Deflection Of Plate Research Articles

Stiffened Plate Analysis by Considering Follow-up Plates in the Effect of One-Way Axial Load on FPSO Vessels

Floating Production Storage and Offloading (FPSO) is the portable offshore structure. The material configuration used is the most important aspect in the FPSO structure design criteria. Plates and Stiffened and plates experience local buckling due to the external load when the hull girder collapsed. The objective of the present study is to analyze the stiffened plates taking the attached plate thickness into consideration on the FPSO in term of plate deformation and deflection located of the bottom area under tension and compression stages. In this study the attached plating thickness is varied according to FPSO data and BKI Rule. The stiffened plate elements located at the bottom are modelled by Tee-Bar element. The simply supported condition is applied to the model and the Non-Linier Finite Element Method (NLFEM) is used for the analysis. The result obtained by NLFEM shows that under tension and compression the stiffened plate of model of the thickened plate of the FPSO, the deflection are 1.75 mm and -1.75 mm, respectively. While for model of corrugated plates with BKI minimum intervening plate thickness the deflection are 1.8 mm and -1.8 mm under tension and compression, respectively.

Small-amplitude waves in a floating poroelastic plate forcing by vertical pitching plate

The linear two-dimensional problem of flexural-gravity waves generated by an oscillating rigid plate build-in a floating poroelastic plate is studied. The problem is coupled. The plate deflections and the hydrodynamics loads are determined at the same time. The liquid under the poroelastic plate is inviscid and incompressible. Dynamics of the floating plate is described by a thin elastic plate equation. Porosity of the floating plate is taken into account only through the liquid flux into the plate. The velocity of the inflow is assumed to be governed by Darcy's law being proportional to the hydrodynamic pressure at the plate/liquid interface. Two cases of the oscillating rigid plate with and without its part in the liquid are considered. The problems are solved by the Fourier transform method for non-zero porosity and by the vertical mode method for elastic plates with zero porosity. The deflection and strain distributions are analyzed depending on the excitation frequency and the porosity. Two models of floating plate porosity, where the hydrostatic pressure is included into Darcy's law (Zavyalova's model) and excluded (Meylan's model), are compared. Plate porosity induces damping to the system. It is shown that the damping rate is non-monotonic with respect to the plate porosity.

The harmonic resonance and singularity analysis of bifurcation for the magnetized elastic plate with action of time-varying magnetic potential

This paper deals with the superharmonic resonance of a ferromagnetic thin rectangular plate in the air-gap magnetic field excited by armature magnetic potential. Electromagnetic forces applied on the plate by the air-gap magnetic field cause the plate to transversal vibrate, which affects the air-gap magnetic field in turn, resulting the vibration and magnetic field coupling. According to the basic electromagnetic field theory and considering the magnetoelastic coupling effect, the air-gap magnetic field intensity is obtained by solving the Laplace's equation satisfied the air-gap magnetic boundary conditions. The electromagnetic force model of soft ferromagnetic plates is determined based on theories of electromagnetic and elasticity. According to the large deflection theory of plates, basic energy relationships and variational equations of the elastic plate are given. Eventually, the nonlinear magnetoelastic vibration equation of ferromagnetic thin plates is derived using Hamilton's principle and Galerkin method. The multi-scale method is used to solve the superharmonic resonance to obtain the amplitude-frequency response equation and the stability discriminant of solutions. The topological analysis of amplitude-frequency equation is carried out using singularity theory, and the bifurcation characteristics of systems on physical parameter planes in different regions are obtained according to the transition set. The correctness of analytical solutions is verified by comparison with numerical solutions. Through numerical calculations, curves of the static deflection and equivalent magnetic force of plate with parameters are given, and the amplitude curves, dynamic phase plane trajectories and time history diagrams of system response with changes in electromagnetic and structural parameters are plotted. Results show that both the decrease of armature magnetic potential amplitude and the increases of plate thickness and initial air-gap thickness reduce the static deflection. The increase of armature magnetic potential amplitude increases the equivalent magnetic force. As the decrease of initial air-gap thickness and the increases of armature magnetic potential amplitude and excitation force amplitude, the amplitudes of the upper branch and lower branch curves representing stable solutions decrease and increase, respectively, and the single-value solution region increases.

Elastic effect on the final deflection of rigid-plastic square plates under pulse loading

Rigid-perfectly plastic (R-PP) models are widely employed in the study of structural impact dynamics. However, due to the complexity of dynamic elastic-plastic behavior and the limitations of numerical simulation, it is of great significance to evaluate the elastic effect on the structural response to pulse loading. This paper examines the validity of the R-PP theoretical solutions on large deflection of pulse-loaded square plates. First, by exploring the characteristic of “plastic membrane” and considering the effect of membrane forces and bending moments on energy dissipation, an energy ratio R and a characteristic time ratio are precisely defined. Then based on the R-PP complete solutions recently developed for square plates under rectangular pressure pulse, the discrepancies in final deflection and in saturated impulse between the R-PP theoretical predictions and the elastic-perfectly plastic (E-PP) simulation results are evaluated and elaborated. It is revealed that the discrepancy in final deflection is dependent on the dimensionless stiffness ζplate and the dimensionless pulse magnitude λ. Moreover, the discrepancies in final deflection are compared between square plates and beams via a thorough analysis of key parameters, indicating that most characteristics of the elastic effect are similar for both cases, i.e., the R-PP solutions for both square plates and beams can reliably provide theoretical predictions for engineering applications if energy ratios R>5, with no limitation on the pulse duration. With the same geometric and material parameters, however, the energy ratio R of square plates is about twice that of beams, the discrepancy in final deflection of plates is larger than that of beams, but the absolute value of the discrepancy in final deflection for the clamped square plates remains in the order of 1/(1.5R) and can be bounded by 1/[4λ(λ-1)].

Hygrothermally-Induced Vibration Analysis of Porous FGM Rectangular Mindlin Plates Resting on Elastic Foundation

The nonlinear vibration response of rectangular plates made of functionally graded porous materials (FGPs) induced by hygrothermal loading is investigated in this article using a numerical approach. The effect of elastic foundation on the vibrations is taken into account according to the Winkler–Pasternak model. Hygroscopic stresses produced due to nonlinear rise in moisture concentration are also considered. The temperature-dependent material properties of plate are computed based on the modified Voigt’s rule of mixture and Touloukian experiments for even and uneven distribution patterns of porosity. Within the framework of the first-order shear deformation plate theory and von-Kármán nonlinearity, Hamilton’s principle is utilized in order to derive the equations of motions. To achieve the temporal evolution of maximum lateral deflection of hygrothermally-induced plates, the generalized differential quadrature (GDQ) and Newmark integration methods are employed. Selected numerical results are presented to study the influences of temperature distribution, porosity volume fraction, moisture concentration, geometrical parameters, elastic foundation parameters and FG index on the geometrically nonlinear vibrations of FG porous plates with various boundary conditions.

Energy Deposition on Analogous Vehicle Panel: Thermal–Structural Response

A proof-of-concept experimental methodology and results are presented for the simulation of direct thermal energy deposition on a hypersonic vehicle panel analog. The methodology involved uniformly heating ceramic plates via joule heating with localized regions of thermal nonuniformity achieved via plate profiling. A parametric study was first performed to quantify the key parameters governing the level of simulated energy deposition achieved. The plate material, profile size, and amperage used to energize the plate were varied in this study, with a total of 108 cases analyzed. The overall plate thermal response, the achieved over the profile section, and the plate deflection were examined in detail. Configurations resulting in high overall plate temperatures with large in the profile section and appreciable deflection were then selected for benchtop testing. Wall temperatures in the range of 686–1144 K were achieved experimentally with peak T in the range of 46–427 K. One plate was visually observed to deflect on the order of 3 mm. The results from this demonstrate the suitability of the presented methodology for generating nonuniform, yet controlled temperature profiles on analogous vehicle panels for future shock-tunnel testing.

Investigation of MEMS Single Turn Meander-Shaped Silicon Carbide Piezoresistive Pressure Sensor on a Clamped Circular Diaphragm for High Pressure Harsh Environment Applications

Silicon-based Microelectromechanical System (MEMS) pressure sensors are extensively used and have the advantages of high accuracy and miniaturization. Despite this, due to inherent material limitations, they are not easily able to withstand high temperatures greater than 150°C. To overcome this disadvantage, Silicon Carbide (SiC) is the preferred material because it has excellent thermomechanical properties and operates above 600°C. Piezoresistive pressure sensors made of Silicon Carbide are ideally able to detect pressures beyond 600°C. Our work presents MEMS Single turn meander-shaped piezoresistive pressure sensor on a circular SiC diaphragm for high pressure applications of pressure range 0–40[Formula: see text]MPa in harsh environment. This work models and analyses the piezoresistive pressure sensor characteristics using an analytical modeling and simulation method to choose the best design. To ascertain its sensitivity, expressions are computationally simulated with MATLAB software using the thin plate and small deflection theory. To evaluate the viability of the model, COMSOL Multiphysics simulation is used. When compared to recent studies, our proposed sensor provides a sensitivity of near about 5.4[Formula: see text]mV/V/MPa across a pressure range of 0–40[Formula: see text]MPa.

Geometrically nonlinear static deflection of stiffened composite plates: A fifth-order equivalent model

Nonlinear reduced-order models (NLROM) have been developed to predict the geometrically nonlinear behaviour of structures with low computational cost. NLROMs built using non-intrusive methods are compatible with commercial FE software and have the potential for wide application in engineering. The challenge of non-intrusive NLROMs is to accurately reproduce the internal force of structures. In literature, the internal force has been assumed to be a cubic polynomial function of generalized coordinates. However, this assumption is effective only for structures with small rigid rotations but not for structures with significant rigid rotations such as cantilever structures. In this paper, we propose a fifth-order polynomial approximation of the internal force for such cases. The nonlinear stiffness tensors of the reduced-order model are built using explicit formulas, ensuring applicability to all structures. Our proposed reduced-order model accurately predicts the nonlinear static deflection of composite plates with complex geometries.

Perencanaan Tebal Perkerasan Kaku Jalan Raya Cadas - Kukun Kabupaten Tangerang

ABSTRACT Portland cement concrete pavement or more commonly called rigid pavement or Rigid Pavement, consists of a Portland cement concrete slab and a foundation layer (may or may not exist) on the subgrade. This concrete slab can use reinforcement or without reinforcement depending on the planning. This is different from flexible pavements where the stiffness of the pavement is obtained from the thickness of the subbase layers, the foundation and the surface layer. Because the most important thing is to know the load-bearing capacity of the structure, the factor that needs to be considered in designing concrete road pavements is the strength of the concrete itself. The varying strength of the subgrade or foundation has little effect on the structural capacity of the pavement (the thickness of the concrete slab). The subbase layer, if used under a concrete slab, is intended as a working floor and for drainage to prevent pumping. Pumping is the event of the release of water accompanied by subgrade grains through joints and cracks or on the pavement edge, due to deflection or vertical movement of the concrete plate due to traffic loads, after free water has accumulated under the concrete plate. Pumping can cause cavities to occur. under the concrete plate causing damage or cracks to the plate Key words: Rigid Pavement,Semen Portland,Pekerasan Lentur , Pumping.

Flexural gravity wave interaction with an articulated heterogeneous plate within the paradigm of blocking dynamics

Surface gravity waves interact with the flexural waves to generate the flexural gravity waves whose characteristics are triggered for higher values of lateral compressive stress to generate multiple propagating wave modes. This investigation examines the scattering of obliquely incident flexural gravity waves due to articulation in two semi-infinite heterogeneous floating elastic plates in finite water depth within a blocking dynamics regime. The dispersion curve demonstrates the existence of three propagating wave modes within the blocking limits. The canonical eigenfunction expansion method used for a single propagating mode is generalized to account for multiple propagating wave modes within the limits of blocking periods. The energy relation is established using the conservation of wave energy flux and Snell's law of refraction, which depends upon the angles and amplitude of the scattered waves along with the wave energy transfer rates. The amplitude of scattering coefficients (energy transfer rate) goes beyond the unit, where the corresponding energy transfer rate (scattering coefficients) diminishes for specific wave periods. Subsequently, complete wave reflection occurs for oblique waves beyond a critical angle of incidence for a fixed period and prior to a critical angle of incidence at a higher angle of incidence. Removable discontinuities occur at the blocking and saddle points, while a jump discontinuity appears due to a change in the incident wave mode in the scattering coefficients. Surface plots reveal the irregular pattern of plate deflection for the period within the blocking limits. Linear time-dependent plate displacement is simulated in two and three dimensions.

Accurate solutions of a thin rectangular plate deflection under large uniform loading

The large deflection of a thin rectangular plate under uniform loading is a classic problem in solid mechanics. However, the equations are challenging to solve due to their strong nonlinearity. To the author’s best knowledge, existing studies have only reported solutions for rectangular plates with immovable clamped edges within the range of loadings a4q/(Dh)<500. In this study, we employ the homotopy analysis method (HAM) to address this problem and obtain accurate solutions even when the loading a4q/(Dh) reaches as high as 105. Additionally, we discover that the central deflection w(0,0)/h follows a scaling law of [a4q/(Dh)]1/3 for loadings a4q/(Dh)>104, which agrees with the scaling law for extremely large deflections. Consequently, we can utilize this scaling law to extrapolate our homotopy series solution from a4q/(Dh)=104 to even larger loadings. Our investigation also reveals that the bending and membrane stresses increase with the loading. The maximum bending stress is located at the edge, while the location of the maximum membrane stress shifts from the plate center towards the edge as the loading increases. Moreover, we find that even for large deflections, the bending stress remains significant at the edge, challenging the assumption of negligible bending stress adopted by the membrane equations. Thus, the membrane equation may over-predict the plate deflection even under large loadings. These findings advance our understanding of the large deflection of a thin rectangular plate with clamped edges, which has important applications in aerospace, ocean, chemical, and microelectronic engineering. The results presented in this paper can also be used to verify other algorithms designed for highly nonlinear problems.

Barrier and bottom topography effects on hydroelastic response of floating elastic plate in a two-layer fluid

The prime intention of this article is to investigate the effect of variable bottom topography and a bottom-sitting porous barrier on the hydroelastic response of an elastic plate floating on a two-layer fluid using small amplitude wave theory. Galerkin's single-mode approximation in each layer for variable bottom topography and the method of eigenfunction expansion for the fluid region of uniform bottom topography are used as mathematical tools to detail the phenomena. In the variable bottom topography, a system of differential equations is solved. By applying matching conditions, jump conditions, and the appropriate boundary conditions, the solution is expressed as an algebraic linear system from which all the unknown constants are evaluated. The effects of different parameters related to the fluid, bottom topography, and porous barrier on the bending moment, shear force, and deflection of an elastic plate are explored. The variations in the bending moments, shear forces, and plate deflection with respect to fluid density are found to be in opposite trends, caused by surface and interfacial waves, respectively. Further, as the density ratio becomes closer to one, the bending moments, shear forces, and plate deflection tend to diminish for interfacial waves. The bottom effect on bending moments, shear forces, and plate deflection is minimal due to surface waves but significant due to interface waves with maximum amplitude in a concave up bottom. The plate deformation can be further reduced using a suitable barrier, as investigated in this article. The findings hold good potential for furthering our understanding of installing an elastic plate in a stratified fluid with fluctuating water depth.

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

In this paper, the bending behavior of rectangular plates with stepped thickness resting on an elastic half-space foundation is investigated through an analytic method. Combined with the bending theory of the rectangular thin and moderately thick plate, the stepped rectangular plate is divided into upper and lower plates, and the Fourier series is used to obtain the analytical solution of the deflection of the plate and the interaction force between the plate and foundation. The influence of the elastic modulus of the plate, plate theory, and the dimension of the plate on the deflection of the stepped rectangular plate is also discussed. The results show that the analytical solution is basically the same as the existing research results, and it is also verified by the analysis results of the models established by ABAQUS software. The deflection at the center of the stepped rectangular plate increases with the increase of the elastic modulus of the upper plate and the decrease of the side length of the upper plate, while the plate theory has little effect on the deflection of the plate. This method not only overcomes some of the disadvantages of numerical methods but also eliminates the assumptions of the Winkler foundation model and the two-parameter foundation model, thus obtaining a more reasonable and accurate bending performance of the stepped rectangular plate resting on the elastic half-space foundation.

A novel EFG meshless-ANN approach for static analysis of FGM plates based on the higher-order theory

An Element Free Galerkin (EFG) meshless formulation and solutions using higher order shear deformation theory with nine degrees of freedom for the static analysis of Functionally Graded Material (FGM) plates are provided. This technique estimates the shape function using Moving Least Squares (MLS) method. The proposed method is validated by comparing the present findings with those in the literature. A novel Artificial Neural Network (ANN) model is developed to forecast the deflection of FGM plates within less computational time. Detailed parametric and convergent studies reveal that the proposed EFG solution and the ANN technique are more efficient than their conventional counterparts. The validation and comparison of the generated results in the present investigation with the other analysis methods revealed that the EFG method and ANN model give more accurate results than the FEM and other meshless methods. The current EFG-ANN model reduces computing time by 99.94% when compared to the EFG approach. Also, the accuracy is enhanced using the EFG approach with HSDT9 for the FGM plate.

Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates

This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes.

Flexural and sinking stiffnesses investigation of metal, glass fiber reinforced plastic and hybrid laminates through a semi‐experimental method

AbstractThe hybrid metal/GFRP laminate is a kind of typical hybrid structure consisting of thin metal sheets and glass fiber reinforced plastic laminates, which combines the benefits of low cost, high strength, excellent impact resistance, and good corrosion resistance. In this work, a semi‐experimental method based on a nondestructive test and the analytic solution of the thin plate's deflection for the flexural and sinking stiffnesses identification of hybrid metal/GFRP laminates was proposed and validated by corresponding numerical simulations. Then, in total 17 different specimens (including metal, GFRP and hybrid metal/GFRP) were prepared and tested by the proposed semi‐experimental method to investigate their flexural and sinking stiffness performances in multiple perspectives (including stiffness per unit mass/volume/price/surface density). The analytic solutions show that the flexural and sinking stiffnesses are proportional to macro equivalent moduli of laminate specimens and proportional to the third power of thicknesses of specimens. The test results show that the stiffnesses per unit mass/density of the 7‐ply GFRP laminate can be comparable to those of the variable‐thickness rolled blank (VRB) made of steels, but the stiffnesses per volume/price of the 7‐ply GFRP laminate are only one fifth to one quarter of those of VRB. It is also found that though the hybrid metal/GFRP laminate with the combination sequence of aluminum plate/5‐ply GFRP/aluminum plate has the lowest GFRP layers' volume fraction, but has the best performances of stiffnesses per unit mass/density. Besides, the VRB part can significantly improve the stiffnesses per unit volume of hybrid metal/GFRP laminates.

Wave scattering by an array of moored floating flexible plates resting on an elastic foundation in the reference of blocking dynamics

Surface gravity wave scattering by an array of floating flexible plates having free/moored edges and resting on a Winkler foundation are studied within the framework of flexural gravity wave blocking. The impact of the floating plates having moored edges compared to that of free edges along with the occurrences of Bragg reflection are analyzed. The study reveals that wave reflection is oscillatory in nature irrespective of the number of plates. Further, the amplitude of wave reflection increases for smaller frequency and decreases for higher frequency in the presence of Winkler foundation. The study depicts the occurrences of removable discontinuities at the blocking frequencies and the existence of a smaller number of extrema in wave reflection outside the blocking limits than within the said limits. Besides, the number of sub-harmonic peaks between two consecutive harmonic peaks in wave reflection depends on the wave frequency, plate length and gap between the consecutive plates. Moreover, the free surface elevations and the floating plate deflections exhibit certain irregularity within the blocking frequencies. The free surface elevation and floating plate deflection in the presence of compressive force wave blocking exhibit the recurrence of scattering of wave pulses in the linear time domain.

The role of blocking dynamics and current on wave scattering due to finite floating elastic plate

The role of wave blocking on flexural gravity wave motion with oblique incidence and current is discussed. The oblique wave incidence due to a finite floating elastic plate is investigated using the eigenfunction expansion method. The role of different wave propagating modes on reflection coefficient is discussed. The reflection and transmission coefficients, the surface elevation, and plate deflection in the presence of current are derived. The effects of flexural rigidity and the uniform current speed on reflection and transmission coefficients are analyzed. The resonating nature of reflection coefficient for some fixed values of plate length is observed. Significant effects of different combinations of wave propagating modes of plate covered regions and open water regions on the reflection and transmission coefficients are observed. The wave energy propagation from reflection coefficient decreases whenever the Froude number increases. It has been found that the amplitude of the plate deflection increases as the value of the Froude number increases. The amplitude and wavelength of the reflection coefficient are higher for the combination of the first propagating mode of the plate covered region and the second propagating mode of the open water region. Moreover, it is found that zero reflection and full transmission occurs periodically. Co-propagating waves are found to transmit more energy while counter-propagating waves reflect more energy. Higher values of flexural rigidity result in reduced wave energy transmission.

A circular plate with a central hole reinforced with agglomerated CNTs under impact loading

PurposeThis article focuses on the low-velocity impact (LVI) output of carbon nanotubes (CNTs)’ reinforcement circular plates, considering agglomeration size effect and clumping of CNTs’ inner side of the agglomerations.Design/methodology/approachA representative volume element (RVE) is used to determine the nanocomposite properties reinforced with agglomerated CNTs with random orientation. First-order shear deformation theory (FSDT) is used to obtain the motion equations of LVI analysis. These equations are handled by developing a Ritz method and Lagrangian mechanics. To extract the mass and stiffness matrices, terms with second and higher degrees are ignored.FindingsFormulation validation is performed by providing various examples, including comparisons with other research and ABAQUS FE code. The effects of agglomeration size, clumping of CNTs’ inner side of the agglomerations, CNT volume fraction and impact location on the responses of impact load, projectile displacement and plate deflection are analytically studied. These achievements illuminate how the influence of agglomeration size is very small on the impact response. Also, the influence of clumping of CNTs’ inner side of the agglomerations is significant, and as it increases, the displacement values and impact time increase, and the impact force decreases.Originality/valueIn this article, to avoid additional calculations, the parameters of the mass matrix and the stiffness coefficients are linearized to obtain the equations of motion of the impact on the circular plate.

Formation of the structure and optimal parameters of the neural network for determining the composite plate deflections

The paper defines the structure of an artificial neural network (ANN), the required amount of data for training and algorithms for their processing to ensure the ability of the network to recognize dependencies between the structure of the composite material and the quantitative parameters of the deformed state under a given load with acceptable accuracy. To test the network, the problem of determining the deflection of a three-layer (glass-film-glass) laminate plate with a wide range of changes in physical and mechanical characteristics and geometric dimensions under conditions of three-point bending was used. It is shown that the most effective is the ANN consisting of two hidden layers with 12 and 6 nodes in the layers, respectively, when processing data based on the Levenberg-Marquardt algorithm. At the same time, the error of the obtained results lies within 0.5% for data from the range used for training the network and within 5% for data outside this range.