Plate Model Research Articles

Biomechanical analysis of an absorbable material for treating fractures of the inferior orbital wall.

To investigate the biomechanical properties and practical application of absorbable materials in orbital fracture repair. The three-dimensional (3D) model of orbital blowout fractures was reconstructed using Mimics21.0 software. The repair guide plate model for inferior orbital wall fracture was designed using 3-matic13.0 and Geomagic wrap 21.0 software. The finite element model of orbital blowout fracture and absorbable repair plate was established using 3-matic13.0 and ANSYS Workbench 21.0 software. The mechanical response of absorbable plates, with thicknesses of 0.6 and 1.2 mm, was modeled after their placement in the orbit. Two patients with inferior orbital wall fractures volunteered to receive single-layer and double-layer absorbable plates combined with 3D printing technology to facilitate surgical treatment of orbital wall fractures. The finite element models of orbital blowout fracture and absorbable plate were successfully established. Finite element analysis (FEA) showed that when the Young's modulus of the absorbable plate decreases to 3.15 MPa, the repair material with a thickness of 0.6 mm was influenced by the gravitational forces of the orbital contents, resulting in a maximum total deformation of approximately 3.3 mm. Conversely, when the absorbable plate was 1.2 mm thick, the overall maximum total deformation was around 0.4 mm. The half-year follow-up results of the clinical cases confirmed that the absorbable plate with a thickness of 1.2 mm had smaller maximum total deformation and better clinical efficacy. The biomechanical analysis observations in this study are largely consistent with the clinical situation. The use of double-layer absorbable plates in conjunction with 3D printing technology is recommended to support surgical treatment of infraorbital wall blowout fractures.

Theoretical and experimental investigations on a data-driven trajectory planning scheme for dynamic shape control of piezo-actuated compliant morphing structures

Piezo-actuated compliant morphing structures can transmit motion and force via elastic deformation with lower weight, simplified design, and higher accuracy, a typical example is the variable camber wing. However, the rapid shape change of compliant structures is a challenging control problem because it often results in a high level of vibration due to the structural flexibility necessary to achieve the morphing requirement. This study presents a model-free data-driven trajectory planning approach based on spline curves and surrogate-based optimization (SBO) to obtain smooth “rest-to-rest” morphing trajectories. The macro-fiber composite (MFC) patches are used for piezoelectric actuators to generate elastic deformation. The flexible beam and variable camber wing are used for both linear numerical simulation and experimental tests with various nonlinearities and uncertainties. An optimization criterion is proposed to minimize both transient and residual vibrations during the “rest-to-rest” motion. An extraordinarily terminal displacement error function is added to eliminate the effects of the hysteresis and creep of the actuator. The control inputs, i.e., voltage profiles for the MFCs, are defined using cubic spline curves via only a few control points. Then, the optimization problem is solved by employing a Kriging surrogate model-based algorithm integrated with the expected improvement (EI) infilling-sampling criterion, which constructs an efficient algorithm similar to reinforcement learning. The optimal morphing trajectories can be highly efficiently obtained by using only 4 control points and less than 150 samplings. The experimental results of both the plate model and the variable camber wing model show that the proposed method can not only achieve a smooth dynamic morphing trajectory with minimized vibration but also automatically compensate for hysteresis and creep. The proposed method provides an effective means for the rapid realization of an optimized morphing trajectory for compliant morphing structures.

FFT-based homogenisation for efficient concurrent multiscale modelling of thin plate structures

AbstractThis paper presents a novel approach to concurrent multiscale analysis, where structures are formulated at both microscopic and macro levels for simulation purposes. The proposed method employs a plate model to formulate structures at both scales, and homogenisation is performed using the FFT-based approach, offering higher efficiency compared to conventional methods. Additionally, the macroscopic tangent operator of the microscopic model is derived through an algorithmically consistent process within the FFT-based framework, incorporating the application of Lippman–Schwinger equations as outlined in this work. The effectiveness of the proposed method is demonstrated through case studies in real simulations, revealing comparable results to traditional multiscale schemes in addressing multiscale thin plate structures. Importantly, the method significantly reduces computing time and memory usage, attributed to the efficiency of plate modelling and the FFT-based homogenisation strategy.

Quantifying stress distribution in ultra-large graphene drums through mode shape imaging

Suspended drums made of 2D materials hold potential for sensing applications. However, the industrialization of these applications is hindered by significant device-to-device variations presumably caused by non-uniform stress distributions induced by the fabrication process. Here, we introduce a methodology to determine the stress distribution from their mechanical resonance frequencies and corresponding mode shapes as measured by a laser Doppler vibrometer (LDV). To avoid limitations posed by the optical resolution of the LDV, we leverage a manufacturing process to create ultra-large graphene drums with diameters of up to 1000 μm. We solve the inverse problem of a Föppl–von Kármán plate model by an iterative procedure to obtain the stress distribution within the drums from the experimental data. Our results show that the generally used uniform pre-tension assumption overestimates the pre-stress value, exceeding the averaged stress obtained by more than 47%. Moreover, it is found that the reconstructed stress distributions are bi-axial, which likely originates from the transfer process. The introduced methodology allows one to estimate the tension distribution in drum resonators from their mechanical response and thereby paves the way for linking the used fabrication processes to the resulting device performance.

Bingham and herschel-bulkley fluids flow regimes in rough-walled rock fractures

Flow of typical non-Newtonian fluids such as cement grouts can experience different regimes as the Reynolds number (Re) changes, understanding of which is important for design and operation of rock grouting in various rock engineering applications. Here, flow regimes of representative non-Newtonian fluids, i.e., Bingham and Herschel–Bulkley (H–B) fluids, are numerically investigated with experimental validations. Three tensile rock fracture surfaces originated from a fine-grained sandstone, a medium-grained sandstone and a medium-grained granite samples are used to create rough-walled fracture models with variable aperture structures. Flow of groundwater, Bingham and H–B fluids through these fractures is numerically simulated respectively, by solving the full mass and momentum conservation equations with the Re ranging from 0.01 to 1000. The regimes for these fluids flowing through the fractures are characterized. Laboratory flow tests are conducted in a cylindrical granite fracture sample to verify the characterized flow regimes. The results reveal important differences of flow regimes between Newtonian and non-Newtonian fluids. Specifically, the transmissivity for water flow is constant when Re is relatively small until the Re reaches certain critical values; the transmissivity for Bingham and H–B fluids flow increases with increasing Re until asymptotically reaches certain peak values, followed by a descending stage when Re is relatively large. The critical (water) and peak (Bingham and H–B fluids) values are affected by surface roughness, that is, a rougher surface results in smaller critical and peak values as well as greater discrepancies compared to the analytical solutions based on the smoothed parallel plates model. These results show that a peak or optimum transmissivity is achievable in a specific range of Re (Re = 10–100 for the fractures studied). This new finding can potentially help optimize the injection pressure or flow rate in rock grouting practices.

Ritz Solutions of Stationary Random Vibrations for GPL-Reinforced FG Rectangular Plate

This paper aims to establish a comprehensive model for evaluating the response characteristics of functionally graded graphene platelet-reinforced composite (FG-GPLRC) rectangular plates under stationary random acceleration excitation. Utilizing the first-order shear deformation theory (FSDT) and Halpin–Tsai assumptions, a dynamic model for the rectangular plate is derived, followed by obtaining the variational solution using the Rayleigh–Ritz method. To describe displacement components associated with dynamic equations and boundary conditions, a spectral geometry method (SGM) is employed. Additionally, a pseudo-excitation method (PEM) is utilized for the analysis of stationary random vibration. The proposed calculation method is validated through convergence analysis and comparative evaluation with existing literature and finite element models. Furthermore, the study investigates the influence of various factors, such as boundary conditions, the number and size of functionally graded rectangular plate layers, GPL distribution types, and material parameters, on the stationary random response attributes of FG rectangular plates. This research contributes to a deeper understanding of the dynamic response of functionally graded materials in structural configurations and offers a valuable analytical approach for researchers in this field.

Non-linear buckling analysis of delaminated hat-stringer panels using variational asymptotic method

This research proposes a computationally efficient methodology using a Constrained Variational Asymptotic Method (C-VAM) for non-linear buckling analysis on a hat-stringer panel with delamination defects. Starting with the geometrically non-linear kinematics, the VAM procedure reduces the three-dimensional (3-D) strain energy functional to an analogous 2-D plate model and evaluates the closed form warping solutions. Utilising the resulting warping solutions and recovery relations for the skin and the stringer, displacement continuity at the three-dimensional level is enforced between the stringer and the skin based on the pristine and delaminated interface regions. Consequently, the constrained matrices obtained from C-VAM is incorporated into an in-house developed non-linear finite element framework. Using the developed formulation, a stiffened panel with delamination of 40 mm between the stringer and the skin is analysed under compression. The results have been validated locally and globally, employing experimental data and 3-D finite element analysis (FEA). Experiments are carried out on the co-cured panel by applying quasi-static loading with displacement-controlled conditions, and 3-D FEA is carried out in Abaqus. Load-response plots have been obtained to validate the results at the global level, and they are in excellent agreement with experiments and 3-D FEA. Subsequently, out-of-plane displacement contour plots are obtained; the number of half waves and wave intensity in 3-D FEA and C-VAM are comparable, although there are minor differences compared to the experimental findings. The proposed framework is shown to be computationally efficient by over 55% as compared to 3-D FEA for performing non-linear buckling analysis on the stiffened composite structure considered in the current work.

Behavior of reinforced CHS T-joints by welding collar plates under load

The paper presents a comprehensive test program on collar plate reinforced CHS T-joints under different preload conditions, in order to investigate the effect of preload and welding thermal on reinforced joints. A total of four specimens, including specimens with and without preload when the collar plates were welded, were tested under brace axial loading. The test results, including welding temperature field, development of strain as well as welding residual deformation during the welding process are measured and presented in this paper. Furthermore, the failure model and compressive strength of the collar plate reinforced T-joints were determined. The test results demonstrated that the localized high temperature and rapid attenuation are the characteristics of the welding temperature field, which instantaneous peak temperature rose to 1808 °C at the local area and attenuated to 600 °C in an elliptic range of about 3.1 cm × 1.7 cm. The failure modes of collar plate reinforced CHS T-joints do not change with preload on the chord and welding thermal. Furthermore, preload on the chord reduces the compressive strength of reinforced joints. The strain distribution and residual deformation are affected by the thermal expansion and cold shrinkage, while the development of the welding temperature field is not affected by the preload. Finally, for compressive strength of CHS T-joints reinforced with collar plate by welding, the applicability of the reduction coefficient due to preload calculated by existing codes was assessed by comparing design values with experimental results. A finite element model by ANSYS, considering the welding heat, was established. Key parameters affecting the strength of the T-joint at the reinforced collar plate under load were identified through parametric study with finite element models. Construction recommendations of welded CHS T-joints are proposed.

Evaluation of carbon emissions for fresh food last-mile delivery: A comparative analysis of two refrigeration methods

This study compares carbon emissions from last-mile fresh food delivery using traditional cold storage plates and a new photovoltaic (PV) direct-drive cooling model. A life cycle analysis shows that while the PV model has higher initial production emissions in six cities, it achieves a 97.95–98.78 % reduction in total emissions over 20 years compared to the traditional model. The cold storage plate model contributes the highest carbon footprint during the use stage, while the photovoltaic direct-drive cooling model has the highest carbon footprint during the production stage. The emission reduction benefits could be achieved during the disposal stage. As the design temperature inside the delivery box increases from -5 °C to 0 °C, the carbon emissions of the photovoltaic direct-drive cooling model decrease by 17.74 %–19.31 %, while those of the cold storage plate model decrease by 13.21 %–18.79 % for different cities. Further increasing the temperature to 5 °C results in a more reduction of 17.03 %–18.24 % for the photovoltaic direct-drive cooling model and 15.22 %–19.71 % for the old storage plate model. This indicates that even minor adjustments in temperature settings can have a substantial impact on reducing the carbon footprint of fresh food delivery.

Substructure-based topology optimization design method for passive constrained damping structures

Abstract This work presents a generalized substructure-based topology optimization method for passive constrained layer damping (PCLD) structures. Here, the model of PCLD structure is obtained by the Kirchhoff–Love thin plate formulation, and the whole structure is assumed to be composed of substructures with different yet connected scales and artificial lattice geometry features. Each substructure is condensed into a super-element to obtain the associated density-related matrices under the different geometry feature parameters, and the surrogate model for the stiffness and mass matrix of PCLD substructures with different densities has been particularly built. Using cubic spline interpolation, the derivatives of super-element matrices to the associated densities can be evaluated efficiently and accurately. The modal loss factor is defined as objective functions and topology optimization for the PCLD structures is formulated based on the model for PCLD plates that are described by combining the condensed substructures. Numerical examples under two lattice patterns of substructures and their corresponding physical tests show that the correctness and superiority of this substructure-based topology optimization approach for PCLD plates are verified.

Mechanical characteristics of new mesh-type elastic plate under different temperatures and vehicle dynamics loads

The dynamic characteristics of the elastic plate are affected by changes in ambient temperature. In this study, tensile tests of rubber materials at different temperatures were conducted, revealing that rubber materials exhibit significant nonlinearity and sensitivity at low temperatures. Finite element models of Groove Elastic Plate (GEP) and New Mesh-Type Elastic Plate (NMTEP) were established, incorporating the corresponding rubber material parameters to simulate temperature effects. The stress, deformation, stiffness, and damping characteristics of the two types of elastic plates were analyzed under varying temperature conditions. Finite element calculations show that NMTEP maintains better structural stability, lower static/dynamic stiffness, and a higher damping ratio at low temperatures. Additionally, dynamic calculations indicate that temperature variations significantly impact the track system's dynamic performance. The vibration and wheel-rail forces for NMTEP are significantly lower than those for GEP under all temperature conditions, suggesting that NMTEP is more conducive to vehicle safety and stability at low temperatures.

Analysis of fluid-structure coupling during the flapping of dragonfly hind wings under different flexible distributions

Abstract To investigate the influence of flexible distribution on the aerodynamic characteristics of a dragonfly hind wing during flapping flight, this study establishes a simplified plate model of the dragonfly hind wing based on the actual size, while neglecting the wrinkled microstructure. Six different flexible distribution patterns are proposed for the model. The overlapping grid technique is employed to achieve fluid-structure coupling calculations during the flapping motion of the dragonfly hind wing, by customizing the Young’s modulus in the solid region to represent different levels of flexibility. The results show that gradually increasing the flexibility along the chordwise direction of the dragonfly wing can induce a stronger leading-edge vortex during flapping, intensifying the accumulation of vorticity near the wingtip and resulting in a higher peak lift coefficient. The flexible wing has a positive impact on the formation and development of the trailing-edge vortex, leading to an increase in the thrust coefficient peak and time-averaged thrust coefficient of the dragonfly hind wing. Consequently, all aspects of the aerodynamic characteristics are significantly improved.

ЖҰҚА ИЗОТРОПТЫ ПЛАСТИНАЛАРДЫҢ ИІЛУІН ТАЛДАУ

In the field of modern construction, thin isotropic plates are widely used. The development of calculation methods and mathematical models for thin isotropic plates of rectangular shape is an important issue. The article examines the bending of a rectangular thin isotropic plate. The method of separation of variables is employed to derive the plate calculation theory. New formulas for the function of deflection and internal forces of the plate are determined. A simplified version of the classical theory is presented, defining the solution to the plate bending problem using simple polynomials. The values of the deflection function and internal forces of a rectangular thin isotropic plate are presented in the form of tables and diagrams. The obtained calculation results are compared with Navier's method and the finite element method. The results obtained completely coincide with the results obtained by other methods and thereby confirm the correctness of the proposed version of the theory.

Bistability-latching criteria in pre-pressurised and electrostatically actuated curved microplates

The study of electrostatically actuated microplates in the presence of a mechanical pressure can further their usage as static pressure/mass sensors. The study was carried out using the Föppl-von-Kármán plate model, from which a reduced order (RO) model was derived that includes both loadings. Bistability criteria were extracted semi-analytically using Berger’s plate model, from which a single degree-of-freedom was taken from its RO counterpart. It was found that in the presence of pressure, bistability interacts with latching in a new manner, requiring two conditions to ascertain if a microplate becomes bistable.

A Phanerozoic gridded dataset for palaeogeographic reconstructions

Global Plate Models are widely used in the Earth Sciences to reconstruct the past geographic position of geological and palaeontological samples. However, the application of Global Plate Models to retrieve ‘palaeocoordinates’ is not trivial. Different Global Plate Models exist which vary in their complexity, spatiotemporal coverage, reference frame, and intended use. Consequently, careful consideration of which models are appropriate for any given research question is required. Here, we document and provide access to reconstruction datasets for five Global Plate Models in the palaeomagnetic reference frame. These datasets provide ‘true’ palaeolatitudes for three discrete global grids reconstructed at one-million-year intervals throughout the Phanerozoic (540–0 Ma), offering three key benefits for the Earth Science community: (1) allow users to look up palaeocoordinates for their samples (e.g. fossil occurrences) through simple indexing without having to learn additional software packages; (2) provide palaeocoordinates which have been generated consistently with thorough documentation; (3) provide static files which preserve model output and which can be used to evaluate palaeogeographic differences between Global Plate Models.

Research on In-Plane Thermal Conductivity Detection of Fuel Cell Bipolar Plates Based on Laser Thermography.

The thermal properties of bipolar plates, being key elements of polymer electrolyte membrane fuel cells, significantly affect their heat conduction and management. This study employed an innovative approach known as a heat flow loop integral method to experimentally assess the in-plane thermal conductivity of graphite bipolar plates, addressing the constraints of traditional methods that have strict demands for thermal stimulation, boundary or initial conditions, and sample size. This method employs infrared thermal imaging to gather information from the surface temperature field of the sample, which is induced by laser stimulation. An enclosed test loop on the infrared image of the sample's surface, situated between the heat source and the sample's boundary, is utilized to calculate the in-plane heat flow density by integrating the temperature at the sampling locations on the loop and the in-plane thermal conductivity can be determined based on Fourier's law of heat conduction. The numerical simulation analysis of the graphite models and the experimental tests with aluminum have confirmed the precision and practicality of this method. The results of 1060 aluminum and 6061 aluminum samples, each 1 and 2 mm in thickness, show a deviation between the reference and actual measurements of the in-plane thermal conductivity within 4.3% and repeatability within 2.7%. Using the loop integral method, the in-plane thermal conductivities of three graphite bipolar plates with thicknesses of 0.5 mm, 1 mm, and 1.5 mm were tested, resulting in 311.98 W(m·K)-1, 314.41 W(m·K)-1, and 323.48 W(m·K)-1, with repeatabilities of 0.9%, 3.0%, and 2.0%, respectively. A comparison with the reference value from the simulation model for graphite bipolar plates with the same thickness showed a deviation of 4.7%. The test results for three different thicknesses of graphite bipolar plates show a repeatability of 2.6%, indicating the high consistency and reliability of this measurement method. Consequently, as a supplement to existing technology, this method can achieve a rapid and nondestructive measurement of materials such as graphite bipolar plates' in-plane thermal conductivity.

Design and Analysis of Orthogonal Polarization Point Diffraction Pinhole Plate

The pinhole plate is a key component of the point diffraction interferometer (PDI). The reasonable improvement and simulation of this device would enhance the application of point diffraction interferometry technology during the measurement of wavefronts. The traditional point diffraction interferometry measurement method is easily disturbed by environmental noise, making it difficult to obtain high-precision dynamic measurements. This paper introduces a four-step phase-shift PDI that can be employed in a common optical path. By using the principle of the finite-difference time-domain method (FDTD), a simulation model of the orthogonal polarization point diffraction pinhole plate (OP-PDPP) structure is established. The results show that when Cr is used as the film material in the pinhole plate, the parameters include a film thickness of 150 nm, a pinhole diameter of 2 μm, a wire grid period of 150 nm, and a wire grid width of 100 nm; in addition, the comprehensive extinction ratio of the pinhole plate is the greatest and the diffraction wavefront error is the smallest. Finally, the constructed experimental system is used to test the wavefront of a flat sample with a 25.4 mm aperture, and the test results are compared with those of the ZYGO interferometer. The difference in the peak-to-valley (PV) value between the OP-PDI and the ZYGO interferometer measurement is 0.0028λ, with an RMS value difference of 0.0011λ; this verifies the feasibility of the scheme proposed in this paper. The experimental results show that the proposed OP-PDPP is an effective tool for high-precision dynamic measurement.

Midline Assembloids Reveal Regulators of Human Axon Guidance.

Organizers are specialized cell populations that orchestrate cell patterning and axon guidance in the developing nervous system. Although non-human models have led to fundamental discoveries about the organization of the nervous system midline by the floor plate, an experimental model of human floor plate would enable broader insights into regulation of human neurodevelopment and midline connectivity. Here, we have developed stem cell-derived organoids resembling human floor plate (hFpO) and assembled them with spinal cord organoids (hSpO) to generate midline assembloids (hMA). We demonstrate that hFpO promote Sonic hedgehog-dependent ventral patterning of human spinal progenitors and Netrin-dependent guidance of human commissural axons, paralleling non-human models. To investigate evolutionary-divergent midline regulators, we profiled the hFpO secretome and identified 27 evolutionarily divergent genes between human and mouse. Utilizing the hMA platform, we targeted these candidates in an arrayed CRISPR knockout screen and reveal that GALNT2 , a gene involved in O-linked glycosylation, impairs floor plate-mediated guidance of commissural axons in humans. This novel platform extends prior axon guidance discoveries into human-specific neurobiology with implications for mechanisms of nervous system evolution and neurodevelopmental disorders.

Induced seismicity at the Laúca reservoir, Angola Craton: Focal mechanisms and implications for the stress field in Western Central Africa

We present the first case of reservoir induced seismicity (RIS) ever reported in the Angola Craton, Laúca reservoir. Impoundment of the reservoir began in late 2017 and seismicity started in March 2018 shortly after the water level reached 86 m. Earthquakes continued to be recorded in the following years, with 287 events detected between March/2018 and April/2024. The largest event had magnitude 3.0 ML. The dam is 156 m tall, and the total reservoir volume is 5,044.85 Hm3. The reservoir area is monitored by two stations, LAUC and ZERO. Seismic data is of high quality, with sharp P- and S-wave arrivals at both stations. We derive a half-space velocity model for the lake area using a composite Wadati diagram and minimization of travel time residuals and locate 90 events with arrivals at both stations. S-to-P converted phases at the surface were used to help constrain hypocentral depths and epicentral locations. We use waveform modeling to determine focal mechanisms for ten events using the program FMNEAR, and invert for the local stress field. We find the faulting regime in the area to be strike-slip and SHMax oriented roughly NE-SW. We compare our results to the broader stress field in western Central Africa and find them to be in agreement with nearby stress determinations from focal mechanisms in the Congo Basin. Our results make an important contribution to the state of knowledge of the stress field in western Central Africa, which can be taken into consideration in future geodynamic models of the Nubian plate as more data is gathered and help further our understanding of stress sources in this region.

An isogeometric analysis of solar panels with a bio-inspired substrate

We in this paper propose a high-performance design using bio-inspired metamaterials for multilayered perovskite solar cell (MPSC) plates. The static bending and free vibrational responses of the newly designed MPSC panels with the presence of the triply periodic minimal surface (TPMS) substrate are subsequently investigated numerically. The displacements of the present plate model are then approximated by five-variable higher-order shear deformation theories (HSDTs). The weak forms are established for both the static bending and free vibration problems and subsequently derive the discrete forms using the NURBS-based isogeometric approach. To enhance the operational efficiency of solar panels in challenging environments, we integrate advanced lightweight architectures based on bio-inspired TPMS structures as a substrate layer into the original solar panel design. In this research, three widely employed TPMS structures: Primitive, Gyroid, and I-graph and Wrapped Package-graph (IWP), are examined in conjunction with two functional grading patterns implemented through the thickness direction. For the first time, the static bending performance of MPSC plates integrated into a TPMS-based substrate layer and subjected to wind pressure as well as thermal conditions is comprehensively studied. In addition, the influence of several significant factors on the free vibration behavior of MPSC plates is also elucidated. The findings show a promising and intriguing design avenue, particularly in the application of high-performance metamaterials to address contemporary challenges in renewable energy usage and environmental protection.