Theoretical and experimental investigation of the resonance responses and chaotic dynamics of a bistable laminated composite shell in the dynamic snap-through mode

The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.

Effects of Sinusoidal Vibration of Crystallization Roller on Composite Microstructure of Ti/Al Laminated Composites by Twin-Roll Casting

A new,innovative vibration cast-rolling technology of “electromagnetic stirring+dendrite breaking+asynchronous rolling” was proposed with the adoption of sinusoidal vibration of crystallization roller to prepare Ti/Al laminated composites,and the effect of sinusoidal vibration of crystallization roller on composite microstructure was investigated in detail.The results show that the metallurgical bonding of titanium and aluminum is realized by mesh interweaving and mosaic meshing,instead of transition bonding by forming metal compound layer.The meshing depth between titanium and aluminum layers (6.6μm) of cast-rolling materials with strong vibration of crystallization roller (amplitude 0.87 mm,vibration frequency 25 Hz) is doubled compared with that of traditional cast-rolling materials (3.1μm),and the composite interfacial strength(27.0 N/mm) is twice as high as that of traditional cast-rolling materials (14.9 N/mm).This is because with the action of high-speed superposition of strong tension along the rolling direction,strong pressure along the width direction and rolling force,the composite linearity evolves from "straight line" with traditional casting-rolling to "curved line",and the depth and number of cracks in the interface increases greatly compared with those with traditional cast-rolling,which leads to the deep expansion of the meshing area between interfacial layers and promotes the stable enhancement of composite quality.

Dynamic analysis of bio-inspired helicoid laminated composite plates resting on Pasternak foundation excited by explosive loading

This paper uses isogeometric analysis(IGA)based on higher-order shear deformation theory(HSDT)to study the dynamic response of bio-inspired helicoid laminated composite(B-iHLC)plates resting on Pasternak foundation(PF)excited by explosive loading.IGA takes advantage of non-uniform rational Bspline(NURBS)basic functions to exactly represent the structure geometry models and the attainment of higher-order approximation conditions.This method also ensures a C1 continuous function in the analysis of transverse shear deformation via HSDT.Furthermore,IGA eliminates the requirement for correction factors and delivers accurate results.Pasternak foundation with two stiffness parameters:springer stiffness(k_(1))and shear stiffness(k_(2)).The derivation of the governing equations is based on Hamilton's principle.The proposed method is validated through numerical examples.A comprehensive analysis of the impact of geometrical parameters,material properties,boundary conditions(BCs),and foundation stiffness on dynamic response of B-i HLC plates is carried out.

Effects of Hydrothermal Environment on the Deformation of the Thin Bamboo Bundle Veneer Laminated Composites

To overcome warping in thin bamboo bundle veneer laminated composites(TBLC),their hydrothermal deformation characteristics were systematically investigated in this study.It was found that TBLCs accelerated the release of internal stress in the thickness direction in a hydrothermal environment,which increased their warpage.TBLCs showed increased warpage in the width and diagonal directions upon increasing the temperature.The warpage of Type E increased by 155.88%and 66.67%in the width and diagonal directions,respectively,when the temperature increased from 25
C to 100
C.The symmetrical TBLC with cross-lay-up and odd layers displayed better hydrothermal stability.We revealed that the deformation of the TBLCs could be regulated under the synergistic effect of water and temperature.These results provide a scientific basis for improving the uniformity of bamboo bundle composite materials and for developing thin bamboo bundle fiber composite materials with designable structures and controllable performance.

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.

ROBUST OPTIMUM DESIGN OF LAMINATED COMPOSITE PLATES

A last-ply failure (LPF) analysis method for laminated composite plates is incorpo- rated into the ?nite element code-ANSYS, and a robust optimum design method is presented. The composite structure is analyzed by considering both in-plane and out-of-plane loads. For a lamina, two major failure modes are considered: matrix failure and ?ber breakage that are characterized by the proper strength criteria in the literature. When a lamina has failed, the laminate sti?ness is modi?ed to re?ect the damage, and stresses in the structure are re-analyzed. This procedure is repeatedly performed until the whole structure fails and thus the ultimate strength is determined. A structural optimization problem is solved with the ?ber orientation and the lamina thickness as the design variables and the LPF load as the objective. Finally, the robust optimum design method for laminates is presented and discussed.

Microstructure and mechanical properties of bio-inspired Cf/Ti/Mg laminated composites

Inspired by an old fish skin structure,the Cf/Ti/Mg laminated composites were fabricated by squeeze casting technology.No porous or voids were found in final composite,and carbon fiber was uniformly dispersed in Mg matrix.Furthermore,the addition of net-shaped Ti adsorbed Al element and facilitated the nucleation of Mg_(17)Al_(12)nearby Ti.The reaction product Al_(4)C_(3)was found at the Cf and AZ91 interface.Mechanical tests indicate that the introduction of Ti could greatly improve the toughness of Cf/Mg composites.

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.

Wave transmission through laminated composite double-walled cylindrical shell lined with porous materials

A study on free harmonic wave propagation in a double-walled cylindrical shell, whose walls sandwich a layer of porous materials, is presented within the framework of the classic theory for laminated composite shells. One of the most effective components of the wave propagation through the porous core is estimated with the aid of a flat panel with the same geometrical properties. By considering the effective wave component, the porous layer is modeled as a fluid with equivalent properties. Thus, the model is simplified as a double-walled cylindrical shell trapping the fluid media. Finally, the transmission loss （TL） of the structure is estimated in a broadband frequency, and then the results are compared.

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.

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.

A 3-Node Co-Rotational Triangular Finite Element for Non-Smooth,Folded and Multi-Shell Laminated Composite Structures

Based on the first-order shear deformation theory,a 3-node co-rotational triangular finite element formulation is developed for large deformation modeling of non-smooth,folded and multi-shell laminated composite structures.The two smaller components of the mid-surface normal vector of shell at a node are defined as nodal rotational variables in the co-rotational local coordinate system.In the global coordinate system,two smaller components of one vector,together with the smallest or second smallest component of another vector,of an orthogonal triad at a node on a non-smooth intersection of plates and/or shells are defined as rotational variables,whereas the two smaller components of the mid-surface normal vector at a node on the smooth part of the plate or shell(away from non-smooth intersections)are defined as rotational variables.All these vectorial rotational variables can be updated in an additive manner during an incremental solution procedure,and thus improve the computational efficiency in the nonlinear solution of these composite shell structures.Due to the commutativity of all nodal variables in calculating of the second derivatives of the local nodal variables with respect to global nodal variables,and the second derivatives of the strain energy functional with respect to local nodal variables,symmetric tangent stiffness matrices in local and global coordinate systems are obtained.To overcome shear locking,the assumed transverse shear strains obtained from the line-integration approach are employed.The reliability and computational accuracy of the present 3-node triangular shell finite element are verified through modeling two patch tests,several smooth and non-smooth laminated composite shells undergoing large displacements and large rotations.

Transient impact responses of laminated composite cylindrical shells

The generalized ray method(GRM) has been successfully used to study the transient elastic wave transmitting in the beams,planar trusses,space frames and infinite layered media.In this letter,the GRM is extended to investigate the early short time transient responses of laminated composite cylindrical shells under impact load.By using the Laplace transformation and referring to the boundary conditions,the ray groups transmitting in the finite laminated cylindrical shells under the shock load are obtained and the transient response related to each ray group can be derived via FFT algorithm.From the numerical results,it is shown that the early short time transient accelerations of the laminated composite cylindrical shell under impact loads are very large.But the short time transient shear strain and displacement are very small.

Interfacial Microstructure and Mechanical Properties of Al Alloy/Mg Alloy Laminated Composite Plates Fabricated by Equal Channel Angular Processing

KAl（7075）alloy/Mg（AZ31）alloy laminated composite plates were successfully fabricated by the equalchannelangular processing（ECAP）by using route A for 1,2,and 3 passes at 573 K,respectively.After fabrication,the 1-pass ECAPed laminated composite plates were annealed at different temperatures.The microstructure evolution,phase constituent,and bonding strength near the joining interface of Al（7075）alloy/Mg（AZ31）alloy laminated composites plates were evaluated with scanning electron microscopy,X-ray diffraction,and shear tests.The experimentalresults indicated that a 20 μm diffusion layer was observed at the joining interface of Al（7075）alloy/Mg（AZ31）alloy laminated composites plates fabricated by the 1-pass ECAP,which mainly included Al_3Mg_2 and Mg_（17）Al_（12） phases.With the increase of passes,the increase of diffusion layer thickness was not obvious and the form of crack in these processes led to the decrease of bonding strength.For 1-pass ECAPed composites,the thickness of diffusion layer remained unchanged after annealed at 473 K,while the bonding strength reached its maximum value 29.12 MPa.However,after elevating heat treatment temperature to 573 K,the thickness of diffusion layer increased rapidly,and thus the bonding strength decreased.

A STUDY OF THE POSTBUCKLING PATH OF CYLINDRICALLY CURVED PANELS OF LAMINATED COMPOSITE MATERIALS DURING LOADING AND UNLOADING

In this paper, Dynamic Relaxation Method is applied to study the postbuckling path of cylindrically curved panels of laminated composite materials during loading and unloading. The phenomenon that loading paths do not coincide with unloading paths has been found. Numerical results are given for cylindrically curved cross-ply panels subjected to uniform uniaxial compression under two types of boundary conditions. The influence of the number of layers, the panels curvature and the initial imperfection on the postbuckling paths is discussed.

Power transmission through double-walled laminated composite panels considering porous layer-air gap insulation

The acoustic behavior of double-walled laminated composite panels consisting of two porous and air gap middle layers is studied within the classical laminated plate theory （CLPT）. Thus, viscous and inertia coupling in a dynamic equation, as well as stress transfer, thermal and elastic coupling of porous material ave based on the Biot theory. In addition, the wave equations are extracted according to the vibration equation of composite layers. The transmission loss （TL） of the structure is then calculated by solving these equations simultaneously. Statistical energy analysis （SEA） is developed to divide the structure into specific subsystems, and power transmission is extracted with balancing power flow equations of the subsystems. Comparison between the present work and the results reported elsewhere shows excellent agreement. The results also indicate that, although favorable enhancement is seen in noise control particularly at high frequencies, the corresponding parameters associated with fluid phase and solid phase of the porous layer are important on TL according to the boundary condition interfaces. Finally, the influence of composite material and stacking sequence on power transmission is discussed.

Electron Beam-Physical Vapor Deposited TiAl-based Laminated Composite Sheet with Nb Layer Toughening

The TiAl-based laminated composite sheet of 150 mm × 100 mm × 0.2 mm, with 24 TiAl layers and 23 Nb layers laid alternately one on another, was successfully fabricated using the electron beam-physical vapor deposition （EB-PVD） method. The microstructure and properties of the sheet were investigated on an atomic force microscope （AFM）, a scanning electron microscope （SEM） and a tensile testing machine. The results indicate that the evenly distributed Nb layers are well joined with the TiAl layers, and the interfaces between layers are transparent, and every interlayer spacing is of about 8μm. The fractures appear to be a mixture of intergranular fractures and somewhat ductile quasi-cleavage ones. Despite its slight influence on ultimate tensile strength, the inserts of Nb layers efficiently increase the room temperature ductility of TiAl-based alloys due to the crack deflection effect.

Analytical model of sound transmission through laminated composite cylindrical shells considering transverse shear deformation

Composite structures are often used in the aerospace industry due to the advantages offered by a high strength to weight ratio. Sound transmission through an infinite laminated composite cylindrical shell is studied in the context of the transmission of airborne sound into the aircraft interior. The shell is immersed in an external fluid medium and contains internal fluid. Airflow in the external fluid medium moves with a constant velocity. An exact solution is obtained by simultaneously solving the first-order shear deformation theory （FSDT） of a laminated composite shell and the acoustic wave equations. Transmission losses （TL） obtained from numerical solutions are compared with those of other authors. The effects of structural properties and flight conditions on TL are studied for a range of values, especially, the Mach number, stack sequences, and the angle of warp. Additionally, comparisons of the transmission losses are made between the classical thin shell theory （CST） and FSDT for laminated composite and isotropic cylindrical shells.

Engineered Wood/Bamboo Laminated Composites for Outdoor Hydrophilic Platforms:Structural Design and Performance

Landscape designers increasingly prefer to use wood/bamboo-based composites for outdoor hydrophilic platforms owing to their natural surface texture,high performance,and sustainability to facilitate extensive interaction between people and water and enable the full range of ecological functions of water resources.In this study,four laminated composite(LC)structures were designed and manufactured using fluffed bamboo and wood veneers.Their surface textures,profile densities,water resistances,and mechanical properties were then evaluated.The type of fluffed veneer of the surface layer determined the texture of the LC surface.The specific structures of fluffed bamboo and wood veneer laminations were found to affect the LC profile density variability,water resistance,and mechanical properties owing to the differences in the strength and interfacial properties of bamboo and wood fibers.Finally,the water resistance and mechanical properties of all four LCs were found to be much higher than the highest level specified in GB/T 20241-2006 for“laminated veneer lumber”and GB/T 30364-2013 for“bamboo scrimber flooring”,indicating that they are promising materials for structures and flooring,particularly for outdoor hydrophilic platforms.

STABILITY OF LAMINATED COMPOSITE CIRCULAR CONICAL SHELLS UNDER EXTERNAL PRESSURE

In this paper, based on the mixed-type theory developed by the same authors, a theoretical analysis is presented for the stability of laminated composite circular conical shells under external pressure. The formulas for critical external pressure are obtained by using the potential energy variation principle. Very good agreement is shown between the theoretical prediction of critical external pressure and the experimental data. Finally, the influence of some parameters on critical external pressure is discussed numerically. The mixed-type theory developed by the same authors and the results obtained in this paper are very useful in aerospace engineering design.