Boundary Conditions Of Plate Research Articles

Multi-objective optimization of variable stiffness laminated plates modeled using Bézier curves

In this paper, intuitive fiber path definition methods using cubic and quadratic Bézier curves are proposed for variable stiffness (VS) laminates designed with Direct Fiber Path Parameterization (DFPP) technique. These methods construct fiber paths with nonlinear angle variation defined by simple design variables that are segment/station angles and multipliers/curvature. At its simplest, balanced symmetric VS laminates defined with two segment/station angles are illustrated, implemented in finite element model under uniaxial compression, and optimized using surrogate based multi-objective non-dominated sorting genetic algorithm (NSGA-II) for maximum buckling load and stiffness. The optimization results of VS laminates using cubic Bézier interpolation and quadratic Bézier approximation curves as fiber paths are compared for three different plate sizes and boundary conditions. The largest simply supported VS laminate that uses cubic Bézier curves of constant curvature as fiber path shows 103% increase in buckling load against 44% reduction in stiffness compared to quasi-isotropic laminate.

Refined model for rectangular thin plates on two-parameter foundations using an iterative procedure

The main purpose of this study is to investigate the influence of soil heterogeneity on the mechanical responses of rectangular plates resting on elastic foundations and to determine reasonable physical model parameters. The bending problem of rectangular thin plates lying on Gibson elastic foundations is solved using an iterative procedure. First, plates and foundations are discussed as a whole system, based on the principle of minimum potential energy. Second, the governing equations and boundary conditions for plates are established. And the equation for the attenuation parameter in the mathematical model is also derived. Then an iterative procedure is used to iterate the two parameters simultaneously, which solves a key issue for the two-parameter foundation model. Third, a double Fourier series with supplementary functions is adopted, and the solution to the bending problem is obtained. The agreements between the numerical results and the literature results prove that the refined model is practical and achievable. The proposed method exhibits a certain universality in analyzing the interactions between rectangular thin plates and elastic foundations. Furthermore, Gibson soil has an influence on the structural responses of rectangular plates on elastic foundations.

Heterogeneous Sediment Input at the Nankai Trough Subduction Zone: Implications for Shallow Slow Earthquake Localization

AbstractSubducted sediment plays a key role in modulating pore pressure and seismic behavior at subduction zones. We investigated the seismic character of incoming sediments to test how sediment and basement variations relate to the along‐strike changes within the accretionary prism and plate boundary conditions at the Nankai Trough. High‐resolution seismic data reveal for the first time the presence of countourite mounded drifts in the Shikoku Basin. These features have probably introduced permeability heterogeneities into an otherwise homogenous mud‐dominant unit. Additionally, we found that normal faults in this unit are more extensive than previously documented, which probably enhances along‐strike fluid transport. The wedge taper is more correlative with the thickness of the mud‐dominant facies than the turbidite thickness. This may be due to the permeability heterogeneities associated with contourite deposits and normal faults, or due to the absence of thick turbidite deposits. Turbidite deposits can either aid the drainage of the margin where they are not confined by basement topography, or contribute to high pore fluid pressures where they are confined by less permeable mudstone or basement topography. When confined turbidite deposits and contourite mounded drifts are subducted, they may contribute to localized compartments of excess pore pressure which provide the necessary conditions for slow slip behavior. We determined that along‐strike variations in seismic behavior are likely related to the subducting basement topographic and sediment characteristics, which vary on a local (<10 km) scale.

Panel flutter analysis of perforated plate repaired by VSCL bonded patch using the multi-patch IGA approach

The crashed structure fixing procedures using the bonded repair patches seems highly frequent in the aeronautical vehicle’s maintenance. The resulting composite repaired perforated thin-walled plate is generally a complex geometry with a relatively high computational cost. The present study focuses on the linear panel flutter analysis of the perforated flat panels repaired on one side by an external bonded tow-steered variable stiffness composite patch. A variable stiffness laminate repair design can increase the composite structural performance. It also provides high flexibility toward tailoring the structure’s mechanical properties. The potent multi-patch NURBS-based isogeometric analysis formulation is implemented based on the first-order shear deformation theory of plates. In the context of the multi-patch geometry modeling approach, the repaired perforated panel is divided into several separate but connected adjacent geometries. Assuming sufficiently thin repair laminates, an aerodynamic loading according to the first-order piston theory is applied. Consequently, the performance and accuracy of the implemented formulation are approved. The panel flutter behavior of various repaired perforated plates is inspected through some parametric studies on geometry, layup, boundary conditions, and flow direction. It is found that the critical flutter pressure parameter is decreased for wider cutouts with the changes dependent on the hole layout. It is found that the optimal position of the VSCL repair and cutout zone depends strongly on the type of base plate boundary conditions.

Tuned deep neural network for computer simulation of chaotic performance of the electromechanical annular system coupled with a piezoelectric patch

In this paper, an attempt is made to extend a nonlinear two-dimensional model for large oscillation and chaotic characteristics of the annular plate coupled with a piezoelectric patch subject to external excitation. For improving the mechanical properties, the core of the electrically structure is reinforced with graphene nanoplatelets. Von-Karman nonlinear theory and Hamilton’s principle are taken into consideration for the exact derivation of the general nonlinear governing equations and boundary conditions of the axisymmetric annular plate coupled with a piezoelectric patch. For developing a precise solution approach, the generalized differential quadrature element method, and Multiple scales technique, are eventually used. The results demonstrate that radius ratio, applied voltage, thickness to radius ratio, and harmonic load have an important role in the nonlinear large oscillation, and chaotic motion of the graphene platelets reinforced composite (GPLRC) annular plate coupled with a piezoelectric patch. The golden and fundamental result of the current research is that, as the thickness of the piezoelectric patch increases, the system's nonlinear frequency decreases, and the area of instability in responses and maximum amplitude or the peak point of the backbone curve of the smart annular plate increases.

Cut-out resonators for tuned vibration suppression of plates

This research investigates a concept for cut-out resonators that exploit a small area of active mass of a host plate structure for sake of tuned, low frequency vibration attenuation. Integrated computational and experimental studies reveal that embedding the resonators at locations offering high bending moment gradient and arranging the central resonator beam along a nodal line of bending moment best excite the first resonator eigenmode for targeted vibration suppression. These results are independent of plate boundary conditions and do not require periodic resonators to achieve notable vibration suppression outcomes. These design concepts may guide the development of resonators for vibration absorption of plates with arbitrary boundary conditions.

Predicting compression-after-impact behavior of thermoplastic composite laminates by an experiment-based approach

An experiment-based approach for predicting the compression-after-impact (CAI) behavior and compressive residual strength of carbon fibre reinforced thermoplastic (CFRTP) composite is presented. The three-dimensional finite element model with an impact-induced damage region obtained from X-ray computed tomography analysis is developed. The unknown stiffness reduction of materials in the damaged region is determined by CAI experiments. The experiment-based bimodular nonlinear constitutive law together with a strain-based failure initiation criterion from the compressive test is developed during the simulation. The virtual CAI test is firstly validated through the comparison work between the results from finite element analysis and the experiments on the CFRTP laminate impacted by 20 J energy. Numerical investigations show the effects of plate geometries and boundary conditions on CAI behavior and residual strength of the CFRTP laminates with the same impact-induced damage.

Transient Vibroacoustic Analysis of Functionally Graded Plates

Abstract This paper presents the vibroacoustic response of pure functionally graded (FG) plates under transient loading of mechanical nature. The functionally graded plate is modeled using the conventional first-order shear deformation theory (FSDT) to incorporate the effects of transverse shear and rotary inertia. The mid-surface variables are determined using the finite element method. Transient structural response is determined using Newmark Beta time marching scheme and the acoustic pressure in the free field is obtained using the time-domain Rayleigh integral. The effective material properties of the FG plate and the transient response of both the structural and acoustic fields have been computed in matlab. The influence of the volume fraction index, thickness ratio, and boundary conditions of pure FG plate on its transient vibroacoustic response is investigated by a detailed parametric study.

Partial wave basis adapted to exterior boundary conditions of an elastic plate

An approach to describing normal elastic vibration modes in confined systems is presented. In a standard treatment of the problem, the displacement field is represented by a superposition of partial waves of a general form, e.g., plane waves. The unknown coefficients of superposition are then obtained from the equation of motion and the full set of boundary conditions. In the proposed approach, the functional form of partial waves is chosen in such a way as to satisfy the boundary conditions on exterior surfaces identically, i.e., even if the unknown quantities determined by the remaining constraints are found in an approximation, numerically or analytically. Some examples of solutions for composite elastic plates are discussed to illustrate the efficiency of the approach and its relevance for applications.

Transverse Vibration Analysis of Axially Moving Trapezoidal Plates

Transverse vibration of axially moving trapezoidal plates is investigated. The differential equation of transverse vibration for a axially moving trapezoidal plate is established by D'Alembert principle. The original trapezoid region can be replaced by regular square region by the medium parameter method for the convenience of calculation. A generalized complex eigenvalue equation is derived by a discrete method (the differential quadrature method). The complex frequency curve of trapezoidal plate is obtained by calculating the eigenvalue equation. The change of the complex frequencies of the axially moving trapezoidal plates with the dimensionless axially moving speed is analyzed. The effects of the aspect ratio and the trapezoidal angle on instability type of the trapezoidal plate are discussed under different boundary conditions. The results of numerical analysis show that there are two main instability types of axially moving trapezoidal plate: divergence and flutter. The modal orders of the two types of instability are also different, which is related to the trapezoidal angle, aspect ratio and boundary condition of the trapezoidal plate.

Consequence of Modified Boundary Condition On Natural Convection in a Porous Medium Saturated by Nanofluid – A Computational Approach

In the present numerical simulation, steady, laminar, two-dimensional flow in a porous medium saturated by nanofluid [1] along an isothermal vertical plate is presented. Here we have studied a more realistic situation where the nanoparticle volume fraction at the plate (boundary condition) is passively controlled by assuming that its flux there is zero. We employ Boungiorno model [2] that treats the nanofluid as a two-component mixture, incorporating the effects of Brownian motion and thermophoresis. Darcy model is utilized for the presence of porous medium. With the help of appropriate similarity variables, the governing nonlinear partial differential equations of flow are changed to a bunch of nonlinear ordinary differential equations. Afterwards, they are reduced to a first order system and integrated using Newton Raphson and adaptive Runge-Kutta methods. The computer codes are developed for this numerical analysis in Matlab environment. Dimensionless stream function (s), longitudinal velocity (s’), temperature (θ) and nanoparticle volume fraction (f) are figured and outlined graphically for various values of four dimensionless parameters, namely, Lewis number (Le), buoyancy-ratio parameter (Nr), Brownian motion Parameter (Nb), and thermophoresis parameter (Nt). The dependence of the reduced Nusselt number on these parameters is illustrated.

On the treatment of hydroelastic slamming by coupling boundary element method and modal superposition method

An efficient fluid and structure interaction (FSI) coupling strategy between boundary element method, i.e. BEM (fluid part), and modal superposition method (structure part) is proposed to study hydroelastic slamming of wedge sections. The coupling strategy possesses simplicity in coding construction by transmission of coordinates, velocity and pressure on the fluid-solid interface. Convergence property of grid size, time step and modal number are first investigated. After that, the accuracy of the model is verified by comparing the numerical results with published ones. Hydroelastic effect associated with plate thickness, deadrise angle, impact velocity and boundary condition is discussed by the comparison between quasi-static, decoupling and coupling solutions, where quasi-static and decoupling solutions are established by neglecting the influence of elastic response of structure on the water flow field. The results show that quasi-static solution underestimates structural maximum response under specified hydroelastic parameters, and a time-lag effect is found between results of decoupling and coupling solutions.

Modal characteristics and manufacturing method of variable stiffness facesheets of sandwich plates made by robotic fiber placement

A variable stiffness (VS) structure of the grid panels is designed for solar wing sandwich plates on satellite. The vibration resistance performances of the VS plate, constant stiffness (CS) plate are evaluated. First, a novel modal analysis model is proposed to investigate the relationship between the fundamental frequency and fiber angles. The fiber direction of grid panel is optimized with the constant curvature arc curves. Then, the equivalent model and the boundary conditions of the sandwich plates under the actual working conditions are built. The modal fundamental frequencies of the VS plate are improved by 31.18% after the optimization. Furthermore, a five-segment method for trajectory planning is proposed. Finally, a variable stiffness grid panel made by robotic fiber placement is realized, which verifies the accuracy of the manufacturing method and simulations.

Identifying all combinations of boundary conditions for in-plane vibration of isotropic and anisotropic rectangular plates

This work presents a combined study of an effective vibration analysis and a counting theory to identify all combinations of boundary conditions for in-plane vibration of isotropic, specially orthotropic and symmetrically laminated rectangular plates. First, a method of analysis is proposed to obtain the in-plane natural frequencies of plates under any in-plane boundary conditions of free, clamp and two types of simple supports, and this method makes it possible to calculate the frequencies of rectangular plates subject to 256(=4 powered by 4) sets of boundary conditions. Secondly, Polya counting theory is introduced to determine theoretically the total number of distinct combinations of plate boundary conditions, and to reduce the 256 sets into the essentially identical subsets of frequencies. In numerical experiments, all sets of natural frequencies are calculated for the rectangular plates with different aspect ratio, material property and lamination, and are sorted into the classes with identical sets of frequencies. The distinct combinations are thus obtained for in-plane vibration of the plates, and it is shown that the number of combinations from the experiment exactly agrees with prediction by Polya counting theory.

Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets

Nonlinear forced vibration of graphene platelet reinforced metal foam (GPLRMF) rectangular plates is investigated. Attention is focused on the primary, superharmonic, and subharmonic resonances of this novel nanocomposite structure. Three kinds of graphene platelet (GPL) pattern and three kinds of porosity distribution are taken into account. Based on the von Kármán nonlinear plate theory, governing equations and general boundary conditions of the GPLRMF plates are obtained via Hamilton’s principle. By introducing stress functions, nonlinear ordinary differential equations of the plates are obtained by using the Galerkin method. Then, frequency–response and force–response relationships of the GPLRMF plates are solved by applying the multiple scale method. A validation study is conducted to verify the present method. Results show that GPLRMF plates exhibit hardening nonlinearity in primary and superharmonic resonances. Dispersing more small-size pores or more GPLs near the middle surface will lead to the larger vibration amplitude and resonance domain of the plates in primary and superharmonic resonances. While uniformly distributed pores or uniformly distributed GPLs will result in the larger vibration amplitude in the case of subharmonic. Moreover, change of porosity coefficient or GPL weight fraction can significantly alter the nonlinear dynamic behavior of GPLRMF plates.

Investigation of buckling characteristics of cracked variable stiffness composite plates by an eXtended Ritz approach

Variable Angle Tow (VAT) composite plates are characterized by in-plane variable stiffness properties, which opens to new concepts of stiffness tailoring and optimization to achieve higher structural performance for advanced lightweight structures where damage tolerance consideration are often mandatory. In this paper, a single-domain eXtended Ritz formulation is proposed to study the buckling behaviour of variable stiffness laminated cracked plates. The plate behaviour is described by the first order shear deformation theory whose generalized displacements, namely reference plane translations and rotations, are expressed via suitable admissible trial functions. These consist of a set of regular terms, built using orthogonal polynomials, augmented with special functions able to describe the crack opening and the singular behaviour at the crack tips; boundary functions are used to ensure the required homogeneous essential boundary conditions. Governing equations are inferred via the stationarity of the energy functional an solved to carry out an extensive study on the buckling behaviour of variable angle tow homogeneous and layered composite plates. The results obtained for homogeneous plates evidence that the crack presence strongly influences the buckling behaviour depending on its length and inclination and plate boundary conditions with a meaningful variability with respect to the fibre paths configuration, which can arrange for better performances with respect to the straight fibre case. Also for cracked laminates the results show that there are several fibre path able to provide higher buckling loads and higher overall axial stiffness with respect to the straight fibre case. In the framework of damage tolerant engineering applications, this allows to select fibre paths that guarantee predefined design levels of buckling load and axial stiffness even in presence of cracks. Finally, this study highlights the potential of the proposed approach for the analysis of the buckling behaviour of cracked composite variable stiffness plates, which provides an efficient analysis tool for the damage tolerant design and optimization of advanced variable stiffness structures.

Nonlinear transient thermoelastic response of FGM plate under sudden cryogenic cooling

Liquified natural gas (LNG) is increasingly used as fuel in marine industry. For transportation and storage purposes it is kept at −163 °C under atmospheric pressure. When LNG gets in contact with a plate, pipe or a tank, it causes very significant thermal load on the structure which has, until that point, been kept at environmental temperature. The current study presents the nonlinear transient thermoelastic response of circular/annular plates which experience sudden cryogenic thermal load. This is the first time that thermoelastic analysis has been presented for any structure under such condition. The material is composed of stainless steel (SUS304) and low-carbon steel (AISI1020) and is functionally graded through the thickness. The novel material configuration proposed in this study has been used for the first time in cryogenic and low-temperature applications. Material properties are evaluated based on available experimental data and assumed to be temperature dependent. The nonlinear governing equations and boundary conditions are obtained with the von Kármán assumption and the first order shear deformation theory. The governing equations are discretized and solved with the Generalized Differential Quadrature Method (GDQM) and Newton-Raphson iterative method. The temporal evolution of the temperature field is obtained by solving Fourier-type heat conduction equation using GDQM and Crank-Nicolson scheme. The results have been validated with axisymmetric FEM models using solid elements. A detailed parametric study has been carried out to investigate the effect of temperature dependency, material distribution, thermal/mechanical boundary conditions, geometrical nonlinearity, and plate size on the thermoelastic response. The results show that transient thermoelastic response of plates under sudden cryogenic cooling can be very different than steady state response. Significant deflections occur in a fraction of a second because of the sudden thermal load and decrease over time. The highest stresses appear predominantly in the initial phase, but can also appear later depending on the plate geometry and boundary conditions. For certain thermal boundary condition, the response of a plate under low-temperature thermal load can qualitatively differ from high-temperature thermal load.

Thrust duplexing and transpression in the Yanshan Mountains: Implications for early Mesozoic orogenesis and decratonization of the North China Craton

AbstractThe configuration and kinematics of fold‐thrust belts are essential for clarifying the plate boundary conditions through which ancient orogenic belts evolved. Temporal and spatial variations in extension versus contraction within convergent plate margins are related to changes in plate kinematics and subduction geometry. The Yanshan Mountains, located along the northeastern margin of the North China Craton and bounded by the Central Asian Orogenic Belt to the north and the Pacific subduction zone to the east, underwent multiple phases of intra‐continental deformation during the Mesozoic. The issue of whether early Mesozoic deformation was extensional or contractional has remained controversial. New regional structural mapping and detailed sedimentological investigations, coupled with age constraints provided by zircon U‐Pb geochronology, provide sufficient temporal and spatial resolution to show that shortening and thrust‐top basin systems dominated during the early Mesozoic. Our results show that the Dengzhangzi Basin within the Lingyuan fold‐thrust belt developed during the construction of a major Late Triassic Chapeng antiformal‐stack duplex system, with episodic, east‐vergent forward‐breaking thrusts and subsequent ‘beheading’ by out‐of‐sequence, top‐to‐east thrusting in the latest Triassic or earliest Jurassic. The neighbouring Guojiadian Basin in the east was generated during top‐to‐SSE sinistral transpression along the Niuyingzi thrust system in the Middle to earliest Late Jurassic. These results support a new model of early craton decratonization involving (a) thrusting along the northern margin of the North China Craton and (b) transpressional deformation in the east driven by the Central Asian Ocean collision and flat‐slab subduction of the Palaeo‐Pacific Plate beneath the East Asian continental margin. Our findings suggest that large‐scale shortening and crustal/lithospheric thickening, triggered by flat‐slab subduction in the North China Craton, were fundamental components of craton decratonization. Subsequent slab roll‐back during the Cretaceous led to lithospheric thinning and crustal extension in the North China Craton.

Nonlinear vibration control of smart plates using nonlinear modified positive position feedback approach

In this paper, nonlinear vibration control of a plate is investigated using a nonlinear modified positive position feedback method that is applied through a piezoelectric layer on the plate. Based on the classical theory of displacement and strain relations with von Karman, intended equations of motion for the smart plate have been obtained. In this model, transverse vibrations are studied and stimulations are performed for the primary resonance. Boundary conditions of the smart plate are simply supported. The plate is thickness symmetrical. Using the Galerkin method the temporal nonlinear equations governing the system have been found. Then, the free and forced vibrations of the structure with the nonlinear modified positive position feedback controller have been solved using the Method of Multiple Scales to obtain an analytical solution. Results show that this controller reduces the amplitude of the vibration by inducing an increase in the damping coefficient. In addition, this provides a higher level of suppression in the overall frequency domain response by increasing the compensator gain. Finally, the results of the analytical solution for the closed-loop nonlinear modified positive position feedback controller are presented and compared with the result of the conventional positive position feedback controller and nonlinear integral resonant controller. The results show that the performance of the nonlinear modified positive position feedback controller is better than other controllers and significantly reduces the vibration amplitude.

Analytical Study of Free Vibrations of Fluid Coupling and Structure in Collision of Turbulent Fluid with FGM Plate

In this paper, the free and forced vibration of a functional rectangular plate in contact with a turbulent fluid is investigated. Functional plates have been considered due to their high thermal resistance to residual stresses. The geometry of the problem is that one side of the reservoir in which the fluid is placed is covered with a plate of Functionally Graded Material (FGM). In order to approximate the displacement of the plate, assuming the third-order theory of shear deformation, trigonometric harmonic test functions are used, which determine the boundary conditions of the simple and fixed plate support. In the equations governing fluid oscillating behavior, the potential velocity of the fluid is obtained by determining the boundary conditions of the fluid in the form of February series functions. To achieve the natural frequency of the plate in contact with turbulent fluid and the shape of the vibrating mode, the Rayleigh-Ritz energy method is used based on the minimum potential energy. In order to check the accuracy of the method used, the results of analytical solution after solving the equations by coding in Wolfram Mathematica software have been compared with numerical solution of Abaqus software and then with accurate results in references, which shows the appropriate accuracy of the solution. Finally, the effect of volumetric coefficient parameters, volume ratio, length ratio, plate thickness ratio, fluid height, reservoir width and boundary conditions on the natural frequency of the plate in contact with turbulent fluid has been investigated and analyzed.