Central Deflection Research Articles

Axisymmetric large deformation problems of thin shallow shells with different moduli in tension and compression

When materials are in tension or in compression, their mechanical properties are essentially different, however, in existing studies it is generally ignored because of the complexity of the analysis. In this paper, a theoretical study of the problem of axisymmetric large deformation of thin shallow shells with different moduli in tension and compression (bimodular thin shallow shells) under uniformly vertical loading is presented. Based on the Föppl–von Kármán equations of flexible thin plates, the governing equation of the axisymmetric large deformation of bimodular thin shallow shells are established by introducing an appropriate curvature modification term from thin shallow shells and a bending stiffness term from bimodular plates. By selecting the central deflection as a perturbation parameter, the perturbation solution of the axisymmetric large deformation problem is derived using the perturbation method. The applications of variation method as well as the implementation of numerical simulation verify, from the theoretical and numerical perspectives, the correctness of the perturbation solution obtained. This study shows that the introduction of different moduli in tension and compression not only affects the relationship of loads vs. central deflection, but also affects the critical values of the rise-thickness ratio of bimodular thin shallow shells when the snapping phenomenon occurs. In particular, the bimodular effect may accelerate or slow down the occurrence of the snapping phenomenon of thin shallow spherical shells, according to the relative magnitude of tensile and compressive moduli. The work presented here will be helpful to analyze the mechanical response of heavily loaded thin shallow shells with obvious bimodular effect.

New quasi-three-, and two-dimensional trigonometric-cubic monomial HSDT for thermal buckling and thermo-mechanical bending analyses of FGM symmetrical/non-symmetrical sandwich plates with hard/soft core

This paper analyses the thermal buckling and thermomechanical bending responses of sandwich plates with FGM face layers, using new quasi-three-, and two-dimensional HSDTs in a unified theoretical formulation. The theory includes both the shear strain illustrated by a new shape function and the stretching effect.The theory makes use of the Hamilton principle to derive the plate governing equations. Then, the Navier procedure solved them for the simply supported boundary conditions. The theory assumed the thermal buckling loads to be uniform, linear, and non-linear distributed through the plate’s thickness, the FGM layers to be isotropically modelled according to a power law and the core layer to be isotropic and homogeneous.After validating the model's analytical solutions with those from the literature (to confirm the model's accuracy), various innovative studies extended the theory. They cover the effects of important parameter variations related to the plate dimensions, material, and the development of the proposed HSDT on the central deflection, stresses, and critical buckling temperature. The theory solutions also present the good performance of the current generalized formulation and the significant influence of the thermal effect. References in the literature can use these findings as foundational data for future research on FGM plates.

Experimental study on dynamic response of aluminum film under two spark bubbles coupling loading

The interaction of two or more bubbles with various structures is involved in many engineering problems, a clear understanding of the dynamic response process of the target under different coupling forms of bubbles loading is helpful to give full play to the value of bubbles in engineering application and avoid relevant harm. In the paper, the dynamic response process of aluminum (Al) film under the loading of a single bubble is first studied, and the deformation modes of the Al film under different bubble sizes and loading distances were considered. Then, two spark bubbles with different phase differences and initial distances are generated by a high-voltage power supply that can delay discharge, and different coupling types of two spark bubbles with different parameter combinations are given. Furthermore, the dynamic response process of the Al film with the loading of different types of coupled jets generated by bubble pairs is studied. In addition, the influence of the bubbles’ loading direction is considered. Finally, the center deflection of Al film with the loading of spark bubble pairs with different phase differences and initial distances is statistically analyzed. It is found that the piercing jet with forward loading is the most likely to cause holes in the Al film, while the relatively moving jet has the weakest damage power. The research results of this paper have a certain reference value for some engineering problems such as ship damage and ice breaking.

Structural Design of Ocean Temperature and Depth Sensor with Quick Response and High Sensitivity

The electrical sensing elements used in the traditional XBT (Expendable Bathythermograph) have problems such as low sensitivity and slow response time, and it is difficult to overcome the complex marine environment using the time–depth formula. In this paper, an ocean temperature depth sensor based on brass diaphragm and liquid filling is designed. The stress response time of FBGs with different lengths and the heat transfer time of different liquid materials are compared, and it is found that a fast response of 51 ms can be obtained by using GaInSn liquid for temperature sensing. The center deflection changes of brass diaphragms with different radii are analyzed, and the brass diaphragms with radius and thickness of 10 mm and 1 mm are selected, which still have good elastic properties under the pressure of 5 MPa. The influence of the inner metal shell section radius on the temperature and depth sensitivity is analyzed. When the final section radius is 3 mm, the temperature sensitivity of the sensor is 1.065 nm/°C, the pressure sensitivity is 1.245 nm/MPa, and the response time of temperature and depth is relatively close. Compared with the traditional temperature and depth sensors using empirical formulas for calculation, the data accuracy is improved, and a wide range of sensitivity can be tuned by adjusting the size of the internal metal shell, which can meet the needs of ocean temperature and depth data detection with high sensitivity and fast response time.

Impact damage assessment of sandwich structures with CFRP face sheets reinforced by CNTs in thermal environment

The damage behaviour of honeycomb sandwich structures with carbon nanotube (CNT) reinforced composite face sheets under high velocity impact at elevated temperatures is investigated in the present study. In order to endure the out-of-plane loading events such as bird hit, runway debris and hail stone impact, CNTs are introduced into the matrix system with the intention of improving the damage resistance. CNT reinforced carbon-epoxy composites with various weight percentages such as 0.2, 0.4, 0.6 and 0.8 were manufactured as quasi-isotropic laminates. Sandwich structures were prepared and tested under high velocity impact at room temperature and elevated temperature (393 K) using a single stage gas gun. Macro structural observations were performed on the perforated specimens and the damage area, depth, central deflection and bulging height were measured. At room temperature, the impact damage pattern was characterized by matrix cracking, fiber breakage, fiber debris, fiber push away, fiber peel up and push delamination. Plastic deformations of the matrix and kink band formation are the significant damage modes in the thermal environment. Adding a higher proportion of nanoscale reinforcement is not always judicious to get improved impact resistance; rather, the temperature dependency must be considered when designing the CFRP composite for structural applications.

Dynamic response of fully-clamped steel plate under laboratory-simulated sequential fragment impact and blast loading

Composite projectile (CP) impact, as a new in-laboratory experimental technique, was further developed to simulate sequential fragment impact and blast loading generated by cased charge explosion. New developments include modification of the equivalent relationships between main loading characteristics from the explosion and the CP impact and the improvement of the experimental setup. Then, it was used to study the dynamic response of a fully-clamped steel plate under simulated sequential fragment impact and blast loading. For comparison, a widely used traditional technique, which decoupled the two load types by generating pressure pulse on the structure with pre-formed holes to simulate the sequential loading, was also employed. Deformation processes, deformation/failure modes, and central deflections of the plates tested using the two different techniques were compared and analyzed. It was found that the traditional technique underestimated the damage caused by sequential fragment impact and pressure pulse: the plate subjected to the CP impact was found to be more susceptible to tearing fractures at high impact velocities. Finite element simulations were subsequently performed and the simulation results were validated against experimental data. The validated FE model was then employed to further evaluate the synergetic effects of sequential fragment simulating projectile (FSP) impact and impulsive loading on the ballistic performance and deformation behavior of the fully-clamped steel plate. Results indicate that while pressure pulse in the sequential loading leads to an enhanced ballistic limit of the plate, FSP impact in the sequential loading causes significant local shear and tensile deformation around the perforation, resulting in plate tearing at a lower impact velocity.

Nonlinear Bending of Sandwich Plates with Graphene Nanoplatelets Reinforced Porous Composite Core under Various Loads and Boundary Conditions

The nonlinear bending of the sandwich plates with graphene nanoplatelets (GPLs) reinforced porous composite (GNRPC) core and two metal skins subjected to different boundary conditions and various loads, such as the concentrated load at the center, linear loads with different slopes passing through the center, linear eccentric loads, uniform loads, and trapezoidal loads, has been presented. The popular four-unknown refined theory accounting for the thickness stretching effects has been employed to model the mechanics of the sandwich plates. The governing equations have been derived from the nonlinear Von Karman strain–displacement relationship and principle of virtual work with subsequent solution by employing the classical finite element method in combination with the Newton downhill method. The convergence of the numerical results has been checked. The accuracy and efficiency of the theory have been confirmed by comparing the obtained results with those available in the literature. Furthermore, a parametric study has been carried out to analyze the effects of load type, boundary conditions, porosity coefficient, GPLs weight fraction, GPLs geometry, and concentrated load radius on the nonlinear central bending deflections of the sandwich plates. In addition, the numerical results reveal that the adopted higher order theory can significantly improve the simulation of the transverse deflection in the thickness direction.

High-velocity impact resistance of stepwise gradient sandwich beams with metal foam cores

This paper aims to reveal the impact resistance of the graded sandwich beams subjected to high-velocity impacts experimentally. By using the one-stage gas gun system, the dynamic response and failure of the sandwich beams are analyzed by considering the effects of core gradient, impulsive loading, and boundary condition. The results show that the dynamic structural response of beams is noticeably influenced by the different initial failure mode under the fully clamped condition. The core gradient configuration is confirmed to have no significant effect on the impact resistance performance in terms of the dynamic central deflection, permanent deformation, and failure modes. Under the simply clamped condition, however, the core gradient effect is confirmed to be the predominant factor for the noticeably changed impact resistance performances of the sandwich beams. Due to the advantages on structural response and core compression, the graded sandwich beams have significantly better impact resistance than the uniform sandwich beam under the low-velocity impact. The negative correlation between this advantage and impulsive intensity indicates that impact resistance of the uniform sandwich beam is superior to that of the graded sandwich beams under the intensive impact. This study provides guidance of the gradient designation of the energy absorption sandwich structure and its subsequent engineering applications.

Dynamic analysis of single–layered graphene sheet subjected to a moving nanoparticle: A molecular dynamics study

The dynamic response of a single–layered graphene sheet (SLGS) subjected to a moving nanoparticle is investigated based on the molecular dynamics (MD) simulations. The time history and maximum value of the sheet’s central point deflection are considered as two main indices and reported under various circumstances. The MD simulation has the ability to provide the time history and maximum value of the central deflection along with the vibration behavior of the GS under a moving nanoparticle. The effect of the sheet’s parameters, such as dimensions, surface tension, and boundary conditions, as well as the nanoparticle’s parameters, including dimensions and velocity, on the dynamic response of the sheet is studied. It was found that the velocity of the nanoparticle does not significantly affect the deflection of the GS, while the boundary conditions and aspect ratio of the sheet have a noticeable impact on the dynamic and vibrational behavior of the GS.

Measurements of concentration distribution of hydrogen jet using deflection of center of the laser spot

The main purpose of this work is to propose a new method to evaluate the concentration distribution of the hydrogen jet by using a He–Ne laser through the jet. This research attempts to apply the expression of concentration Gaussian distribution, the refraction formula of inhomogeneous refractive index medium, and the concentration inversion function to disclose the displacement of the center of the laser spot at different heights in the gas jet. The spot images of the laser beam passing through the gas jet at three vertical heights z = 10d, 20d, 30d, and different radial positions are obtained. The radial spatial asymmetry of the gas jet is also found in the experiment. Finally, the calculated concentration distribution curve and the fluent simulation curve, it is found that the two results are very similar. Our findings show that the error between the concentration distribution of this method and the simulated concentration distribution reaches 2.43%.

Response analysis of functionally graded piezoelectric plate resting on elastic foundation under thermo-electro environment

The paper investigates the static, bending and vibration responses of the functionally graded piezoelectric plate (FGPP) resting on the two/three-parameter foundation under a thermo-electro environment. Hamilton’s principles are used with first-order shear deformation theory to obtain the governing equations. They are solved using nine noded interpolation functions with 63 degrees of freedom (DOFs) per element. It is observed that the two-parameter foundation has a shear layer dominant, and the three-parameter foundation has an additional layer of spring that plays a significant role in the static bending and vibrational behavior of the CB/UCB conditions FGPP. The applied electrical voltage and the temperature change affect the static bending, and vibrational results as the rise in temperature lead to the plate’s softening. An increase in voltage leads to a reduction in the stiffness of the plate. Also, Sg-law significantly influences the dimensionless frequency, center deflection, and axial stress compared to other laws.

Electromechanical modelling and stress analysis of RF MEMS capacitive shunt switch

This paper presents the simulation results as well as calculated results of a proposed RF MEMS shunt switch with Electro-mechanical modelling and stress gradient characteristics. The analysis is done with three membrane structures such as plane beam, incorporated with and without perforations, and non-uniform meander type beam, these are simulated in the COMSOL Multi-physics tool. The various model analysis are carried out for different values of residual stress gradients such as different structures, materials, and beam thickness. The analysis are characterized that the higher values of stress gradient are not desirable for switching action. By analyzing all the results we have observed that the stress analysis for the non-uniform meandered type switch obtained maximum stress of 35.6 MPa, and center deflection of 0.06 MPa/μm, the deformations of the beam which is the least among the considered switches.

Geometrically Nonlinear Study of Functionally Graded Saturated Porous Plates Based on Refined Shear Deformation Plate Theory and Biot’s Theory

This research presents the geometrically nonlinear investigation of functionally graded saturated porous material (FGSPM) plate under undrained conditions. In conjunction with von Karman’s nonlinearity, the refined shear deformation plate theory (RSDPT) is implemented to model the FGSPM plate. The effective material characteristics of the saturated porous plate change constantly in the thickness direction. The pores of the saturated porous plate are examined in fluid-filled conditions. Thus, the constitutive equations are established using Biot’s linear poroelasticity theory. The governing equations are developed by combining a nonlinear finite element technique with Hamilton’s principle. Then, the direct iterative approach is utilized to extract the geometrically nonlinear numerical results. The emphasis is placed on exploring the effects of numerous parameters such as Skempton coefficient, volume fraction grading index, porosity volume index, porosity distributions, and boundary conditions during the extensive numerical analyses on the linear frequency, large amplitude frequencies, and nonlinear central deflections of the FGSPM plate. It is evident from the investigation that saturated fluid in the pores substantially impacts the nonlinear deflection and vibration behavior of the FGSPM plate.

Deflection Prediction of Rehabilitation Asphalt Pavements through Deep Forest

The deep forest is a powerful deep-learning algorithm that has been applied in certain fields. In this study, a deep forest (DF) model was developed to predict the central deflection measured by a falling weight deflectometer (FWD). In total, 11,075 samples containing information related to pavement structure, traffic conditions, and weather conditions were extracted from the LTPP dataset. The performance of the DF model with custom backend settings was compared with that of models random forest (RF), multilayer perceptron (MLP), and DF built on the sklearn backend. All four deep-learning algorithms could identify the complex relationship between central deflection and relevant feature variables with high accuracy and stability. The learning and generalization abilities of DF was stronger than those of MLP and RF. The predictive performance and computation time of DF (custom) were better than those of DF (sklearn), indicating that the custom model was superior to the highly encapsulated model with sklearn as the backend. Feature importance analysis indicated that the drop load of FWD was the key factor influencing deflection. In addition, structural number, annual precipitation, and annual kilo equivalent standard axle load (kESAL) are very important features related with deflection. The feature importance of rehabilitation improvement thickness was less than the drop load, climatic factors, kESAL, structural number, and layer thickness.

Higher-order finite element solution of graphene platelets reinforced nanocomposite curved panels with uniform/non-uniform porosity

This paper reveals the deformation behavior of graphene platelets reinforced (GPLR) nanocomposite shell panels including the porosity effects. The graphene platelets are assumed to be uniformly distributed across the thickness of the panel. The spatial-dependent elastic properties of the nanocomposite are computed via the modified Halpin-Tsai micromechanics scheme including the porosity effect. Three different patterns of porosity distribution are assumed through the thickness of the panel structure, namely, uniformly distributed (UD), non-uniformly distributed (ND-Type A), and non-uniformly distributed (ND-Type B). The kinematics of the present shallow shell structure is based on the equivalent single-layer higher-order theory via Green-Lagrange geometric nonlinearity. The weak form is governed through the principle of virtual work and further solved using 2D-isoparametric finite element approximations in conjunction with Picard’s successive iteration scheme. The convergence of the present model is achieved by performing a mesh refinement process and the accuracy of the model is verified by comparing numerical results with previously published literature. Finally, the influence of porosity distribution is analyzed on the center deflection of GPLR nanocomposite curved panels subjected to uniform and sinusoidal loads of different panel geometry under different support conditions.

Low-velocity impact analysis of functionally graded porous circular plate reinforced with graphene platelets

ABSTRACT In this study, the low-velocity impact analysis of functionally graded (FG) porous circular plate reinforced with graphene platelets based on the first-order shear deformation theory is presented for the first time. The governing equations are derived using Hamilton's principle. A modified Hertzian contact law is used to model the contact force between the annular plate and the impactor. FEM approach in conjunction with the Picard method is employed to solve the governing equations of the plate under low-velocity impact. The results of the present study are compared with previous studies, and a good agreement can be seen between the results. The effects of different parameters such as porosity distribution and porosity coefficients, various GPL patterns and the weight fractions of Nano-filler on the contact force and transverse displacement of the circular plate are investigated. The results show that the effect of porosity distribution on the time history of contact force and transient central deflection of the structure is more than other parameters.

Determination of multi-physics effective properties, and actuation response of triply periodic minimal surface based novel photostrictive composites: A finite element analysis

This paper presents the novel triply periodic minimal surface (TPMS) based photostrictive composite as an alternative to naturally occurring photostrictive materials. The non-thermal, light-induced mechanical strain i.e., photostriction involves the simultaneous action of photovoltaic effect and converse piezoelectric effect. All the effective elastic, dielectric, piezoelectric, and pyroelectric properties are evaluated using the finite element analysis and compared with traditional micromechanical models for fibrous composites. Degenerated shell element is used to simulate the actuation response of unimorph cantilever and simply supported beams bonded with TPMS based photostrictive composite. The proposed photostrictive composite consists of poly{4,8-bis[5-(2-ethyl-hexyl) thiophen-2-yl] benzo[1,2-b:4,5-b’] dithiophene-2,6-diyl-alt-3-fluoro-2-[(2-ethyl-hexyl) carbonyl] thieno[3,4-b] thiophene-4,6-diyl} (PTB7-Th) as photovoltaic polymer matrix and Pb(Mg1/3Nb2/3)O3–0.35PbTiO3 (PMN-35PT) as TPMS—based filler material. The proposed TPMS based photostrictive composite induces 10 times larger actuation than 0–3 photostrictive composite. Also, the maximum deflection (3.22×10−5 m) of cantilever smart beam, achieved with Schoen-I-WP based photostrictive composite, is more than that achieved with Schoen-gyroid based photostrictive composite i.e., 2.78×10−5 m. Similar trends are obtained for simply supported smart beam where the center deflection for Schoen-I-WP based photostrictive composite and Schoen-gyroid based photostrictive composite are found to be 4.04×10−6 m and 3.49×10−6 m, respectively. The proposed novel photostrictive composite has potential for future wireless actuation applications.

Döner Kanatlı İHA’larda İçe Eğimli Yerleştirilmiş Pervanelerin Askıda Kalma Direngenliğine Etkisi

Rotary Wing UAVs (RWUAV) with control inputs (thrust, pitch torque, roll torque, yaw torque; 4 at total) less than the degree of freedom (3 angular motion, 3 linear motion; 6 at total) can move in the X-Y plane by rotating the thrust vectors, i.e their bodies. Deflections caused by external disturbances like winds are also eliminated by angular positioning which creates tractions against disruptive drag forces. However, the fact that the thrust vectors (propeller axis) placed perpendicular to the flight plane do not intersect in space carries the outer center of rotation of the platform to infinity, causing linear acting forces to deflect the system in the same direction in both translation and rotation. This coupling leads to an increase in the net deflection of the geometric center. It is observed that the deflection of the geometric center decreased and converged to the pure translation curve as the propeller placement angles decreased. With the study reported here, it has been analytically modeled and demonstrated how inward tilted propellers increase the hover stiffness of the platform against external disturbances. For future studies, the phenomenon suggesting inward tilted propellers may enhance the platform maneuverability by forming the outer rotation center (thrust vectors’ intersection point) is developed.

Impulse saturation in metal plates under confined blasts

The phenomenon of impulse saturation is revisited for metal plates subjected to confined blasts through a combination of experiments, numerical simulations, and analytical modeling. Internal blast experiments were performed on the fully-clamped aluminium square plate where its transient inelastic (mode I) response was recorded using three-dimensional digital image correlation (DIC). A methodology was proposed to idealise the confined blast induced pulse-pressure through a validated numerical model. An analytical model was developed to predict the transient central deflection of the aluminium plate under the idealised pulse pressure, where the predictions were shown to be in reasonable agreement with the DIC measurements. Parametric studies were performed to elucidate the effect of standoff distance and confinement geometry on the saturation duration, saturated impulse and deflection. It was found that both the pulse-shape and saturated impulse strongly influence the saturated deflection during internal blast loadings.

Analysis of transversely isotropic piezoelectric bilayered rectangular micro-plate based on couple stress piezoelectric theory

This paper develops a novel model of transversely isotropic piezoelectric bilayered rectangular micro-plate with a distributed load based on the couple stress piezoelectric theory. The governing equation is derived according to the variation principle. The numerical results are acquired based on the Fourier series method. Based on the new model, static deformation behaviors such as the size-dependent central deflection, the distribution of the axial strain, the distribution of the axial stress along the thickness and the normalized electrical potential of a simply supported bilayered micro-plate are investigated. It is found that the normalized center deflection shows apparent size-dependence when the thickness-length scale parameter ratio is smaller than about 10. Meanwhile, compared with the published paper, when the ratio is less than 10, the normalized center deflection predicted by the present model is smaller and more applicable. The influences of the length-width ratio on the center deflection for different conditions are also discussed in details. Moreover, the axial strain is greater in the plane further from the neutral plane, and the distribution of the axial stress is piecewise. In addition, if the ratio of piezoelectric layer thickness to length parameter is smaller than about 2, the normalized electrical potential caused by the piezoelectric effect shows stronger size-dependence. The novel model can be used to design the piezoelectric micromachined ultrasonic transducer.