Computer simulation of shearing deformation in polymer systems with polar groups

In this work,shear strain modeling in materials consisting of a thin polymer layer(~15 nm),adhesive bonded to a rigid substrate,considered not to be impacted by deformation,was performed.A discrete-continuum model of chains system with a given stiffness with polar groups is developed.The polymer chain was considered in the framework of the persistene model,and the polar groups were based on the lattice model on the tetragonal lattice.It was assumed that the main contribution to the energy of interchain interactions is due to the potential of the polar groups and was calculated using the Metropolis algorithm.The potential interactions between the nearest polar groups of chains included the energy of dipole–dipole interactions(Keesom energy)and the Lennard–Jones potential.It is taken into account that the possible orientations of the polar groups are determined by the average elongation of the chain.Calculations showed that the dependence of free energy on the interchain distance has two minima.The first minimum is characterized by the orientational ordering of the polar groups,the second—by their disordered state.The depth and position of the minima depend on temperature,bending stiffness of the chain,the modulus of the dipole moment of the polar groups and the depth of the potential well in the Lennard–Jones energy.A step-by-step simulation of shear strain in a polymer layer in an orientationally disordered state was carried out.The obtained stress–strain diagrams make it possible to estimate the value of the elastic limit and also to determine the stresses at the points of phase transitions from a disordered to an orientationally ordered state.

Mechanical stress and deformation analyses of pressurized cylindrical shells based on a higher-order modeling

In this research,mechanical stress,static strain and deformation analyses of a cylindrical pressure vessel subjected to mechanical loads are presented.The kinematic relations are developed based on higherorder sinusoidal shear deformation theory.Thickness stretching formulation is accounted for more accurate analysis.The total transverse deflection is divided into bending,shear and thickness stretching parts in which the third term is responsible for change of deflection along the thickness direction.The axisymmetric formulations are derived through principle of virtual work.A parametric study is presented to investigate variation of stress and strain components along the thickness and longitudinal directions.To explore effect of thickness stretching model on the static results,a comparison between the present results with the available results of literature is presented.As an important output,effect of micro-scale parameter is studied on the static stress and strain distribution.

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.

Bending results of graphene origami reinforced doubly curved shell

The present work investigates higher order stress,strain and deformation analyses of a shear deformable doubly curved shell manufactures by a Copper(Cu)core reinforced with graphene origami auxetic metamaterial subjected to mechanical and thermal loads.The effective material properties of the graphene origami auxetic reinforced Cu matrix are developed using micromechanical models cooperate both material properties of graphene and Cu in terms of temperature,volume fraction and folding degree.The principle of virtual work is used to derive governing equations with accounting thermal loading.The numerical results are analytically obtained using Navier's technique to investigate impact of significant parameters such as thermal loading,graphene amount,folding degree and directional coordinate on the stress,strain and deformation responses of the structure.The graphene origami materials may be used in aerospace vehicles and structures and defence technology because of their low weight and high stiffness.A verification study is presented for approving the formulation,solution methodology and numerical results.

Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

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).

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.

DEFORMATION OF MOISTURE FLUX CIRCULATION SURROUNDING THE LANDFALL TYPHOON “BILIS”

The deformation parameter （DP）, which is defined as the product of shear deformation and stretching deformation of moisture flux circulation, is introduced. The tendency equation of DP is derived in pressure coordinates. Furthermore, DP is used to diagnose the deformation character of moisture flux circulation in the periphery of Bilis. The analysis showed that before Bilis landed, DP presented eight abnormal areas, which distributed alternately and closely encircled the low-pressure center. This indicated that the moisture flux circulation in the periphery of Bills rotated counterclockwise and stretched longitudinally and latitudinally to deform. After Bilis landed, DP weakened gradually and its regular pattern of horizontal distribution loosened. The shear and stretching deformations of moisture flux circulation surrounding Bilis weakened after the typhoon landed. The deformation of moisture flux circulation in the periphery of Bilis mainly appeared in the middle-lower troposphere. There existed 1/2 phase difference between the shear and stretching deformations in the vertical-latitudinal cross section and a π/4 phase difference between them on the horizontal plane. As Bilis landed and further moved inland of China, the intensities of DP, shear and stretching deformations decreased, meanwhile their vertical and horizontal structures became irregular. The chief dynamic factors responsible for the deformation of moisture flux circulation in the periphery of Bilis were the three terms associated with the three-dimensional advection transportation of DP, square difference between shear and stretching deformations coupling with Coriolis parameter, and horizontal gradient of geopotential height before Bilis landed. The last two dynamic factors impacted jointly on the deformation of moisture flux circulation after Bilis landed.

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。

Deformation Localization and Shear Fracture of a Rapidly Solidified Al-Fe-V-Si Alloy at Elevated Temperature

The tensile and fatigue behavior of a dispersoid strengthened, powder metallurgy Al-Fe-V-Si alloy at ambient and elevated temperatures was investigated. The results show that the strength and ductility of the alloy decrease significantly with increasing temperature and decreasing strain rate. Micro-structural examinations reveal that this change in mechanical behavior with increasing temperature is related to the mode of deformation of the alloy. Further observations show that localized shear deformation is responsible for the losses in both strength and ductility of the alloy at elevated temperature.

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.

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.

DEFORMATION LOCALIZATION AND SHEAR BAND FRACTURE IN STRONG ANISOTROPY SHEET TENSION

The tensile deformation localization and the shear band fracture behaviors of sheet metals with strong anisotropy are numerically simulated by using Updating Lagrange finite element method, Quasi-how plastic constitutive theory([1]) and B-L planar anisotropy yield criterion([2]). Simulated results are compared with experimental ones. Very good consistence is obtained between numerical and experimental results. The relationship between the anisotropy coefficient R and the shear band angle theta is found.

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.

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