Plate Aspect Ratio Research Articles

Use of a Refined Theory for Three-Dimensional Bending Analysis of Isotropic Rectangular Thick Plates

In this paper, a refined plate theory (Alternative II theory) is presented for the three-dimensional bending analysis of an Isotropic thick plate. The theory has similarity to the first order shear deformation theory but requires no shear correction factors. The kinematics equations were developed based on the Alternative II Refined plate theory. Thereafter, using a complete three-dimensional constitutive relation, the total potential energy was developed. A governing equation and two compatibility equations were obtained by the variation of the total potential energy with respect to displacement and rotations respectively. Solving the governing and compatibility equations, a polynomial displacement function was obtained. The stiffness coefficients were then obtained using the displacement function. Thereafter, the equations for the in-plane normal and shear stresses, transverse normal and shear stresses as well as the lateral displacement were developed using the stiffness coefficients and the displacement function. Numerical values of the lateral displacement parameters were determined for a rectangular plate of aspect ratio 2.0, 1.0 and 0.5 for span to thickness ratios of 20, 10 and 7.14286. Also, numerical values of the lateral displacement and stresses were determined for a square plate for span to thickness ratios of 4, 10, 100 and 1000. The results from this work were compared with the work of previous researchers using simple percentage difference. It was observed that refined plate theories overestimate the lateral displacement of a plate. Hence, three-dimensional analysis is recommended for thick plate analysis.

Ultimate strength assessment of randomly pitted stiffened panels considering stiffener corrosion

Stiffened panels are renowned for their exceptional load-bearing capabilities due to their high strength-to-weight ratio and are extensively utilized in ship and marine structures. Nevertheless, they are susceptible to failure under compression, particularly in marine environments where corrosion leads to material and structural degradation. Stiffener corrosion was not involved adequately in current studies, with an unclear synergistic effect of corrosion damage with structural configurations. This paper introduces a numerical modeling approach to develop finite element (FE) models of panels with random pitting corrosion, considering both corrosion on the plating and stiffeners. These FE models are validated against existing experiments and empirical formulae and employed to investigate the effect of random pitting damage on the ultimate strength of panels. The study examines the impact of various structural parameters, such as plate aspect ratio, plate slenderness ratio, stiffener slenderness ratio, and the height-to-thickness ratio of stiffener web, on ultimate strength under different levels of pitting damage. Additionally, the load-bearing behavior and failure modes of damaged panels are analyzed. An artificial neural network (ANN) is developed to predict the ultimate strength of pitted panels. The findings indicate that the ultimate strength of panels with stiffener corrosion in the form of random pitting corrosion leads to a more significant reduction by about 17.7% than that without stiffener corrosion, potentially altering the failure mode. The proposed ANN model accurately predicts the ultimate strength of pitted panels with and without stiffener corrosion, with a mean relative error of approximately 1.1% compared to FE analysis results.

An experimental study on heat transfer using electrohydrodynamics (EHD) over a heated vertical plate.

The Corona effect offers significant potential for improving heat transfer efficiency in air. This study thoroughly examined how a single corona discharge affects heat transfer on a heated vertical flat plate. Key parameters tested included corona voltage, the aspect ratio of the vertical plate (y/L), and the inter-electrode discharge gap ratio (x/d). The findings revealed that increasing the corona voltage and decreasing the discharge gap enhanced heat transfer efficiency along the vertical surface. A predictive formula for the local Nusselt number was developed to characterize heat transfer on the plate. Additionally, Particle Image Velocimetry (PIV) was used to analyze the corona wind generated by the discharge. The study observed that the corona wind formed a vortex in the upstream region, which resulted in lower heat transfer rates upstream compared to the downstream region.

Influence of Transverse Normal Strain on Buckling and Vibration of Sandwich Plates

This study presents the buckling and free vibration behavior of simply supported square and rectangular sandwich plates. A third-order shear deformation theory considering both the transverse shear and normal deformations is used. The condition of zero transverse shear stresses on the top and bottom surfaces of the plate is satisfied. Hence, the present theory does not require the shear correction factor generally associated with the first-order shear deformation theory. Governing equations and boundary conditions are obtained using the principle of minimum potential energy. The closed-form solutions of simply supported sandwich plates are obtained. The effect of the side-to-thickness ratio and plate aspect ratio on buckling and free vibration responses of simply supported square and rectangular sandwich plates is examined. Parametric effects of face sheet thickness ratios and load factor upon the critical buckling load for uniaxial and biaxial buckling analysis of square and rectangular sandwich plates for different staking sequences are studied. All numerical solutions are obtained using MATLAB® programs. The results obtained from the present theory are compared with those from classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, and the exact three-dimensional elasticity solutions as applicable.

A novel approach for buckling optimization of stiffened piezolaminated composite plates

This study presents a novel approach for optimizing the critical buckling load of the stiffened piezolaminated composite plates using a self-adaptive special relativity search (SASRS) algorithm. The fiber orientations in the layers are considered as design variables. The stability equations are first derived based on the classical laminated plate theory (CLPT) with von Karman nonlinearity. The optimization problem is implemented in MATLAB. The optimization results are obtained to indicate the effecs of various boundary conditions, applied voltages, grid shapes, angles of diagonal ribs, and plate aspect ratios on the optimal design. Numerical investigations are carried out for 10-ply symmetrical stiffened piezolaminated plates. The robustness and efficiency of the proposed SASRS algorithm in maximizing the critical buckling load of the stiffened piezolaminated plates are demonstrated by comparing the optimized results from the standard special relativity search (SRS) algorithm. It is found that the proposed optimization method has better performance than the SRS algorithm.

First Failure Load of Rectangular Laminated and Sandwich Plates Using Isogeometric Analysis

This paper investigates the first failure load of simply supported and clamped laminate and sandwich plates loaded by a distributed normal traction on the top surface. A third-order shear and normal deformable plate theory, the isogeometric basis functions, and five failure criteria, namely, the maximum stress, the Tsai–Wu, the Tsai–Hill, the Hoffman, and the Hashin for laminated plates, and only the Tsai–Hill criterion for sandwich plates are used in this study. Of these, Hashin’s criteria distinguish between the fiber and the matrix failure. The in-plane stresses are found from the plate displacements and Hooke’s law, and the transverse stresses are recovered by integrating the equilibrium equations through the thickness. Effects of the plate aspect ratio, the fiber angle, the face sheet materials, and the core materials on the first failure load are identified. The computed results are found to agree well with those reported in the literature. Whereas the five failure criteria for laminated plates predict nearly the same value of the first failure load, they do not provide the same location of the failure initiation.

Revealing the Effects of Polymer Additives on Zn Dendrite Suppression in Aqueous Zn Batteries via in-Situ EC-AFM

Polyethylene glycol (PEO) is a commonly used polymer in the field of batteries for achieving flat and uniform electrodes to enhance the performance of batteries, such as lithium batteries and zinc (Zn) batteries. However, the impact of PEO on the electrochemical deposition of Zn metal on electrodes remains uncertain. In this study, we selected ZnSO4 solution as electrolyte and copper (Cu) substrates as electrodes, which are widely applied in Zn batteries. We used in situ electrochemical atomic force microscopy (EC-AFM) to observe the nucleation and growth of Zn metal plates on the Cu substrate in the presence of different concentrations of ZnSO4 and PEO additives. Our results indicate that PEO biases the crystallographic orientation of the initially deposited Zn metal nuclei, but does not have an obvious influence on subsequent growth. Based on our findings, we hypothesize that PEO primarily interacts with the Cu substrate to adjust the interfacial energy of the Cu-electrolyte interfaces. In contrast, due to the lack of apparent change in the Zn growth rate, we postulate that PEO does not affect the delivery rate of Zn2+ to the electrode surface. The consistent aspect ratio of the Zn plates combined with the lack of an effect on growth rates further suggests that PEO does not interact significantly with the surface of the newly formed Zn plates. The Zn metal will undergo surface reorganization in a mildly acidic aqueous solution as a result of oxidation of Zn, which is not affected by PEO adsorption. Our findings provide both insight into the underlying mechanism by which PEO promotes electrode flattening in Zn batteries and a standardized protocol for elucidating the impact of additives on the morphological evolution of interfaces during electrochemical deposition.Work by C.O. was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

Aeroelastic Stability and Design of Laminated Composite Sandwich MRE Plates Using Surrogate Metaheuristics Optimization

Sandwich composite materials with elastomeric cores and high-strength face layers have widespread applications in various engineering sectors as passive damping structural materials. This study examines the dynamic properties of sandwich plate with laminated composite face layers and smart magnetorheological elastomer (MRE) core under the action of the aerodynamic and hygrothermal loads. The dynamic model based on Kirchhoff’s plate theory is employed and the equations of motion are derived using Hamilton’s principle. The flow conditions are assumed supersonic and modeled by the first-order piston theory. The natural frequencies and aerodynamic pressure distributions are obtained from finite element model. Upon validating the model, the effects of various factors such as moisture, temperature and plate geometry on the critical aerodynamic pressure for different boundary conditions and magnetic fields are studied. Using these parametric data, a regression model is developed using Back-Propagation Neural Network to predict the critical aerodynamic pressure as a function of effective geometrical parameters. In order to enhance the aerodynamic stability, the critical aerodynamic pressure is maximized by the optimal selection of plate aspect ratio, face layer ply orientation sequence and core layer thickness ratio via the modified teaching–learning-based optimization (MTLBO) technique employing the trained neural network-based surrogate model. The approach is very convenient and it has been found that nondimensional aerodynamic pressure along with loss factor has improved almost twice. In the sensitivity analysis study, it is noticed that changes in aspect ratio around the optimal point have a relatively drastic effect on the critical aerodynamic pressure at all the face layer ply configurations.

Thermomechanical bending of functionally graded carbon nanotubes reinforced composite plate by meshless method

AbstractFunctionally graded (FG) carbon nanotubes (CNTs) reinforced composite possessing continuously varied material properties have received extensive concern in the area of aviation, automotive, military, and spaceflight. The nonlinear bending of FG CNT composite is performed by developing a novel meshless model on the base of Smoothed Particle Hydrodynamics (SPH) method. The equivalent temperature relative material properties of composite is established in the light of the extended rule of mixture model. Different gradient dispersions of CNTs are taken into account and modeled. The governing equations are explored using the Mindlin theory and discretized though a symmetric SPH method with high prediction ability. The developed model is verified by analyzed several examples and compared to the solution obtained in literature. Influences of CNT dispersion, content, plate aspect ratio, boundary conditions and lamination angle on the bending response are elaborated. The present study provides an alternative potential method to solve the mechanical performances of FG CNT composites based on the meshless SPH formulation.Highlights Thermo‐mechanics of FG‐CNTRC is firstly solved by SPH method. The model is verified by solving the benchmarks in literature. Nonlinear bending behaviors of FG‐CNTRC are demonstrated. The minimum deflection take place in FG‐X type composite. For laminate plate, the smallest deformation occurs in 0° CNTRC.

Dynamic stability of the Mindlin-Reissner plate using a time-modulated axial force

A time-periodic axial force acting on a continuous structure can be destabilized by parametric excitation. Moreover, it is capable of increasing the equivalent damping and shortening the transient vibrations. In this work, this concept is extended, and dynamic stability of a Mindlin-Reissner plate is analyzed. The FE formulation for the four-node plate element is derived by employing the variational approach including the action of an axial force. The stability of the time-periodic system is evaluated both numerically and analytically, using Floquet theory and first-order approximation based on the averaging method, respectively. The influence of plate length, thickness, and aspect ratio on dynamic stability is highlighted. It is demonstrated that the instability tongue at a parametric combination resonance frequency of the summation type is shifted toward higher axial force amplitudes by increasing the plate width and decreasing the plate length. Alternatively, the axial force acting in the vicinity of a parametric combination frequency of the difference type shows a parametric antiresonance which is maximized by exactly the opposite tuning of the plate design. This guideline is important when plate design under the action of a harmonic axial force is considered.

Influence of the CNT addition on the mechanical performance of three-phase composite plates

This work has analyzed the bending, free vibration and buckling performance of a three-phase (CNT/Polymer/Carbon fiber) composite plate as a function of the carbon fiber volume fraction and the CNT volume fraction, under several values of the plate aspect ratio (a/b) and the plate slenderness parameter (h/b), and considering the presence of defects due to the poor dispersion on the CNTs. Based on a two-steps homogenization technique, the mechanical properties of the carbon fibers reinforced –CNT enriched– polymeric matrix are computed. Then, the mechanical response of the plate is computed according to the first-order shear deformation plate theory solutions presented in Reddy’s books. The numerical results have revealed the presence, in three-phase (CNT/Polymer/Carbon fiber) composite plates, of a CNT volume fraction threshold above which the bending, free vibration and buckling performance of the plate decay with the carbon fiber volume fraction.

Bevameter pressure-sinkage testing on snow

Pressure-sinkage tests for determining vehicle sinkage on soft soils can be done using a bevameter. In this study, pressure-sinkage tests were performed on snow, which, like soil, is a granular material. However, unlike soil, snow layers are inhomogeneous with varying properties. For tracked vehicles, the shape of the track print is rectangular, which is why rectangular plates are often used for pressure-sinkage tests. The aim of this study was to see if smaller circular plate or smaller rectangular plates can be used instead of larger rectangular plates, and to understand the possible limitations of using small plates. Radius for the circular plate was chosen to be equal to the width of the rectangular plate. Three measuring sessions were performed at different locations during different snow conditions using circular pressure plates and rectangular pressure plates of different aspect ratios. The results show that smaller rectangular plates can be used if the width of the plates remains the same, or circular plates can be used if the radius of the circular plate is equal to the width of the rectangular plate. Limitation comes with increasing pressure, which occurs more quickly with larger-area plates, as larger plates sense solid ground more rapidly than smaller plates. To avoid this, snowpack thickness should be a minimum of five times thicker than maximum sinkage.

Continuous precipitation behavior of Mg17Al12 phase during multiple steps of twinning-aging procedure in Mg-Al alloys

Twinning was regarded as an effective way to modify the precipitation in Mg alloys. Two procedures were designed to illustrate twinning-aging consequence on Mg17Al12 phase evolution. The effect of multiple steps of twinning-precipitation on the morphology and density of the continuous precipitates inside the twins and the matrix were comprehensively analyzed through phase-orientation related observation. The results show the shape of precipitates in twins was similar to that in the matrix as the CPs mostly lay on the basal planes with an asymmetric-lozenges shape. The CPs were remarkably refined and its density became much higher inside twins. Moreover, the aspect ratio of the CP plates in twins was around 45% of that in the matrix, which means the CPs inside twins became more globular. The precipitation behavior of Mg17Al12 phase inside double extension twins was different from the primary twin or the matrix. The Mg17Al12 phases lay on both basal and prismatic planes can be observed in double twins of two-step precipitation. The growth behavior of pre-precipitates in twins is different from those in the matrix. The growth rate along its thickness became higher than that in the matrix, which is probably related to dislocation-assisted diffusion at the basal plane.

Effect of heat treatment on microstructure and mechanical properties of Mg-6Gd-3Y-0.5Zr alloy fabricated by wire arc additive manufacturing

Heat treatment is necessary for GW63K (Mg-6Gd-3Y-0.5Zr, wt%) alloy fabricated by wire are additive manufacturing (WAAM) to improve the mechanical properties before final applications. Considering the unique solidification process and microstructure of WAAMed GW63K alloys, the heat treatment parameters must be different from the cast or forged ones. Thus, the present paper investigated the influence of solution temperature and time on the microstructure and mechanical properties of WAAMed GW63K, as well as the aging temperature and time. It was found that the as-deposited alloy exhibited fine equiaxed α-Mg grains with an average size of 13 μm and few eutectic phase Mg24(Gd, Y)5 around the grains. The proper temperature of solution treatment was 480℃ and the proper time was 0.5 h, lower and shorter than cast ones. After solution treatment, the average size of α-Mg grains almost remained the same and nearly all of the eutectic phase dissolved. To exert precipitation strengthening to a larger extent, we conduct aging treatment at 175°C, 200°C, and 225°C and draw their age-hardening curves. Besides, a superior strength /ductility trade-off was obtained peak aging at 200°C for 80 h, with the ultimate tensile strength of 337±8 MPa, yielding strength of 231±2 MPa, and elongation of 8.9±1.0%. This outstanding strength can be accounted for by the refinement strengthening of fine microstructure inherited from as-deposited GW63K alloy and precipitation strengthening from dense β′ precipitates with a remarkable plate aspect ratio. Besides, suitable β′ precipitates could support a favorable work hardening effect and compatible deformation capability.

The Application of the Modified Lindstedt–Poincaré Method to Solve the Nonlinear Vibration Problem of Exponentially Graded Laminated Plates on Elastic Foundations

The solution of the nonlinear (NL) vibration problem of the interaction of laminated plates made of exponentially graded orthotropic layers (EGOLs) with elastic foundations within the Kirchhoff–Love theory (KLT) is developed using the modified Lindstedt–Poincaré method for the first time. Young’s modulus and the material density of the orthotropic layers of laminated plates are assumed to vary exponentially in the direction of thickness, and Poisson’s ratio is assumed to be constant. The governing equations are derived as equations of motion and compatibility using the stress–strain relationship within the framework of KLT and von Karman-type nonlinear theory. NL partial differential equations are reduced to NL ordinary differential equations by the Galerkin method and solved by using the modified Lindstedt–Poincaré method to obtain unique amplitude-dependent expressions for the NL frequency. The proposed solution is validated by comparing the results for laminated plates consisting of exponentially graded orthotropic layers with the results for laminated homogeneous orthotropic plates. Finally, a series of examples are presented to illustrate numerical results on the nonlinear frequency of rectangular plates composed of homogeneous and exponentially graded layers. The effects of the exponential change in the material gradient in the layers, the arrangement and number of the layers, the elastic foundations, the plate aspect ratio and the nonlinearity of the frequency are investigated.

The assessment of electric voltage influence on vibrational behavior of intelligent sandwich plates with GO-reinforced metal foam core and piezoelectric actuator face sheets

In this research, it is tried to study the effect of the external electric voltage on the vibrational behavior of a smart sandwich plate made of graphene oxide-strengthened metal foam nanocomposite core and two piezoelectric face sheets for the first time. The sandwich plate is modeled utilizing first-order shear deformation theory. The effective material properties of the core layer are estimated with the aim of the blend of Halpin-Tsai micromechanical model and rule of the mixture while considering different graded graphene oxide distribution patterns. Additionally, various porosity distributions are regarded in the metal matrix of the core layer. The partial differential equations of motion are derived using Hamilton’s principle and the derived governing equations are solved through Navier’s solution. To perform an accurate verification, the obtained results are compared with different literature investigations. Afterward, the influence of various important variants including external electric voltage, aspect ratio of plate, core to face sheet thickness ratio, different porosity distribution patterns, porosity coefficient, nanofillers weight fraction, and various distribution patterns of graphene oxides on the dimensionless frequency of smart sandwich plate in the framework of a group of tables and figures.

Buckling analysis of rectangular plates with rotationally restrained edges subjected to linearly varying in-plane loading

This study addresses a comprehensive procedure for the buckling behavior of rectangular plates with rotationally restrained edges. They are subjected to uniaxial in-plane load that varies linearly from compression to bending. The load is applied to opposite edges with variable boundary conditions, ranging from simply supported to clamped. The other edges can also be free, guided, or between them. For the first time, the generalized integral transform technique (GITT) is applied to the buckling equation of such a plate. The integral kernel perfectly satisfies the plate boundary conditions and its constituent terms are limited to the approximate range of ±1 which prevents the numerical instability. The transformed equation is a set of linear algebraic equations which establish an eigenvalue problem. The plate buckling coefficient, and corresponding mode shape (contours of the buckled plate, the number of half-waves in each direction, etc.) are presented according to variations of the edge relative stiffness as well as the plate aspect ratio, the loading shape, and Poisson's ratio. The latter parameter has a significant effect on the buckling behavior when at least one of the edges is free, guided, or between them. This portion is developed for auxetic materials (negative Poisson's ratios), and it was concluded that the minimum buckling load mostly occurs as the Poisson's ratio tends to zero.

Natural frequency analysis of bidirectional functionally graded plates based on a refined shear theory using nonconforming finite elements

In this study, we investigate the free vibrations of functionally graded plates using the refined shear deformation theory. These plates have material properties that vary in two directions: the z-axis and the x-axis. The variation follows a bidirectional gradation described by a power law based on the Voigt rule of mixture. The displacement field is characterized by four variables, chosen in such a way that shear strain and stress vanish, and traction is free at the upper and lower surfaces of the plate. This eliminates the need for a shear correction factor, as required in the first-order shear deformation theory. We derive the equations of motion and related boundary conditions using Hamilton’s principle and a finite element approach. The proposed element ensures C1-continuity by including the first derivative of the transverse deflection in the kinematic field. For spatial discretization, we employ a rectangular element with four nodes and two interpolation schemes. Lagrangian shape functions are used for in-plane displacement, while a Hermitian scheme is employed for transverse deflection. This enables us to determine the natural frequencies of the 2D-FG plates. We demonstrate the validity, convergence, and accuracy of the proposed element through illustrative examples and compare it with previous literature. Furthermore, we conduct numerical analyses to examine the effects of transverse shear function, boundary conditions, plate aspect ratio, slenderness ratio, and gradation indices on the natural frequencies. The developed model provides insights into the significance of natural frequencies in the design of various structural elements, including 2D-FG plates.

A novel formula for predicting the ultimate compressive strength of the cylindrically curved plates

"The present study aims to develop an empirical formula to predict the ultimate compressive strength of unstiffened cylindrically curved plates. Drawing from an extensive analysis of 400 unique curved plate scenarios under longitudinal compression, we investigated critical parameters: the flank angle (denoted as θ), plate aspect ratio (denoted as a/b), and plate slenderness ratio (denoted as β). The ANSYS Nonlinear Finite Element Method (NLFEM) was employed to assess each scenario, considering the average level of initial imperfections (denoted as 0.1β2t) and configurations of one-bay and one-span. It is important to note that the models were designed without accounting for the effects of residual stresses. The simulation data generated from this analysis served as the foundation for developing our empirical formula. The proposed formula strongly agreed with the numerical simulations and experimental test results. This research provides structural engineers with a reliable predictive tool, aiding in more accurate predictions of the ultimate limit state (ULS) of curved plates during early design phases.

Natural Frequency Characteristics of Stiffened FG Multilayer Graphene-Reinforced Composite Plate with Circular Cutout Resting on Elastic Foundation

In this research, natural frequency response of functionally-graded multilayer graphene-reinforced composite plate with circular cutout reinforced by orthogonal stiffeners is investigated for the first time. The structure is surrounded by Winkler-type elastic support. The plate is composed of polymethyl methacrylate (PMMA) as matrix material and reinforced by graphene platelets (GPLs). The material of the orthogonal stiffeners is the same as that for the matrix. Rule of mixtures and Halpin–Tsai approach are applied to estimate the effective material properties of the composite plate. Third-order shear deformation plate theory and finite element procedure is employed to obtain the element matrices of the structure. Natural frequencies and mode shapes of the stiffened plate are reported for different variables such as nanofillers dispersion patterns, width and height of the stiffeners, aspect ratio of plate, plate thickness ratio, weight fraction of nanofillers, number of stiffeners, boundary conditions, elastic foundation stiffness parameter and size of circular cutout. The obtained results denote that with the addition of a set of stiffeners, fundamental frequency enhanced up to 32.3% with just about 10% increase of mass.