stalk and steel, were selected from discrete element simulation parameters to characterize the moisture content of cotton stalk, and the accumulation angle–discrete element parameter model was established. The p-value of the model was less than 0.0001, and the relative error was only 2.67%. Based on the moisture content–stacking angle model and the stacking angle–discrete element parameter model, the moisture content–discrete element parameter model was constructed. The model was verified by the cylinder-lifting method and the plate-drawing method, and the relative error was only 2.79%. Finally, the model was further verified by comparing the effect of the throwing uniformity between the mechanical simulation test and field test, and the relative error was only 4.75%. The test proves that the moisture content–discrete element parameter model is accurate and reliable, not only providing the design basis and support for the mechanization research of cotton stalk conveying and returning to the field in Xinjiang but also providing ideas for the calibration of discrete element simulation parameters of other crop straws. Full article

To address the inefficient crushing of fertilizer during the mechanized spreading process caused by the caking of high-humidity organic fertilizer, a fertilizer spreader with a combined rotor and lining plate crushing mechanism was proposed in this paper. With the introduction of the basic structure and working principle of the spreader, a particle group model for an organic fertilizer consisting of both caked and bulk fertilizer was built, based on the Hertz–Mindlin model with bonding and the Hertz–Mindlin model with JKR contact, in EDEM to construct an organic fertilizer-crushing-and-spreading model. With the rotor speed, the axial distance of the hammer, and the number of circumferential hammer groups as the experimental factors and the maximum broken bond rate of the caked organic fertilizer and the minimum coefficient of variation of spreading uniformity as the experimental indices, the Box–Behnken test method was employed to establish regression equations for response surface analysis and multi-objective optimization of the test results. The results indicated that, when the rotor speed was 6.47 Hz, the axial distance of the hammer was 90.30 mm, the number of circumferential hammer groups was five, the broken bond rate reached 90.86%, and the coefficient of variation was 21.45%. Verification tests under these conditions showed a broken bond rate of 90.03% and a coefficient of variation of 22.12%, which were consistent with the optimization results. Therefore, our research provides a reference for the structural design of an organic fertilizer spreader and the optimization of its working parameters. Full article

Based on the three-dimensional (3D) linear elasticity theory of piezoelectric semiconductor (PS) structures, inspired by the variational principle and the Mindlin plate theory, a two-dimensional (2D) higher-order theory and equations for thin-film devices are established for a rectangular coordinate system, in which Newton’s law (i.e., stress equation of motion), Gauss’s law (i.e., charge equation of electrostatics), Continuity equations (i.e., conservation of charge for holes and electrons), drift–diffusion theory for currents in semiconductors, and unavoidable thermo-deformation-polarization-carrier coupling response in external stimulus field environment are all considered. As a typical application of these equations, the static characteristic analysis of electromechanical fields for the extensional deformation of a PS thin-film device with thermal field excitations is carried out by utilizing established zeroth-order equations and the double trigonometric series solution method. It is revealed that the extensional deformations, electric potential, electron and hole concentration perturbations, and their current densities can be controlled actively via artificially tuning thermal fields of external stimuli. Especially, a higher temperature rise can induce a deeper potential well and a higher potential barrier, which can play a vital role in driving effectively motions and redistributions of electrons and holes. Overall, the derived 2D equations as well as the quantitative results provide us some useful guidelines for investigating the thermal regulation behavior of PS thin-film devices. Full article

In order to investigate the contact characteristics of the mechanical parts of the brewing robot with wine lees particles, it is essential to calibrate the parameters of the discrete elemental model of wine lees particles. This paper proposes a method based on tests of the angle of repose. The simulation test is conducted to establish a regression model and combined with physical tests to find optimization. The contact model used in simulation modeling is Hertz-Mindlin with Johnson-Kendall-Roberts. Not all discrete element model parameters of wine lees particles have a significant impact on the angle of repose, so screening through Plackett-Burman Design is performed. The results indicate that the restitution coefficient between wine lees particles and restitution coefficient between wine lees particle and steel plate have a significant impact on angle of repose. Additionally, another parameter that is difficult to obtain, namely surface energy (JKR), also plays a crucial role. The optimal value interval for these three parameters is determined by the steepest ascent test, and a linear regression model for angle of repose is built through Box-Behnken Design. The optimal values obtained are as follows: restitution coefficient between wine lees particles—0.603; restitution coefficient between wine lees particle and steel plate—0.595; JKR—0.083. Finally, in order to verify the accuracy of calibrated parameters, simulation verification tests are carried out which show that there is only a relative error rate at 0.18% between simulated angle of repose and actual angle of repose, indicating that accurate calibration parameters were achieved. This study can provide reference for selecting discrete element model parameters for wine lees particles in future research endeavors. Full article

Plates are flat structural elements whose thickness is small in relation to the size of the surface. Their use may include engine foundations, reinforced concrete bridge elements or parts of various floating structures. Consequently, knowledge of their mechanical behavior under static and dynamic loads is of primary importance in engineering applications and of interest from a structural point of view. As a result, numerous works existing in the literature have investigated the mechanical properties of plates using various plate models, such as Reissner’s theory, Levinson’s theory, Kirchhoff’s theory and Mindlin’s theory, and their static and dynamic behavior has been examined. In the present paper the truncated Uflyand–Mindlin plate equation is proposed. According to Uflyand–Mindlin theory, an alternative theoretical formulation is presented for the free-vibration analysis of plates, and the equations of motion and the general corresponding boundary conditions are derived. This paper develops the truncated Uflyand–Mindlin plate equation, i.e., without the fourth-order derivative, by means of the direct method and variational formulation. The first-order shear deformable plate theory developed by Elishakoff, which takes into account rotational inertia and shear deformation and does not include a fourth-order time derivative, is variationally derived here. This derivation complements that performed by Mindlin some 70 years ago. The innovative aspect of the suggested strategy is that variational and direct methods for studying plate dynamics are analogous. Finding the third equation of the reduced Uflyand–Mindlin equations, the accompanying boundary conditions and their mathematical resemblance are the goals of the presented formulations. In order to solve the dynamic equilibrium problem of a truncated Uflyand–Mindlin equation via a variational formulation, it is demonstrated that the differential equations and the corresponding boundary conditions have the same form as those found using the direct technique. This paper successfully completes this task. Finally, in order to validate the effectiveness and correctness of the proposed procedure, a numerical example of the case of a plate simply supported at all four ends is proposed. Full article

Precision seeding technology is an important component of agricultural mechanization production. The precise regulation of seed movement behavior is the core of precision sowing technology and the key to improving the quality of single seed precision sowing. To accurately obtain the interaction law between seeds and soil after touching the soil, it is necessary to conduct comprehensive physical experiments to determine the simulation parameters of the seed and soil. This article takes coated cotton seeds as the research object, and the basic physical parameters of coated cotton seeds are measured through biological experiments. Based on the Hertz–Mindlin with bonding V2 contact model, a simulation model of compression between coated cotton seeds and soil is established. Using peak compression force as the response value, a combination of physical experiments and simulation simulations was used to calibrate the simulation parameters of the simulation mode of coated cotton seeds and soil. Through PB testing, it was found that four factors have a significant impact on the peak compressive force, and the parameter range was obtained. The Poisson’s ratio of coated cotton seeds was 0.14–0.26. The static friction coefficient between coated cotton seeds and steel plate was 0.38–0.58. The static friction coefficient between soil and soil was 0.3–1.2. The rolling friction coefficient between soil and soil was 0.1–0.6. Through response surface experiments with four factors and three levels, regression models were established between various factors and response values, and the optimal combination of simulation parameters was determined: the Poisson’s ratio of coated cotton seeds was 0.21; the static friction coefficient between coated cotton seed and steel plate was 0.47; the static friction coefficient between soil and soil was 0.34; and the rolling friction coefficient between soil and soil was 0.59. Based on the optimal parameter combination, the simulation of compression between coated cotton seeds and soil was continued, and the variation law of soil particle bonding bonds at different positions of coated cotton seeds during the compression process was obtained. This study provides a basis for exploring the interaction mechanism between the trencher seed soil of precision seeders and optimizing the design of critical components of cotton precision seeders. Full article

Given the lack of accurate and reliable discrete element simulation parameters to study the interactions between soft soil and soil casting components after ginseng land cultivation in Northeast China and the design of ginseng land-specific borders, this paper calibrates the relevant model parameters of ginseng soil using the Hertz–Mindlin with JKR contact model in EDEM to standardize the contact parameters between soil particles and between soil and Q235 steel in soft soil after cultivation in ginseng land. Taking the soil particle accumulation angle as the response value, a Box–Behnken design (BBD) was introduced to establish a regression model for the soil accumulation angle; the surface energy, static friction coefficient, rolling friction coefficient, and coefficient of restoration parameters were obtained, respectively, through the optimization of the model, at which time, the simulated value of the soil accumulation angle was 37°, which is a 4% relative error to the actual measured accumulation angle of 35.5°. Taking the sliding friction angle of the soil on the Q235 steel plate as the response value, the regression model of the soil sliding friction angle was obtained based on the BBD. The static friction factor, rolling friction factor, and coefficient of restitution between the soil particles and the Q235 steel were obtained, respectively. Based on the combination of these parameters, the simulated value of the sliding friction angle was 32.2°, which is a 2% relative error to the measured accumulation angle of 31.5°. To verify the accuracy of the optimized simulation parameters, field and simulation tests of soil-throwing components were conducted. The results show that the maximum relative error between the measured value and the simulation value is 5.6% and 3.4%. The error is within an acceptable range, and the simulation test and field test soil-throwing effects are the same, which verifies the accuracy and reliability of the reference soil parameter calibration. The results of the study can be used for discrete element simulation analysis of the interaction between ginseng loam and touchdown components and their structural optimization. Full article