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.

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。

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.

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.

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.

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).

Comparison of contribution of sub-rapid cooling and shear deformation to refinement of Fe-rich phase in hypereutectic Al-Fe alloy during rheo-extrusion

A hypereutectic Al-3Fe(wt.%)alloy was subjected by rheo-extrusion,and the effect of sub-rapid cooling and shear deformation on the refinement of Fe-rich phase was investigated.The results showed that both the primary Fe-rich phase and eutectic Fe-rich phase in the solidified Al-Fe alloy were finer than the platelike Fe-rich phase in the as-cast Al-Fe alloy with the same content of Fe.The solidified Al-Fe alloy was subjected to three stages of shear deformation,and both the primary Fe-rich phase and eutectic Fe-rich phase were fractured and the average length was refined to 400 nm,while Fe-rich phase in the as-cast Al-3Fe(wt.%)alloy was platelike and its average length was 40 pm.The tensile strength and elongation of the hypereutectic Al-3Fe(wt.%)alloy containing nanosized Fe-rich phase were 162 MPa and 25.78%while those of the as-cast AI-3Fe(wt.%)alloy containing coarse platelike Fe-rich phase were 102 MPa and 16.84%,respectively.In the refineme nt of Fe-rich phase in hypereutectic Al-Fe alloy during rheo-extrusion,the three stages of shear deformation contributed more than sub-rapid cooling.

DIFFERENTIAL QUADRATURE METHOD FOR BENDING OF ORTHOTROPIC PLATES WITH FINITE DEFORMATION AND TRANSVERSE SHEAR EFFECTS

Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.

Analysis on Shear Deformation for High Manganese Austenite Steel during Hot Asymmetrical Rolling Process Using Finite Element Method

Based on the rigid-plastic finite element method（FEM）, the shear stress field of deformation region for high manganese austenite steel during hot asymmetrical rolling process was analyzed. The influences of rolling parameters, such as the velocity ratio of upper to lower rolls, the initial temperature of workpiece and the reduction rate, on the shear deformation of three nodes in the upper, center and lower layers were discussed. As the rolling parameters change, distinct shear deformation appears in the upper and lower layers, but the shear deformation in the center layer appears only when the velocity ratio is more than 1.00, and the absolute value of the shear stress in this layer is changed with rolling parameters. A mathematical model which reflected the change of the maximal absolute shear stress for the center layer was established, by which the maximal absolute shear stress for the center layer can be easily calculated and the appropriate rolling technology can be designed.

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.

Some Observations of Flow Localization and Shear Cracking in Pearlite during Deformation

Flow localization, which is an importantmode of deformation in engineering materi-als, has been the interesting subject ofa number of experimental observationsand theoretical investigations in recentyears. However, the basic mechanism ofthe phenomena is not well understood atpresent. In a tensile test, the initiationand growth of a shear band are often simul-taneous. Therefore, it is rather difficult

Bending and stress analysis of polymeric composite plates reinforced with functionally graded graphene platelets based on sinusoidal shear-deformation plate theory

The bending and stress analysis of a functionally graded polymer composite plate reinforced with graphene platelets are studied in this paper.The governing equations are derived by using principle of virtual work for a plate which is rested on Pasternak’s foundation.Sinusoidal shear deformation theory is used to describe displacement field.Four different distribution patterns are employed in our analysis.The analytical solution is presented for a functionally graded plate to investigate the influence of important parameters.The numerical results are presented to show the deflection and stress results of the problem for four employed patterns in terms of geometric parameters such as number of layers,weight fraction and two parameters of Pasternak’s foundation.

Analysis of antisym metric cross-ply laminates using high-order shear deformation theories:a meshless approach

For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation.

DYNAMIC RESPONSE OF LAMINATED ORTHOTROPIC SPHERICAL SHELLSINCLUDING TRANSVERSE SHEAR DEFORMATION AND ROTATORY INERTIA

In this paper.the equations of motion of axisymmetrically laminated cylindrical orthotropic spherical shells are derived.Theeffects of transverse shear deformation and rotatory inertia are considered.On this basis,the dynamic response of spherical shells under axisymmetric dynamic load is calculated using the finite difference method The effects of material parameters.structural parameters and transverse shear dgformation are discussed.

KRMN-TYPE EQUATIONS FOR A HIGHER-ORDER SHEARDEFORMATION PLATE THEORY AND ITS USE IN THE THERMAL POSTBUCKLING ANALYSIS

arman-type nonlinear large deflection equations are derived occnrding to theReddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.