Neutral Plane Research Articles

Insights from the numerical analysis of axially loaded piles in liquefiable soils

Axially loaded piles in liquefiable soils can undergo severe settlement due to an earthquake event. During shaking, the settlement is caused by the decreased shaft and tip capacity from excess pore pressures (ue) generated around the pile. Post shaking, soil settlement from the reconsolidation of liquefied soil surrounding the pile results in the development of additional load (known as drag load), causing downdrag settlement of the pile. Estimating the axial load distribution and pile settlement is essential for designing and evaluating the performance of axially loaded piles in liquefiable soils. In practice, a simplified neutral plane solution method is used, where the liquefied soils are modeled as a consolidating layer without considering the effect of ue generation/dissipation. A TzQzLiq analysis models the load and settlement response of axially loaded piles in liquefiable soils by accounting for the effect of excess pore pressure (ue) generation/dissipation on the shaft and tip capacity. This paper presents the deficiencies of the simplified neutral plane method in predicting the drag load as well as the downdrag settlement by comparing it with the TzQzLiq analysis validated with hypergravity model tests. The results show that the drag load and the downdrag settlement predicted by the neutral plane method might be over- or under-estimated depending on the pile load, the rate of ue dissipation, and the soil settlement. For the cases studied, it was found that most of the pile settlement occurs during shaking due to the decrease in the pile's tip resistance from the development of ue in the soil surrounding it. While large drag loads develop during reconsolidation, the resulting downdrag settlement is small. While the neutral plane method generally predicted a downdrag settlement comparable to that of the TzQzLiq analysis, it overpredicted drag load and could not predict co-seismic settlement. Finally, the study advocates for the development and use of a displacement-based procedure (accounting for all the mechanisms occurring during and after an earthquake event) such as based on TzQzLiq analysis in accurately evaluating the performance of the pile (i.e., the pile settlement and the maximum load), thus providing an overall safe, efficient, and optimized design.

Effect of porous defects on mechanical behavior of functionally graded materials

Porous defects in functionally graded materials (FGMs) significantly change their mechanical behavior, in particular, affecting the displacement of the neutral plane and stress distribution. Defects such as porosity reduce material bending strength while enhancing compression strength and can lead to significant transverse effects. The purpose of this study is to clarify the influence of porosity on transverse effects based on new kinematic model. This research consider in detail a particular case of this model, that allows take into account two Poisson`s effects separately. This study examines the influence of porosity on FGM, highlighting the critical role of changes in Poisson’s ratio through thickness. The theory used for analytical solution satisfies the nullity of the shear stresses at the upper and lower surfaces of the plate without using the shear correction factor. The network of pores proposed to be empty or filled with low-pressure air and material properties graded by thickness according to power-law and exponential models. Navier solution method is used to solve the governing differential equations of equilibrium. The concentration of porosity at the center of the plate or in separate layers results in a reduction in normal tensile stresses along the longitudinal coordinate, suggesting that strategic placement of porosity can be used to reduce stress concentrations, potentially enhancing the structural integrity and performance of functionally graded materials under mechanical loading.

Bending of polymer films: a method for obtaining a compressive modulus of thin films.

Due to the advent of various foldable electric devices, it is becoming increasingly important to understand the bending properties of film materials. Bending of isotropic materials may be trivial if elastic deformation is small within a range of linear elasticity, which is often the case for bending. However, bending of polymer films, often used in recent foldable devices, may not be the case. Polymer films are frequently fabricated with stretching, which induces anisotropic orientation of molecular chains. In addition, there are many studies on bimodulus materials, which suggest the importance of the difference in tensile and compressive elastic moduli, i.e., the importance of elastic asymmetry, considering that bending involves compression and extension. In this study, we extended the standard linear elastic theory to include elastic anisotropy and elastic asymmetry and developed a method for obtaining compressive moduli of films, which cannot be obtained by a simple compression test because thin films under compression buckle at small strains. Our method is based on a bending test combined with a uniaxial tension test, which allows the measurement of Poisson's ratio in addition to Young's modulus, which are both anisotropic and asymmetric. To test our theory and method, we further performed experiments on biaxially stretched poly(ethylene terephthalate) (PET) films. As a result, we found non-negligible anisotropy in Poisson's ratio and non-negligible asymmetry (bimodulus) in tensile and compressive moduli. We further justify our framework by demonstrating a clear data collapse to show agreement between experiment and theory, clarifying limitations. Our results suggest the importance of elastic anisotropy and elastic asymmetry in bending of industrial films and give fundamental knowledge on this subject, which would be useful for applications. Such applications include the control of the position of the neutral plane and precise measurements of elastic moduli and Poisson's ratio, which are crucial, e.g., for the development of tough flexible electric devices and for the structural designs using compliant mechanisms.

Lightweight structure and unequal length flexible support design of a 1.3×1.2 m rectangular, horizontally supported mirror

A lightweight rectangular mirror designed for a space telescope features a lightweight structure and an innovative unequal length flexible support design. This design incorporates a three-point back support structure, which maintains the surface accuracy of the mirror assembly in a horizontal optical testing layout. The topology optimization design method is applied for the lightweight design of a SiC mirror. According to the principle that optimal gravity surface accuracy of the mirror is achieved when the pivot center of the flexible support coincides with the neutral plane of the mirror, an unequal length flexible support scheme is proposed. Furthermore, a “neck-shrinking” flexible support structure is designed to enhance the comprehensive surface quality of the mirror assembly, achieving better than λ/140 (RMS = 4.5 nm, λ=632.8nm). Following the completion of mirror polishing, an optical test system is established. The test results confirm that the surface shape accuracy satisfies the requirements of the design index. In addition, the mechanical design has been corroborated through dynamic testing.

Simultaneous Necking and Barreling Deformation Behaviors in Bending of Single-Crystal Gold Micro-Cantilever.

Necking and barreling deformation behaviors occurred simultaneously during the bending test of a single-crystal gold micro-cantilever (sample A) with the loading direction parallel to the [1-10] orientation and the neutral plane parallel to the [110] orientation. In contrast, for another single-crystal gold micro-cantilever, sample B, with the loading direction aligned parallel to the [0.37 -0.92 0.05] orientation and the neutral plane parallel to the [0.54 0.28 0.78] orientation, predominant slip band deformation was noted. Sample A exhibited activation of four slip systems, whereas sample B demonstrated activity in only a single-slip system. This difference suggests that the presence of multiple slip systems contributes to the concurrent occurrence of necking and barreling deformations. Furthermore, variations in the thickness of the micro-cantilevers resulted in observable strengthening, indicating that the effect of sample size is intricately linked to the geometry of the cross-section, which we have termed the "sample geometry effect".

In vivo analysis of ankle joint kinematics and ligament deformation of chronic ankle instability patients during level walking.

Introduction: Chronic ankle instability (CAI) carries a high risk of progression to talar osteochondral lesions and post-traumatic osteoarthritis. It has been clinically hypothesized the progression is associated with abnormal joint motion and ligament elongation, but there is a lack of scientific evidence. Methods: A total of 12 patients with CAI were assessed during level walking with the use of dynamic biplane radiography (DBR) which can reproduce the in vivo positions of each bone. We evaluated the uninjured and CAI side of the tibiotalar and subtalar joint for three-dimensional kinematics differences. Elongation of the anterior talofibular ligament (ATFL), calcaneofibular ligament (CFL), and posterior talofibular ligament (PTFL) were also calculated bilaterally. Results: For patients with CAI, the dorsiflexion of the tibiotalar joint had reduced (21.73° ± 3.90° to 17.21° ± 4.35°), displacement of the talus increased (2.54 ± 0.64mm to 3.12 ± 0.55mm), and the inversion of subtalar joint increased (8.09° ± 2.21° to 11.80° ± 3.41°). Mean ATFL elongation was inversely related to mean dorsiflexion angle (CAI: rho = -0.82, P < 0.001; Control: rho = -0.92, P < 0.001), mean ATFL elongation was related to mean anterior translation (CAI: rho = 0.82, P < 0.001; Control: rho = 0.92, P < 0.001), mean CFL elongation was related to mean dorsiflexion angle (CAI: rho = 0.84, P < 0.001; Control: rho = 0.70, P < 0.001), and mean CFL elongation was inversely related to mean anterior translation (CAI: rho = -0.83, P < 0.001; Control: rho = -0.71, P < 0.001). Furthermore, ATFL elongation was significantly (CAI: rho = -0.82, P < 0.001; Control: rho = -0.78, P < 0.001) inversely correlated with CFL elongation. Discussion: Patients with CAI have significant changes in joint kinematics relative to the contralateral side. Throughout the stance phase of walking, ATFL increases in length during plantarflexion and talar anterior translation whereas the elongation trend of CFL was the opposite. This understanding can inform the development of targeted therapeutic exercises aimed at balancing ligament tension during different phases of gait. The interrelationship between two ligaments is that when one ligament shortens, the other lengthens. The occurrence of CAI didn't change this trend. Surgeons might consider positioning the ankle in a neutral sagittal plane to ensure optimal outcomes during ATFL and CFL repair.

Vibration Study of Functionally Graded Microcantilever Beams in Fluids Based on Modified Couple Stress Theory by Considering the Physical Neutral Plane

Theoretical studies on the vibration of microcantilever beams in fluids, which are commonly used in micro- and nanoelectromechanical systems (MEMS/NEMS). When microcantilever beams are subjected to photo-thermal excitation, they show that the material properties such as the dynamic response and the one-dimensional temperature field will show significant differences from the macroscopic properties when the size appearance of the microbeam decreases to the scale below a dozen micrometers. In this paper, by correcting the scale constants of the beams, the photothermal vibration model of the microbeam is established using the physical neutral plane theory. The one-dimensional heat transfer equations and scale-corrected temperature field of the microcantilever beam under laser excitation are derived, which are solved by Galerkin’s method, based on the theory of thermoelasticity, the hydrodynamic model of the beams vibrating in incompressible liquids proposed by Sader et al. and the theory of Euler–Bernoulli beams. The equations governing the vibration of micro-cantilever beams corrected for scale effects in different fluids when subjected to photothermal excitation are obtained. The results show that the temperature field, resonant frequency, and quality factor of the microbeam will have a significant upward drift when the size of the microbeam is close to the scale parameter, and the scale effect has a non-negligible influence on the macroscopic performance parameters; the upward drift is gradually weakening when the thickness to scale ratio gradually increases. Finally, the property of the beam is almost the same as that of the theory when the thickness of the beam is 10 times the scale constant. The correction of the theory by the scale effect is insignificant.

Vibration Analysis of Porous Cu-Si Microcantilever Beams in Fluids Based on Modified Couple Stress Theory.

The vibrations in functionally graded porous Cu-Si microcantilever beams are investigated based on physical neutral plane theory, modified coupled stress theory, and scale distribution theory (MCST&SDT). Porous microcantilever beams define four pore distributions. Considering the physical neutral plane theory, the material properties of the beams are computed through four different power-law distributions. The material properties of microcantilever beams are corrected by scale effects based on modified coupled stress theory. Considering the fluid driving force, the amplitude-frequency response spectra and resonant frequencies of the porous microcantilever beam in three different fluids are obtained based on the Euler-Bernoulli beam theory. The quality factors of porous microcantilever beams in three different fluids are derived by estimating the equation. The computational analysis shows that the presence of pores in microcantilever beams leads to a decrease in Young's modulus. Different pore distributions affect the material properties to different degrees. The gain effect of the scale effect is weakened, but the one-dimensional temperature field and amplitude-frequency response spectra show an increasing trend. The quality factor is decreased by porosity, and the degree of influence of porosity increases as the beam thickness increases. The gradient factor n has a greater effect on the resonant frequency. The effect of porosity on the resonant frequency is negatively correlated when the gradient factor is small (n<1) but positively correlated when the gradient factor is large (n>1).

Forming of monoaxially curved thin-walled T-section integral panels by double-sided laser peening

Thin-walled T-section integral panels are widely used in the aerospace industry for achieving lightweight and high performance, but their strict manufacturing requirements present challenges to current forming processes. This study proposes the double-sided laser peening (DSLP) process and develops corresponding models to achieve the forming of monoaxially curved T-section integral panels. An eigen-force model is derived to describe deformation behavior and reveal the underlying forming mechanism. The results indicate that bending deformation is driven by the moment originally induced by the in-plane eigen-force deviating from the neutral plane. Full-covered DSLP on the skin results in bending deformation towards the stiffeners, and vice versa. Additionally, DSLP on complementary regions induces identical bending deformations in opposite directions. The undesired bending distortion appeared in single-sided laser peening is eliminated by DSLP, as the action point of the eigen-force migrates to the neutral plane of the skin or stiffeners after DSLP, thereby preventing the generation of bending moments. Subsequently, drawing inspirations from topology optimization methods, a customized process planning model is developed for DSLP of monoaxially curved T-section panels. The globally convergent method of moving asymptotes is applied to solve the process planning model. The formed T-section panels, guided by the solution of the process planning model, exhibit good consistency with the objective shape. By unleashing the potential of double-sided laser peening in driving bending, this study provides a novel strategy for forming large-scale complex panels with stiffeners.

Experimental Measurement of the Stress Gradient in a Bent Sheet

Stress gradients were experimentally measured in a 316 stainless steel sheet after bending with a press brake. Two different tool radii and three different bend angles were used to produce plastically bent sheets. Microhardness tests were performed across the thickness of the bent sheet, and a correlation between microhardness and strength was experimentally determined and was used to obtain the stress gradient. The position of the experimentally determined neutral plane correlated well with theory. Theoretical calculations of the stress gradient were made using a power law constitutive equation along with a simple mechanics analysis of plastic bending. Four of the six bending experimental conditions had reasonable correlation with the theoretical calculations. Ideas for improving this experimental method are discussed.

Model refinements with experimental validation in piezoelectric plate actuators

The axisymmetric vibration analysis of circular plates with piezoelectric layers and step changes in plate thickness is conducted. For the chosen configurations, it is necessary to solve a coupled system of differential equations for extensional and flexural vibration to obtain accurate modal results. The adopted computational approach is based upon the classical transfer matrix method. Instead of employing analytical solutions in the form of e.g. Bessel functions, matrix exponentials of the system matrix are directly computed in the transfer matrices for finding highly accurate solutions. The developed approach has enabled the complete quantitative modal analysis in piezoelectric actuators. The procedure is firstly verified against available analytical results for natural frequencies and modes shapes in circular homogeneous plates, and by using finite element simulations for plates with asymmetric step changes in thickness. Ultimately, the developed approach is validated against experimental results of relevance to applications in piezoelectric synthetic jet actuation. The obtained numerical results for modal parameters and frequency response functions are in excellent agreement with the available analytical results, and with previous and newly presented in the paper experimental data, when considering the inherent uncertainty in parameter values. Based on extensive experimental results, realistic damping is introduced in the model of piezoelectric plate actuators. Importantly, it is shown that solutions of high accuracy can be obtained by a more general coordinate system than that traditionally linked to the plate neutral plane(s).

Flexible multi-electrode neural probe using active-matrix design of transistor array

To realize a brain-machine interface, a neural probe is one of key hardware. For the neural probe, a high spatial resolution of an electrode array, high electrical sensitivity, and mechanical flexibility remain challenging and essential issues. In regard to these, implantable multi-electrode neural probe employing active-matrix design with field effect transistors (FETs) can attract attention due to their advantages of a suitable integration density and good signal-amplifying abilities. Therefore, we developed a flexible multi-electrode neural probe employing an active-matrix design based on a two-transistor (2T) scheme for application to a flexible neural signal recording probe. As a proof of concept, 4 × 8 electrode array (32 channels) with TFTs was demonstrated. For the flexible active-matrix design, back-gate indium-gallium-zinc-oxide (IGZO) thin film transistors (TFTs) were fabricated on a polyimide (PI). The TFTs used here can amplify signals and achieve a switching function to drive the active matrix. The probe structure was encapsulated by the same PI material again to achieve flexibility with good reliability, as the sandwich-like structure can induce a neutral plane on the TFT and electrodes. To ensure a high signal-to-noise ratio, the structural and process parameters of the TFT were studied. Among different annealing times and temperatures of the IGZO TFT, the optimized annealing condition of the TFT was found to be 250 °C a 1 hour on a flexible substrate. The width over length of the transistors was optimized to 50 μm/10 μm, and the field-effect mobility was 8.33 cm2/V·s. The on current was 2.28 × 10−6 A at a low driving voltage of 5 V. The transconductance was 2.16 μS and the threshold voltage (Vth) was 1.6 V. By applying 5 V, the switching TFT was turned on, and a doubly amplified signal (> 2.4 times) could be measured on the drain line. The electrode array probe with the active-matrix design can use for accurate neural recording and herald a new generation of flexible neural probes with high spatial resolutions.

Stress distribution in multilayer structural element subjected to skew bending

Results of researches on strength and stiffness of diagonally bending sandwich girders having geometric and/or stiffness asymmetry have been given. A mathematical module for calculation of normal strain (strength) and stiffness on bending at any cross-section point of sandwich girder has been proposed. The kinetics of stiffness on bending and strength variation dependences when geometric parameters of a cross-section and tension modulus ratios of girder layers are changing have been examined. It has been established that the strength of a diagonally bending sandwich girder on the whole depends on the position of the centre of stiffness and the position of the neutral plane.

Ultrathin (∼30 µm) flexible monolithic perovskite/silicon tandem solar cell

The efficiency of rigid perovskite/silicon tandem solar cells has reached 33.9%. However, there has been no report on flexible perovskite/silicon tandem solar cells due to the challenge of overcoming the poor light absorption of ultrathin silicon bottom cells while maintaining their mechanical flexibility. Herein, we report the first demonstration of the perovskite/silicon tandem solar cell based on flexible ultrathin silicon. We show that reducing the wafer thicknesses and feature sizes of the light-trapping textures can significantly improve the flexibility of silicon without sacrificing light utilization. In addition, the capping of the perovskite top cells can further improve the device’s mechanical durability by shifting the neutral plane toward the silicon surface that is prone to fracture. Finally, the resulting ultrathin (∼30 µm) flexible perovskite/silicon tandem solar cell achieves a certified stabilized efficiency of 22.8% with an extremely high power-to-weight ratio of 3.12 W g−1. Moreover, the flexible tandems exhibit remarkable bending durability, maintaining 98.2% of their initial performance after 3000 bending cycles at a radius of only 1 cm.

Experimental and numerical investigations on fire development in a timber-based compartment with identification of characteristic events

An experiment and numerical simulations were carried out to investigate the mechanism of the incipient and growth stages of a building fire. The building, constructed in the 1980s with wooden components, has one compartment and one opening. The average fire load density was 1495.3 MJ/m2, including the wooden columns, beams, furniture, etc. The evolution of indoor temperature, gas concentration, gas flow rate and burning behaviors were obtained and analyzed. To better understand the fire development process, we identified characteristic events, including pilot fire, incipient fire, pre-flashover fire spread, ceiling jet period, and flashover and spill plume. By defining dimensionless time (τ = ti/tflashover), it was found that the fire development process simulated by Fire Dynamic Simulator experienced the same characteristic events as the experiment. In this work, when flashover occurred, the neutral plane height decreased to about half the height of the opening, the velocity of hot smoke outflow was higher than 3 m/s, and the maximum thickness of the wood charred layer reached 1 cm. Two theoretical methods to estimate the heat release rate (HRR) in the fuel-controlled stage before flashover were proposed. The HRRs at the time of flashover with the two methods are at the same order of 5 MW, and the error between them was within 18.1%, which verifies the feasibility of the above methods to a certain extent. This study helps to learn the characteristics of early and growth stages of building fires with wooden components.

Free vibration of cracked FGM Mindlin plate in fluid

The free vibration of cracked functionally graded material (FGM) plate in fluid is investigated in this paper. The material components are supposed following the power law and formulated by the Voigt model. The Mindlin plate theory (MPT) including the shear deformation effect is established and the physical neutral plane is adopted to simplify the derivation due to the in-plane displacements of this plane assumed as zero. A massless linear rotational spring model (LRSM) is established to simulate the through-width surface crack. The hydrodynamic pressure at the fluid-plate interface is derived by the potential flow theory, and is regarded as the added mass of cracked FGM plate during the analyses of fluid-plate coupled vibration. The derivation and discretization of vibrational equations for cracked FGM plates in fluid are respectively achieved though the Hamilton’s principle and differential quadrature (DQ) method. The frequencies and mode shapes are iteratively calculated with these values of the vacuum case. The influences of immersed depth, fluid density, gradient index, crack depth, crack location, length-to-width ratio, length-to-thickness ratio, and boundaries on vibration characteristics are conducted in the section of numerical results. The present vibration analyses of cracked structures can be applicable to avoid structural resonance and failure.

Nonlinear postbuckling and snap-through instability of movable simply supported BDFG porous plates rested on elastic foundations

This study presents, for the first time, a novel mathematical model that can address the nonlinear buckling, postbuckling, and snap-through of bidirectional functionally graded porous simply supported plates rested on elastic foundation and subjected to uniaxial/biaxial compressive loads. The parabolic shear deformation plate theory and the von Kármán strain nonlinearity are employed to derive governing equilibrium equations relative to neutral surface plane. The governing equations that consist of four nonlinear-coupled variable-coefficients partial differential equations are discretized by using the differential/integral quadrature method. The solution methodology depends on whether the discretized nonlinear algebraic system is homogeneous (with zero force vector) or nonhomogeneous. A homogeneous system can be formulated and solved as a nonlinear eigenvalue problem. Pseudo-arc-length continuation is implemented with a proposed iterative method to predict the load-deflection paths whether the system is homogeneous or not. Theoretical analysis and numerical results indicate that the type of porosity and position of in-plane loading have significant effects on the pitchfork-bifurcation or snap-through instability response of the bidirectional functionally graded porous plate. Parametric studies are presented to illustrate the impact of gradation indices, geometrical properties, porosity, and foundation constants on the postbuckling responses of bidirectional functionally graded porous plates. The proposed model may be used in designing nuclear, marine, aerospace, and civil structures with bi-directional functionally graded material constituents.

A weak subducting slab at intermediate depths below northeast Japan.

Knowledge of the state of stress in subducting slabs is essential for understanding their mechanical behavior and the physical processes that generate earthquakes. Here, we develop a framework which uses a high-resolution focal mechanism catalog to determine the change in the position of the neutral plane before and after the M9 Tohoku-oki earthquake to determine that the deviatoric stress within the slab at intermediate depths must be very low (∼1 MPa). We show that by combining the static stress calculated from coseismic slip distributions with the stress orientations before and after the mainshock, we can determine the full deviatoric stress tensor within the subducting slab at intermediate depths. These results preclude earthquake source mechanisms that require large background driving stresses, favoring a mechanically weak subducting slab, thus providing quantitative constraints on the physical processes that generate intermediate-depth earthquakes.

Ultrathin Encapsulation Strategies with Predefined Gate Dielectric Surface Area for Flexible Crystalline Silicon Nanomembrane-Based MOS Capacitors

Ultrathin encapsulation strategies show huge potential in wearable and implantable electronics. However, insightful efforts are still needed to improve the electrical and mechanical characteristics of encapsulated devices. This work introduces Al2O3/alucone nanolaminates using hybrid atomic/molecular layer deposition for ultrathin encapsulation structures employed in crystalline silicon nanomembrane (Si NM)-based metal-oxide-semiconductor capacitors (MOSCAPs). The comprehensive electrical and mechanical analysis focused on the encapsulated and bare MOSCAPs with three gate dielectric diameters (Ø) under planar and bending conditions, including concave bending radii of 110.5 mm and 85 mm as well as convex bending radii of 77.5 mm and 38.5 mm. Combined with the Ø-related mechanical analysis of the maximum strain in the critical layers and the practical investigations of electrical parameters, the encapsulated MOSCAPs with Ø 160 μm showed the most stable electro-mechanical performance partly due to the optimized position of the neutral mechanical plane. Comparison of the electrical changes in Al2O3/alucone-encapsulated MOSCAPs with Ø 160 μm, Ø 240 μm, and Ø 320 μm showed that it is beneficial to define the gate dielectric surface area of 0.02 to 0.05 mm2 for Si NM-based wearable electronics. These findings are significant for leveraging the practical applications in ultrathin encapsulation strategies for reliable operations of crystalline Si NM-based integrated circuits.

Bending and free vibration analysis of FG circular plates using a five unknown high order shear deformation theory

In this study, the bending and free vibrations of functionally graded material (FGM) circular plates are investigated using a new quadrilateral finite element based on a five-unknown high-order shear deformation theory. The proposed model accounts for a quadratic distribution of the transverse shear stress through the plate thickness and zero transverse shear stress at the top and bottom surfaces of the plate. The properties of the plate are changed through its thickness according to a power law in which the index varies from 0 value for a fully ceramic plate to infinity for a fully metallic plate. The concept of the physical neutral plane is introduced to avoid membrane-bending coupling. The total potential energy principle and the kinetic energy are used to derive the elementary rigidity and mass matrices. The performance and the convergence of the developed element are demonstrated through examples from the literature. Furthermore, the effect of various parameters, such as the power law index and the radius-to-thickness ratio, on the plate behavior is also considered.