Least Square Finite Element Model for Analysis of Multilayered Composite Plates under Arbitrary Boundary Conditions

Laminated composites are widely used in many engineering industries such as aircraft, spacecraft, boat hulls, racing car bodies, and storage tanks. We analyze the 3D deformations of a multilayered, linear elastic, anisotropic rectangular plate subjected to arbitrary boundary conditions on one edge and simply supported on other edge. The rectangular laminate consists of anisotropic and homogeneous laminae of arbitrary thicknesses. This study presents the elastic analysis of laminated composite plates subjected to sinusoidal mechanical loading under arbitrary boundary conditions. Least square finite element solutions for displacements and stresses are investigated using a mathematical model, called a state-space model, which allows us to simultaneously solve for these field variables in the composite structure’s domain and ensure that continuity conditions are satisfied at layer interfaces. The governing equations are derived from this model using a numerical technique called the least-squares finite element method (LSFEM). These LSFEMs seek to minimize the squares of the governing equations and the associated side conditions residuals over the computational domain. The model is comprised of layerwise variables such as displacements, out-of-plane stresses, and in- plane strains, treated as independent variables. Numerical results are presented to demonstrate the response of the laminated composite plates under various arbitrary boundary conditions using LSFEM and compared with the 3D elasticity solution available in the literature.

Nonlinear vibrations of a composite circular plate with a rigid body

The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented.The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory.The equilibrium configurations due to weights are determined and validated by the finite element method(FEM).A nonlinear model for the vibration around the equilibrium configuration is established.Moreover,the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated.The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model.This leads to interesting phenomena.For example,considering weights increases the natural frequency.Furthermore,when the influence of weights is considered,the vibration response of the plate becomes asymmetrical.

Research on stability of laminated composite plate under nonlinear aerodynamic load

In this paper,we propose an finite element approach based on classical plate theory to investigate the dynamic stability of a layered composite plate subject to nonlinear aerodynamic load.This study considers the influence of temperature,nonlinear geometry,and nonlinear aerodynamic load on composite plate structures simultaneously.Specifically,the present work conduct comparison the results of the critical pressure value between the nonlinear aerodynamic load and the linear aerodynamic load,thereby pointing out some necessary cases which must consider the nonlinearity of aerodynamic load for calculating the aerospace structures.We determine the critical pressure value and vibrational amplitude response of the plate by means of calculation.The outcomes of our calculations can be useful in designing and repairing body shells and wings of aircraft equipment.

ANALYSIS OF NONLINEAR DYNAMIC RESPONSE FOR VISCOELASTIC COMPOSITE PLATE WITH TRANSVERSE MATRIX CRACKS

Based on the Schapery three-dimensional viscoelastic constitutive relationship with growing damage, a damage model with transverse matrix cracks for the unidirectional ?bre rein- forced viscoelastic composite plates is developed. By using Karman theory, the nonlinear dynamic governing equations of the viscoelastic composite plates under transverse periodic loading are es- tablished. By applying the ?nite di?erence method in spatial domain and the Newton-Newmark method in time domain, and using the iterative procedure, the integral-partial di?erential gov- erning equations are solved. Some examples are given and the results are compared with available data.

Application of the quadrilateral area coordinate method:a new element for laminated composite plate bending problems

Recently, some new quadrilateral finite elements were successfully developed by the Quadrilateral Area Coordinate （QAC） method. Compared with those traditional models using isoparametric coordinates, these new models are less sensitive to mesh distortion. In this paper, a new displacement-based, 4-node 20-DOF （5-DOF per node） quadrilateral bending element based on the first-order shear deformation theory for analysis of arbitrary laminated composite plates is presented. Its bending part is based on the element AC-MQ4, a recent-developed high-performance Mindlin-Reissner plate element formulated by QAC method and the generalized conforming condition method; and its in-plane displacement fields are interpolated by bilinear shape functions in isoparametric coordinates. Furthermore, the hybrid post-rocessing procedure, which was firstly proposed by the authors, is employed again to improve the stress solutions, especially for the transverse shear stresses. The resulting element, denoted as AC-MQ4-LC, exhibits excellent performance in all linear static and dynamic numerical examples. It demonstrates again that the QAC method, the generalized conforming condition method, and the hybrid post-processing procedure are efficient tools for developing simple, effective and reliable finite element models.

Double Hopf bifurcation of composite laminated piezoelectric plate subjected to external and internal excitations

The double Hopf bifurcation of a composite laminated piezoelectric plate with combined external and internal excitations is studied. Using a multiple scale method, the average equations are obtained in two coordinates. The bifurcation response equations of the composite laminated piezoelectric plate with the primary parameter resonance, i.e., 1：3 internal resonance, are achieved. Then, the bifurcation feature of bifurcation equations is considered using the singularity theory. A bifurcation diagram is obtained on the parameter plane. Different steady state solutions of the average equations are analyzed. By numerical simulation, periodic vibration and quasi-periodic vibration responses of the Composite laminated piezoelectric plate are obtained.

STUDY ON THE RESPONSE TO LOW-VELOCITY IMPACT OF A COMPOSITE PLATE IMPROVED BY SHAPE MEMORY ALLOY

Improvement from the pseudo-elastic effect of shape memory alloy （SMA） on the low-velocity impact （LVI） resistance of a composite plate is investigated by the finite element method （FEM）. The stiffness matrix of the dynamic finite element equation is established step by step and the martensite fraction is obtained at each time step. The direct Newmark integration method is employed in solving the dynamic finite element equation, while the impact contact force is determined using the modified Hertz＇s law. It is found that SMA can effectively improve the performance of a composite structure subjected to low-velocity impact. Numerical results show that the deflection of a SMA-hybrid composite plate has been reduced approximately by thirty percent when the volume fraction of the embedded SMA reaches 0.3.

DETECTION OF DELAMINATION IN A COMPOSITE PLATE BY SEM

A numerical method of integration of Green's functions of strip element method (SEM) is proposed The response of ultrasonic source generated by a transducer on the surface of a multi ply composite plate containing a delamination is analyzed by the use of SEM The numerical results show that the scanning features of the ultrasonic waves may be used to identify the delamination inside the composite plate.

Nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film-shaped memory alloy composite plate subjected to in-plane stochastic excitation

The nonlinear dynamic characteristics and optimal control of a giant magnetostrictive film （GMF）-shaped memory alloy （SMA） composite plate subjected to in-plane stochastic excitation are studied. GMF is prepared based on an SMA plate, and combined into a GMF-SMA composite plate. The Van der Pol item is improved to explain the hysteretic phenomena of GMF and SMA, and the nonlinear dynamics model of a GMF-SMA composite cantilever plate subjected to in-plane stochastic excitation is developed. The stochastic stability of the system is analyzed, and the steady-state probability density function of the dynamic response of the system is obtained. The condition of stochastic Hopf bifurcation is discussed, the reliability function of the system is provided, and then the probability density of the first-passage time is given. Finally, the stochastic optimal control strategy is proposed by the stochastic dynamic programming method. Numerical simulation shows that the stability of the trivial solution varies with bifurcation parameters, and stochastic Hopf bifurcation appears in the process; the system＇s reliability is improved through stochastic optimal control, and the first- passage time is delayed. A GMF-SMA composite plate combines the advantages of GMF and SMA, and can reduce vibration through passive control and active control effectively. The results are helpful for the engineering applications of GMF-SMA composite plates.

Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO:A novel hybrid intelligent method

An effective hybrid optimization method is proposed by integrating an adaptive Kriging(A-Kriging)into an improved partial swarm optimization algorithm(IPSO)to give a so-called A-Kriging-IPSO for maximizing the buckling load of laminated composite plates(LCPs)under uniaxial and biaxial compressions.In this method,a novel iterative adaptive Kriging model,which is structured using two training sample sets as active and adaptive points,is utilized to directly predict the buckling load of the LCPs and to improve the efficiency of the optimization process.The active points are selected from the initial data set while the adaptive points are generated using the radial random-based convex samples.The cell-based smoothed discrete shear gap method(CS-DSG3)is employed to analyze the buckling behavior of the LCPs to provide the response of adaptive and input data sets.The buckling load of the LCPs is maximized by utilizing the IPSO algorithm.To demonstrate the efficiency and accuracy of the proposed methodology,the LCPs with different layers(2,3,4,and 10 layers),boundary conditions,aspect ratios and load patterns(biaxial and uniaxial loads)are investigated.The results obtained by proposed method are in good agreement with the literature results,but with less computational burden.By applying adaptive radial Kriging model,the accurate optimal resultsebased predictions of the buckling load are obtained for the studied LCPs.

NONLINEAR BUCKLING BEHAVIOR OF DAMAGED COMPOSITE SANDWICH PLATES CONSIDERING THE EFFECT OF TEMPERATURE-DEPENDENT THERMAL AND MECHANICAL PROPERTIES

On the basis of the first-order shear deformation plate theory andthe zig-zag deformation as- sumption, an incremental finite elementformulation for nonlinear buckling analysis of the composite sandwichplate is deduced and the temperature-dependent thermal and mechanicalproperties of composite is consid- ered. A finite element method forthermal or thermo-mechanical coupling nonlinear buckling analysis ofthe composite sandwich plate with an interfacial crack damage betweenface and core is also developed.

Free Vibration Analysis of Symmetrically Laminated Composite Plates on Elastic Foundation and Coupled with Stationary Fluid

Free vibration analysis of symmetrically laminated composite plates resting on Pasternak elastic support and coupled with an ideal, incompressible and inviscid fluid is the objective of the present work. The fluid domain is considered to be infinite in the length direction but bounded in the depth and width directions. In order to derive the eigenvalue equation, Rayleigh-Ritz method is applied for the fluid-plate-foundation system. The efficiency of the method is proved by comparison studies with those reported in the open literature. At the end, parametric studies are carried out to examine the impact of different parameters on the natural frequencies.

Hot compressive deformation of eutectic Al-17at%Cu alloy on the interface of the Cu-Al composite plate produced by horizontal continuous casting

On the interface of the Cu-Al composite plate from horizontal continuous casting,the eutectic microstructure layer thickness ac-counts for more than 90%of the total interface thickness,and the deformation in rolling forming plays an important role in the quality of the composite plate.The eutectic microstructure material on the interface of the Cu-Al composite plate was prepared by changing the cooling rate of ingot solidification and the deformation in hot compression was investigated.The results show that when the deformation temperature is over 300℃,the softening effect of dynamic recrystallization ofα-Al is greater than the hardening effect,and uniform plastic deformation of eutectic microstructure is caused.The constitutive equation of flow stress in the eutectic microstructure layer was established by Arrhenius hy-perbolic-sine mathematics model,providing a reliable theoretical basis for the deformation of the Cu-Al composite plate.

Application of Mullite Composite Lining Plates in Rotary Coke Tanks for Coke Dry Quenching Equipment

To reduce the burning loss and the spalling and to improve energy efficiency,the mullite composite lining plates were used to replace cast steel or alloy lining in rotary coke tanks for coke dry quenching equipment.The results show that:the dense mullite composite lining plate in the cone part has the density of 2.20 g·cm^(-3) and the wear test,s volume loss of 4.08 cm^(3),and the light weight mullite composite lining plate in the straight cylinder part has the density of 1.95 g·cm^(-3) and the wear test,s volume loss of 17.6 cm^(3).After using,there is no shrinkage gap,no burn loss or holes in the plates,indicating good sealing of the mullite composite lining plates.The lining plate for the cone part has low burning loss,without spalling for more than half a year.The outer surface temperature of coke tanks adopting the cast steel or the alloy lining is 480 to 570℃,while that of the ones adopting mullite composite lining plates is 120 to 170℃,showing a largely improved insulating property.Adopting mullite composite lining plates on the basis of the current coke tank cage,the lining plates can be timely treated and wholly replaced,improving the service life and reducing the maintenance workload.

Analysis of Second-Harmonic Generation of Low-Frequency Dilatational Lamb Waves in a Two-Layered Composite Plate

We analyze the effect of second-harmonic generation（SHG） of primary Lamb wave propagation in a two-layered composite plate, and then investigate the influence of interfacial properties on the said effect at low frequency. It is found that changes in the interfacial properties essentially affect the dispersion relation and then the maximum cumulative distance of the double-frequency Lamb wave generated. This will remarkably influence the efficiency of SHG. To overcome the complications arising from the inherent dispersion and multimode natures in analyzing the SHG effect of Lamb waves, the present work focuses on the analysis of the SHG effect of low-frequency dilatational Lamb wave propagation. Both the numerical analysis and finite element simulation indicate that the SHG effect of low-frequency dilatational Lamb wave propagation is found to be much more sensitive to changes in the interfacial properties than primary Lamb waves. The potential of using the SHG effect of low-frequency dilatational Lamb waves to characterize a minor change in the interfacial properties is analyzed.

Time-varying nonlinear dynamics of a deploying piezoelectric laminated composite plate under aerodynamic force

Using Reddy’s high-order shear theory for laminated plates and Hamilton’s principle, a nonlinear partial differential equation for the dynamics of a deploying cantilevered piezoelectric laminated composite plate, under the combined action of aerodynamic load and piezoelectric excitation, is introduced. Two-degree of freedom(DOF)nonlinear dynamic models for the time-varying coefficients describing the transverse vibration of the deploying laminate under the combined actions of a first-order aerodynamic force and piezoelectric excitation were obtained by selecting a suitable time-dependent modal function satisfying the displacement boundary conditions and applying second-order discretization using the Galerkin method. Using a numerical method, the time history curves of the deploying laminate were obtained, and its nonlinear dynamic characteristics,including extension speed and different piezoelectric excitations, were studied. The results suggest that the piezoelectric excitation has a clear effect on the change of the nonlinear dynamic characteristics of such piezoelectric laminated composite plates. The nonlinear vibration of the deploying cantilevered laminate can be effectively suppressed by choosing a suitable voltage and polarity.

LOW VELOCITY RESPONSE CHARACTERISTICS OF COMPOSITE PLATE WITH EMBEDDED SHAPE MEMORY ALLOY

This paper analyzes the characteristics of utilizing shape memory e?ect (SME) of shape memory alloy (SMA) in improving the low velocity impact resistance performance of com- posite plate by using ?nite element method. The constitutive relation for SMA hybrid composite plates is presented. The analytic model of ?nite element for SMA composite plate subjected to low velocity impact is established. The modi?ed Hertz’s contact law is used to determine the impact contact force. The computing procedures for solving the ?nite element equation using Newmark direct integration method are given. The numerical modelling results show that the SMA can e?ectively improve the low velocity impact resistance performance of composite plate.

CALCULATION OF STRESSES IN A MULTIPLY-CONNECTED ANISOTROPIC PLATE USING STRESS FUNCTIONS OF MULTIPLE COMPLEX VARIABLES

On the basis of anisotropic mathematical elasticity,using multiple conformal representations, the stress functions of multiple complex variables for an infinite multiply-connected anisotropic plate are de- rived.The functions are developed in Fourier series on unit circles,and the unknown coefficients of the functions are determined by undetermined coefficients method.Then the stresses in the plate can be calcu- lated.A plate containing multiple elliptical holes or cracks is discussed,and the corresponding FORTRAN77 program is developed.Five examples are given.The results show that this method is very effective and convenient.

Effect of heat treatment on the microstructure and mechanical properties of structural steel–mild steel composite plates fabricated by explosion welding

Two dissimilar steel plates,structural steel and mild steel,were joined by explosion welding to form a composite.The composite was then heat-treated by quenching at 840℃ for 30 min followed by tempering at 200℃ for 3 h.The microstructure was investigated under an optical microscope and a scanning electron microscope.The mechanical properties were measured using Vickers microhardness and Charpy impact tests.The results show a deformed interface with typical wave features at the welding zone,but no defects were observed.Moreover,the ferrite in the parent plate in the weld zone was elongated due to the strong plastic deformation from the explosion.After heat treatment,the hardness of the flyer plate(structural steel)was over HV0.2800,while that of the parent plate(mild steel)was HV0.2200.The increase in hardness was due to the presence of martensite.Moreover,the average impact energy was increased from 18.5 to 44.0 J following heat treatment;this is because of the formation of recrystallized grains at the weld interface,which is due to the dynamic recovery and local recrystallization,and the strong elemental diffusion that occurred between the two plates.

Scale effects on nonlocal buckling analysis of bilayer composite plates under non-uniform uniaxial loads

Scale effects are studied on the buckling behavior of bilayer composite plates under non-uniform uniaxial compression via the nonlocal theory. Each isotropic plate is composed of a material that is different from others, and the adhesive between the plates is modeled as the Winkler elastic medium. According to the symmetry, effects of the Winkler non-dimensional parameter, the thickness ratio, the ratio of Young＇s moduli, and the aspect ratio are also considered on the buckling problem of bilayer plates, where only the top plate is under the uniaxial compression. Numerical examples show that the Winkler elastic coefficient, the thickness ratio, and the ratio of Young＇s moduli play decisive roles in the buckling behavior. Nonlocal effect is significant when the high-order buckling mode occurs or the aspect ratio is small.