APPROXIMATE VIBRATION ANALYSIS OF LAMINATED CURVED PANEL USING HIGHER-ORDER SHEAR DEFORMATION THEORY

An approximate analysis for free vibration of a laminated curved panel(shell)with four edges simply supported(SS2),is presented in this paper.The transverse shear deformation is considered by using a higher-order shear deformation theory.For solving the highly coupled partial differential governing equations and associated boundary conditions,a set of solution functions in the form of double trigonometric Fourier series,which are required to satisfy the geometry part of the considered boundary conditions,is assumed in advance.By applying the Galerkin procedure both to the governing equations and to the natural boundary conditions not satisfied by the assumed solution functions,an approximate solution,capable of providing a reliable prediction for the global response of the panel,is obtained.Numerical results of antisymmetric angle-ply as well as symmetric cross-ply and angle-ply laminated curved panels are presented and discussed.

Shear deformation and plate shape control of hot-rolled aluminium alloy thick plate prepared by asymmetric rolling process

Asymmetric rolling （ASR）, as one of severe plastic deformation （SPD） methods to make ultra-fine materials with enhanced performance is mainly used to prepare foil and thin strip. The asymmetrical rolling was achieved by adjusting the diameters of the upper roll and the bottom roll and was used to prepare hot-rolled thick plate of 5182 aluminium alloy. The shear deformation and plate shape control were experimentally studied. The experimental results show that asymmetrical rolling has a significant effect on metal deformation stream and can somehow refine microstructure and improve the uniformity of microstructure and properties. The asymmetrical rolling process can also reduce the rolling force. However, bending of rolling plate often happens during asymmetrical rolling process. The factors affecting the bending were discussed.

Closed-form solution to thin-walled box girders considering effects of shear deformation and shear lag

Considering three longitudinal displacement functions and uniform axial displacement functions for shear lag effect and uniform axial deformation of thin-walled box girder with varying depths,a simple and efficient method with high precision to analyze the shear lag effect of thin-walled box girders was proposed.The governing differential equations and boundary conditions of the box girder under lateral loading were derived based on the energy-variational method,and closed-form solutions to stress and deflection corresponding to lateral loading were obtained.Analysis and calculations were carried out with respect to a trapezoidal box girder under concentrated loading or uniform loading and a rectangular box girder under concentrated loading.The analytical results were compared with numerical solutions derived according to the high order finite strip element method and the experimental results.The investigation shows that the closed-form solution is in good agreement with the numerical solutions derived according to the high order finite strip method and the experimental results,and has good stability.Because of the shear lag effect,the stress in cross-section centroid is no longer zero,thus it is not reasonable enough to assume that the strain in cross-section centroid is zero without considering uniform axial deformation.

Closed-form solution for shear lag effects of steel-concrete composite box beams considering shear deformation and slip

Based on the consideration of longitudinal warp caused by shear lag effects on concrete slabs and bottom plates of steel beams,shear deformation of steel beams and interface slip between steel beams and concrete slabs,the governing differential equations and boundary conditions of the steel-concrete composite box beams under lateral loading were derived using energy-variational method.The closed-form solutions for stress,deflection and slip of box beams under lateral loading were obtained,and the comparison of the analytical results and the experimental results for steel-concrete composite box beams under concentrated loading or uniform loading verifies the closed-form solution.The investigation of the parameters of load effects on composite box beams shows that:1) Slip stiffness has considerable impact on mid-span deflection and end slip when it is comparatively small;the mid-span deflection and end slip decrease significantly with the increase of slip stiffness,but when the slip stiffness reaches a certain value,its impact on mid-span deflection and end slip decreases to be negligible.2) The shear deformation has certain influence on mid-span deflection,and the larger the load is,the greater the influence is.3) The impact of shear deformation on end slip can be neglected.4) The strain of bottom plate of steel beam decreases with the increase of slip stiffness,while the shear lag effect becomes more significant.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory

This study focusses on establishing the finite element model based on a new hyperbolic sheareformation theory to investigate the static bending,free vibration,and buckling of the functionally graded sandwich plates with porosity.The novel sandwich plate consists of one homogenous ceramic core and two different functionally graded face sheets which can be widely applied in many fields of engineering and defence technology.The discrete governing equations of motion are carried out via Hamilton’s principle and finite element method.The computation program is coded in MATLAB software and used to study the mechanical behavior of the functionally graded sandwich plate with porosity.The present finite element algorithm can be employed to study the plates with arbitrary shape and boundary conditions.The obtained results are compared with available results in the literature to confirm the reliability of the present algorithm.Also,a comprehensive investigation of the effects of several parameters on the bending,free vibration,and buckling response of functionally graded sandwich plates is presented.The numerical results shows that the distribution of porosity plays significant role on the mechanical behavior of the functionally graded sandwich plates。

Thermoelastic Analysis of Non-uniform Pressurized Functionally Graded Cylinder with Variable Thickness Using First Order Shear Deformation Theory(FSDT) and Perturbation Method

Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

THIRD ORDER SHEAR DEFORMATION MODEL FOR LAMINATED SHELLS WITH FINITE ROTATIONS:FORMULATION AND CONSISTENT LINEARIZATION

The paper presents an approach for the formulation of general laminated shells based on a third order shear deformation theory. These shells undergo finite (unlimited in size) rotations and large overall motions but with small strains. A singularity-free parametrization of the rotation field is adopted. The constitutive equations, derived with respect to laminate curvilinear coordinates, are applicable to shell elements with an arbitrary number of orthotropic layers and where the material principal axes can vary from layer to layer. A careful consideration of the consistent linearization procedure pertinent to the proposed parametrization of finite rotations leads to symmetric tangent stiffness matrices. The matrix formulation adopted here makes it possible to implement the present formulation within the framework of the finite element method as a straightforward task.

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

ON THE REFINED FIRST-ORDER SHEAR DEFORMATION PLATE THEORY OF KARMAN TYPE

A new refined first-order shear-deformation plate theory of the Karman type is presented for engineering applications and a new version of the generalized Karman large deflection equations with deflection and stress functions as two unknown variables is formulated for nonlinear analysis of shear-deformable plates of composite material and construction, based on the Mindlin/Reissner theory. In this refined plate theory two rotations that are constrained out in the formulation ate imposed upon overall displacements of the plates in an implicit role. Linear and nonlinear investigations may be mode by the engineering theory to a class of shear-deformation plates such as moderately thick composite plates, orthotropic sandwich plates, densely stiffened plates, and laminated shear-deformable plates. Reduced forms of the generalized Karman equations are derived consequently, which are found identical to those existe in the literature.

THE EFFECT OF TRANSVERSE SHEAR DEFORMATION ON STRESS CONCENTRATION FACTORS FOR SHALLOW SHELLS WITH A SMALL CIRCULAR HOLE

Simplified equations are derived for the analysis of stress concentration for shear-deformable shallow shells with a small hole. General solutions of the equations are obtained, in terms of series, for shallow spherical shells and shallow circular cylindrical shells with a small circular hole. Approximate explicit solutions and numerical results are obtianed for the stress concentration factors of shallow circular cylindrical shells with a small hole on which uniform pressure is acting.

Layerwise third-order shear deformation theory with transverse shear stress continuity for piezolaminated plates

Regarding laminated structures,an electromechanically coupled Finite Element(FE)model based on Layerwise Third-Order Shear Deformation(LW-TOSD)theory is proposed for sta-tic and dynamic analysis.LW-TOSD ensures the continuity of in-plane displacements and trans-verse shear stresses.The current LW-TOSD can be applied to arbitrary multi-layer laminated structures with only seven Degrees of Freedom(DOFs)for each element node and eliminates the use of the shear correction factors.Moreover,a shear penalty stiffness matrix is constructed to sat-isfy artificial constraints to optimize the structural shear strain.A dynamic finite element model is obtained based on LW-TOSD using the Hamilton's principle.First,the accuracy of the current model is validated by comparing with literature and ABAQUS results.Then,this study carries out numerical investigations of piezolaminated structures for different width-to-thickness ratios,length-to-width ratios,penalty stiffness matrix,boundary conditions,electric fields and dynamics.

Shear Deformation of DLC Based on Molecular Dynamics Simulation and Machine Learning

Shear deformation mechanisms of diamond-like carbon(DLC)are commonly unclear since its thickness of several micrometers limits the detailed analysis of its microstructural evolution and mechanical performance,which further influences the improvement of the friction and wear performance of DLC.This study aims to investigate this issue utilizing molecular dynamics simulation and machine learning(ML)techniques.It is indicated that the changes in the mechanical properties of DLC are mainly due to the expansion and reduction of sp3 networks,causing the stick-slip patterns in shear force.In addition,cluster analysis showed that the sp2-sp3 transitions arise in the stick stage,while the sp3-sp2 transitions occur in the slip stage.In order to analyze the mechanisms governing the bond breaking/re-formation in these transitions,the Random Forest(RF)model in ML identifies that the kinetic energies of sp3 atoms and their velocities along the loading direction have the highest influence.This is because high kinetic energies of atoms can exacerbate the instability of the bonding state and increase the probability of bond breaking/re-formation.Finally,the RF model finds that the shear force of DLC is highly correlated to its potential energy,with less correlation to its content of sp3 atoms.Since the changes in potential energy are caused by the variances in the content of sp3 atoms and localized strains,potential energy is an ideal parameter to evaluate the shear deformation of DLC.The results can enhance the understanding of the shear deformation of DLC and support the improvement of its frictional and wear performance.

Mass transport in a highly immiscible alloy on extended shear deformation

Forced mixing to a single-phase or supersaturated solid solution(SSS)and its prerequisite microstructure evolution in immiscible systems has been a focus of research for fundamental science and practical applications.Controlling the formation of SSS by shear deformation could enable a material design beyond conventional equilibrium microstructure in immiscible systems.Here,a highly immiscible Cu-50 at.%Cr binary alloy(mixing enthalpy of∼20 kJ mol^(−1))was employed to investigate the microstructure evolution and localized tendencies of SSS during severe shear deformation.Our results demonstrate the dislocation mediated microstructural refinement process in each phase of the binary alloy and the mechanisms associated with localized solute supersaturation as a function of shear strain.Pronounced grain refinement in the softer Cu phase occurs owing to the strain localization driving the preferential dynamic recrystallization.The grain refinement of the Cr phase,however,is enabled by the progressive evolution of grain lamination,splitting,and fragmentation as a function of shear strain.The solute supersaturation is found to be strongly dependent on the local environments that affect the dislocation activity,including the level of microstructure refinement,the interfacial orientation relationship,the mechanical incompatibility,and the localized preferential phase oxidation.Ab initio simulations confirm that it is more favorable to oxidize Cr than Cu at incoherent Cu/Cr interfaces,limiting the mass transport on an incoherent boundary.Our results unveil the mechanism underpinning the non-equilibrium mass transport in immiscible systems upon severe deformation that can be applied to produce immiscible alloys with superior mechanical properties.

Micro Defects Evolution of Nickel-Based Single Crystal Superalloys during Shear Deformation:A Molecular Dynamics Study

Nickel-based single crystal superalloys have become the main structural materials of the aero-engines due to excellent high-temperature strength.The micro defects evolution of nickel-based single crystal superalloys under shear deformation was investigated by molecular dynamics(MD)simulations in the present study.It is found that the interfacial dislocations decompose into Shockley dislocations under low shear stress,resulting in the plastic deformation of the Ni phase.The initial plastic deformation of the Ni3Al phase is caused by Shockley dislocations cutting into the Ni3Al phase.The following deformation from low temperature to medium temperature is controlled by dislocation slip,but the deformation at high temperature is changed.It is also found that the microvoid evolution can be divided into void growth and coalescence during shear deformation.The microvoid could prevent dislocation entanglement,accelerate dislocation decomposition,and promote earlier plastic deformation under relatively low temperatures.

Size-dependent thermomechanical vibration characteristics of rotating pre-twisted functionally graded shear deformable microbeams

A three-dimensional(3D)thermomechanical vibration model is developed for rotating pre-twisted functionally graded(FG)microbeams according to the refined shear deformation theory(RSDT)and the modified couple stress theory(MCST).The material properties are assumed to follow a power-law distribution along the chordwise direction.The model introduces one axial stretching variable and four transverse deflection variables including two pure bending components and two pure shear ones.The complex modal analysis and assumed mode methods are used to solve the governing equations of motion under different boundary conditions(BCs).Several examples are presented to verify the effectiveness of the developed model.By coupling the slenderness ratio,gradient index,rotation speed,and size effect with the pre-twisted angle,the effects of these factors on the thermomechanical vibration of the microbeam with different BCs are investigated.It is found that with the increase in the pre-twisted angle,the critical slenderness ratio and gradient index corresponding to the thermal instability of the microbeam increase,while the critical material length scale parameter(MLSP)and rotation speed decrease.The sensitivity of the fundamental frequency to temperature increases with the increasing slenderness ratio and gradient index,and decreases with the other increasing parameters.Moreover,the size effect can suppress the dynamic stiffening effect and enhance the Coriolis effect.Finally,the mode transition is quantitatively demonstrated by a modal assurance criterion(MAC).

Pressure generation under deformation in a large-volume press

Deformation can change the transition pathway of materials under high pressure,thus significantly affects physical and chemical properties of matters.However,accurate pressure calibration under deformation is challenging and thereby causes relatively large pressure uncertainties in deformation experiments,resulting in the synthesis of complex multiphase materials.Here,pressure generations of three types of deformation assemblies were well calibrated in a Walker-type largevolume press(LVP)by electrical resistance measurements combined with finite element simulations(FESs).Hard Al_(2)O_(3) or diamond pistons in shear and uniaxial deformation assemblies significantly increase the efficiency of pressure generation compared with the conventional quasi-hydrostatic assembly.The uniaxial deformation assembly using flat diamond pistons possesses the highest efficiency in these deformation assemblies.This finding is further confirmed by stress distribution analysis based on FESs.With this deformation assembly,we found shear can effectively promote the transformation of C60 into diamond under high pressure and realized the synthesis of phase-pure diamond at relatively moderate pressure and temperature conditions.The present developed techniques will help improve pressure efficiencies in LVP and explore the new physical and chemical properties of materials under deformation in both science and technology.

Restrained torsion of open thin-walled beams including shear deformation effects

A first-order torsion theory based on Vlasov theory has been developed to investigate the restrained torsion of open thin-walled beams. The total rotation of the cross section is divided into a free warping rotation and a restrained shear rotation. In first-order torsion theory, St. Venant torque is only related to the free warping rotation and the expression of St. Venant torque is derived by using a semi-inverse method. The relationship between the warping torque and the restrained shear rotation is established by using an energy method. The torsion shear coefficient is then obtained. On the basis of the torsion equilibrium, the governing differential equation of the restrained torsion is derived and the corresponding initial method is given to solve the equation. The relationship between total rotation and flee warping rotation is obtained. A parameter λ, which is associated with the stiffness property of a cross section and the beam length, is introduced to determine the condition, under which the St. Venant constant is negligible. Consequently a simplified theory is derived. Numerical examples are illustrated to validate the current approach and the results of the current theory are compared with those of some other available methods. The results of comparison show that the current theory provides more accurate results, In the example of a channel-shaped cantilever beam, the applicability of the simplified theory is determined by the parameter study of λ.

Vibration of functionally graded sandwich doubly curved shells using improved shear deformation theory

Nonlinear forced vibrations and natural frequency of sandwich functionally graded material doubly curved shallow shell with a rectangular base are investigated. The sandwich functionally graded material(FGM) doubly curved shell is subjected to a harmonic point load at centre. The sandwich doubly curved shell with homogeneous face sheets and FGM face sheets is considered respectively when the natural frequencies are studied. Reddy's third order shear deformation theory is expanded in which stretching effects in thickness are considered by introducing the secant function. Hamilton's principle and von-Karman type nonlinear geometric equation are applied to obtain partial differential equation of the FGM sandwich doubly curved shell. Comparative studies with other shear deformation theories are carried out to validate the present formulation. Navier method is used to discuss the natural vibration frequencies of the FGM sandwich doubly curved shell. Numerical simulation is applied to demonstrate the nonlinear dynamic responses of the FGM sandwich doubly curved shell. Multiple periods, quasi-period and chaos are detected for the dynamic system for different core thickness.

Electrical Power Generation Using Dynamic Piezoelectric Shear Deformation Under Friction

A new electrical power generation device based on high-frequency dynamic piezoelectric shear deformation under friction is developed.During the operation of a moving plate compressed and sliding on the top of a piezoelectric patch with constant velocity,dynamic shear deformation of the elastic piezoelectric patch is excited by periodic friction force and status(sliding and stick)variation.The dynamic piezoelectric shear strain can then generate continuous electrical power for energy absorbing and harvesting applications.The design of the piezoelectric couple device is first provided,and its mechanism,dynamic response and electric power generation under friction are described by a detailed iteration model.By comparing with previous experimental results,the accuracy of the proposed model is proven.Through numerical studies,the influences of the equivalent mass of the system,the velocity of the sliding object,the static friction coefficient and its lower limit,as well as the friction force delay rate on the power generation are obtained and discussed.The numerical results show that with the proposed design,up to 50-Watt maximum electrical power could be generated by a piezoelectric patch with a dimension of 20×2×6 cm under continuous friction with the moving plate at the velocity of 15 m/s.The possible bi-linear elastic stiffness variation of the system is also introduced,and the threshold of bi-linear elastic deformation,where the system stiffness changes,can be optimized for obtaining the highest power generation.