Effect Of Shear Strain Research Articles

Large Deflection Stability of Slender Beam-Columns with Semirigid Connections: Elastica Approach

The large-deflection elastic analysis of slender beam-columns of symmetrical cross sections with semirigid connections under end loads ~forces and moments! including the effects of out-of-plumbness is developed in a classical manner. The classical theory of the ''Elastica'' and the corresponding elliptical functions are utilized in the proposed method which can be used in the large-deflection stability analysis of slender beam-columns with rigid, semirigid, and simple connections under any combination of end loads ~conserva- tive and nonconservative!. The proposed method consisting of a closed-form solution of the Elastica can also be utilized in the large deflection analysis of beam-columns whose connections suffer from flexural degradation or, on the contrary, flexural stiffening. The main limitation of the Elastica is that only flexural strains are considered ~the effects of axial and shear strains are neglected !. Therefore results from the proposed method are theoretically exact from small to very large curvatures and transverse and longitudinal displacements for plane beam-columns under bending actions. The large-deflection analysis of a beam-column with flexible connections at both ends becomes a complex problem requiring the simultaneous solution of at least two highly nonlinear equations with elliptical integrals. The solution of this problem becomes even more complex when the end connections are nonlinear or the direction of the applied end load changes ~like ''follower'' loads !. The validity and effectiveness of the proposed method and equations are verified against available solutions of very large deflection elastic analysis of beam-columns. Four comprehensive examples are included for verification and easy reference.

Stability of elastic and viscoelastic plate in gas flow taking into account shear strains under stochastic excitation

For the solution of stability problems for nonconservative systems the Bubnov–Galerkin method is often applied. In such a case functions of displacements are expanded in forms φ i (x) of proper oscillations of the elastic system. For obtaining more correct results in the expansion of displacements a significant number of terms should be kept. However, it should be kept in mind that with the increase of an ordinal number of modes in the indicated expansion of displacements the effect of shear strains and of the rotatory inertia increases, too. In the present work this problem is investigated for elastic and viscoelastic plates in a supersonic gas flow under a stochastic excitation.

Finite deformation plate theory and large rigid-body motions

A refined non-linear first-order theory of multilayered anisotropic plates undergoing finite deformations is elaborated. The effects of the transverse shear and transverse normal strains, and laminated anisotropic material response are included. On the basis of this theory, a simple and efficient finite element model in conjunction with the total Lagrangian formulation and Newton–Raphson method is developed. The precise representation of large rigid-body motions in the displacement patterns of the proposed plate elements is also considered. This consideration requires the development of the strain–displacement equations of the finite deformation plate theory with regard to their consistency with the arbitrarily large rigid-body motions. The fundamental unknowns consist of six displacements and 11 strains of the face planes of the plate, and 11 stress resultants. The element characteristic arrays are obtained by using the Hu–Washizu mixed variational principle. To demonstrate the accuracy and efficiency of this formulation and compare its performance with other non-linear finite element models reported in the literature, extensive numerical studies are presented.

Aeroelasticity of Composite Aerovehicle Wings in Supersonic Flows

A comprehensive aeroelastic model developed toward investigating the static divergence, e utter, and dynamic aeroelastic response of composite aerovehicle wings to sharp-edged gust and blast loads in supersonic e owe eld is presented. The aerovehicle wings are modeled as an anisotropic composite thin-walled beam structure featuring circumferentially asymmetric stiffness lay up that generates preferred elastic couplings. A number of nonclassical effects, such as transverse shear, warping restraint, and three-dimensional strain effects, are incorporated in the structural model. Based on the concept of two-dimensional indicial functions considered in conjunction with the aerodynamicstriptheoryextendedtothree-dimensionalwingmodel,theunsteadyaerodynamicloadsinsupersonic e ows are derived. The effect of elastic tailoring and the implications of transverse shear, warping restraint on divergence and dynamic response of selected wing cone gurations are investigated, and pertinent conclusions are outlined. Nomenclature AR = wing aspect ratio, L=b a.s/ = geometric quantity; see Eq. (2) and Fig. 3 aij = one-dimensional global stiffness coefe cients a1 = undisturbed speed of sound b;d = semichord and semidepth of the beam normal cross section, respectively bi = inertia coefe cient Eij = Young’ s modulus of orthotropic materials in the material coordinate system h.s/ = wall thickness as the function of the midline

Properties of Polymer Composites Based on Polysaccharides and Their Fabrication in Conditions of Solid-Phase Deformation under Pressure

The processes that take place in cellulose, chitosan, and their composites under the simultaneous effect of shear strains and pressure were investigated. Electron microscopy, IR spectroscopy, and NMR relaxation showed that dispersion of particles and amorphization of the structure with an increase in microregions with high adsorption potential take place in the individual polymers and their composites. It was found that when cellulose and cellulose—chitosan composites are ground, more intensive disordering of the structure with rearrangement of the initial system of hydrogen bonds takes place with an increase in the treatment temperature, and an inverse temperature dependence is found for chitosan. Films obtained from acetic acid solution of the mixture treated in an extruder have a high sorption capacity for copper ions and an anomalously high rate of chemisorption of copper in comparison to the additive capacity.

Analysis of Composite Structures

1R16. Analysis of Composite Structures. - C Decolon (Dept of Mech, Conservatoire Natl des Arts et Metiers, France). Hermes Sci Publ, Paris. Distributed in USA by Taylor & Francis Publ, New York NY. 2002. 336 pp. ISBN 1-56032-982-3. $135.00.Reviewed by E Armanios (Sch of Aerospace Eng, Georgia Inst of Tech, Atlanta GA 30332-0150).This book, comprising three parts and four appendices, provides a mathematical presentation of the governing equations for laminated composite plates and beams. The first part is devoted to the anisotropic constitutive relationships with emphasis on orthotropic materials. Hygrothermal effects are covered. Maximum stress and strain failure criteria are presented as well as Tsai-Hill, Tsai-Wu, and Hoffman polynomial based criteria. The second part treats laminated plates. The governing equations for thin plates based on the Kischhoff-Love assumptions are presented first. Symmetric orthotropic plates are studied for the cases of bending, vibration, and buckling. The stiffness coefficients for asymmetrical cases are presented as well. Bending, vibration, and buckling is presented for thin plates with asymmetric cross-ply as well as asymmetric balanced stacking sequences. Thermo-elastic behavior is considered through the derivation of the 3D and plane stress constitutive relationships for orthotropic off-axes layups. Applications to balanced and symmetric laminates are presented. Moderately thick orthotropic symmetric plates are analyzed using Reissner-Mindlin assumptions. Cylindrical bending of thin and moderately thick laminated plates is presented for the cases of bending, vibration, and buckling. The third part considers symmetrical beams starting with axial loading and followed by bending, including transverse shear strain effects. Applications to bending, vibration, and buckling are provided. Four appendices are devoted to the derivation of the governing equations for laminated plates. In the first two appendices, the governing equations of small and large transverse displacements of plates are derived by integrating the equations of motion. The third and fourth appendices use a variational formulation to obtain the governing equations for laminated plates based on Kirchoff-Love and Reissner-Mindlin assumptions, respectively. The book aims at presenting the basis for the analysis of composites structures. As such, minimum derivation of equations is provided mainly in appendices. The focus is on the mathematical presentation of governing equations and closed-form solutions. The book is suited as a reference for graduate students and practitioners of mechanics of laminated composites. Its appealing feature is the systematic and compact presentation of the governing equations of beams and laminated composite thin and moderately thick plates including small and large transverse displacements, into a single reference. The figures adequately illustrate the boundary and loading conditions associated with the development of the governing equations. None of the equations are numbered making it difficult at times to follow the mathematical presentation sequence across sections and chapters. The inclusion of references to specific works by some investigators would enhance the author’s presentation and comments within the text of the book. Analysis of Composite Structures should be a good reference for purchase by graduate students and practicing scientists and engineers.

Effects of Shear Strain and Drawing Pass on the Texture Development in Copper Wire

Effects of Shear Strain and Drawing Pass on the Texture Development in Copper Wire

Thickness-dependent renormalization of strain effects on self-organized InAs quantum dots grown on GaAs

The thickness-dependent renormalization of strain effects on self-organized InAs quantum dots has been systematically investigated. The photoluminescence-emission energy shift for the smaller quantum dots reveals both the hydrostatic and shear strain effects. However, the characteristics of the larger quantum dots are attributed predominantly to the hydrostatic effect. Furthermore, due to the elastic stiffness constant difference, the GaAs matrix-dependent characteristics were prevailed in the smaller quantum dots, while InAs-like properties were observed in the larger ones. All results indicate that the strain effect plays a major role in the emission energy of InAs quantum-dot heterosystems.

Stability of Elastomeric Isolation Bearings: Experimental Study

Elastomeric isolation bearings are required to be stable at high shear strains, which occur during strong earthquakes. Hence, rigorous determination of the critical axial load during design is important. Currently, the critical load is determined using the small displacement Haringx theory and modified to account for large shear strains by an approximate correction factor. The objective of this study is to experimentally determine the effect of horizontal displacement or shear strain on critical load and to study the validity of the approximate correction factor. Experiments were conducted on a series of elastomeric bearings with low shape factors. Test procedure and test results are presented in detail. It is shown that the critical load decreases with increasing horizontal displacement or shear strain. It is also shown that substantial critical load capacity exists at a horizontal displacement equal to the width of the bearing and is not zero, as predicted by the correction factor. It is further shown that the approximate formula is not conservative at smaller displacements and overly conservative at larger displacements. The critical loads obtained from experiments are compared with results from finite element analyses and nonlinear analytical solutions; the comparisons indicate that the effect of large horizontal displacements on the critical load can be reliably predicted.

磁性材料 Ｓｒフェライト粉とその成形体の磁気特性に及ぽすメカノフュージョン処理の影響

To investigate effects of shear stress and shear strain on the magnetic properties of Sr-ferrite powder, the powder was milled by a mechanofusion (MF) apparatus, and its magnetic characteristics were studied. Coercive force of the MF-milled powder was decreased with milling time, and it reached the constant value of 140 kA⋅m-1 as milling time was longer than 30 min. Reduction of the coercive force of the milled powder was found to slightly improve degree of powder particle alignment under applied magnetic fields. M-type ferrite phase of the original Sr-ferrite powder remains unchanged after the MF-milling treatment. The mean particle size of the powder was increased by a MF-milling treatment longer than 30 min due to aggregation of the powders. As a result, the optimum MF-milling time was in the range from 15 min to 30 min under the experimental conditions of this study.

Simple and effective elements based upon Timoshenko–Mindlin shell theory

The simple and effective mixed models are developed for the analysis of multilayered anisotropic Timoshenko–Mindlin-type shells. The effects of the transverse shear and transverse normal strains, and laminated anisotropic material response are included. The precise representation of rigid body motions in the displacement patterns of curved shell elements is considered. This consideration requires the development of the strain–displacement equations of the Timoshenko–Mindlin-type theory with regard to their consistency with the rigid body motions. The fundamental unknowns consist of six displacements and eleven strains of the face surfaces of the shell, and 11 stress resultants. The element characteristic arrays are obtained by using the Hu–Washizu mixed variational principle. Numerical results are presented to demonstrate the high accuracy and effectiveness of the developed mixed models and to compare their performance with other finite-element models reported in the literature.

Magnetoelastic effects in the antiferromagnetic spin-density wave alloy Cr+0.16 at% Pt

Measurements of the elastic constants and nonlinear acoustic properties of incommensurate spin-density wave Cr+0.16 at% Pt are reported. The observed hysteretic behaviour of the nonlinear acoustic properties in the antiferromagnetic phase is related to the effects of both volume and shear strains.

A general linear theory of laminated composite shells featuring interlaminar bonding imperfections

This paper is devoted to the foundation of a general linear theory of laminated composite anisotropic shells of arbitrary shape and curvature, in which the effect of the interfacial damage induced by the imperfect bonding between the constituent laminae is incorporated. In this context, the imperfect interface conditions are described in terms of linear relations between the interface tractions in the normal and tangential directions, and the respective displacement jumps. In addition to the effects of imperfectly bonded interfaces, the theory incorporates the effects of transverse shear and transverse normal strain, the dynamic effects, as well as the anisotropy of constituent material layers. Due to its general character, this theory can contribute to a more reliable prediction in the linear range of the load carrying capacitiy and failure of laminated composite shell structures featuring imperfectly bonded interfaces.

BOUNDARY-VALUE PROBLEMS OF THE THEORY OF THIN AND NONTHIN ORTHOTROPIC SHELLS WITH ACCOUNT OF NONLINEARLY ELASTIC PROPERTIES AND LOW SHEAR RIGIDITY OF COMPOSITE MATERIALS

The basic geometric and physical relations and resolving equations of the theory of thin and nonthin orthotropic composite shells with account of nonlinear properties and low shear rigidity of their materials are presented. They are derived based on two theories, namely the theory of anisotropic shells employing the Timoshenko or Kirchhoff-Love hypothesis and the nonlinear theory of elasticity and plasticity of anisotropic media in combination with the Lagrange variational principle. The procedure and algorithm for the numerical solution of nonlinear (linear) problems are based on the method of successive approximations, the difference-variational method, and the Lagrange multiplier method. Calculations of the stress-strain state for a spherical shell with a circular opening loaded with internal pressure are presented. The effect of transverse shear strains and physical nonlinearity of the material on the distribution of maximum deflections and circumferential stresses in the shell, obtained according to two variants of the shell theories, is studied. A comparison of the results of the problem solution in linear and nonlinear statements with and without account of the shell shear strains is given. The numerical data obtained for thin and nonthin (medium thick) composite shells are analyzed.

Strength of nanoscale copper under shear

Properties and processing of copper have received much interest among the electronics community mainly because of its low electrical resistance. One of its important application fields is in electrical interconnections. Mechanical properties of such nanoscale copper connections are, however, not well known and understood. In this article we study the effects of shear strain and stress in several nanoscale copper systems consisting of about 200 000 atoms with the effective-medium theory and molecular dynamics method. The role of polycrystalline microstructure on the shear strength is analyzed. It seems that the strength decreases as the grain size decreases, in contrast to macroscopic systems. In single crystals we study dislocation initiation and propagation. The results indicate that both sub- and supersonic dislocations may be present in copper. The minimum stress and strain, at which a dislocation initiated in a single crystal was 1.2 GPa and 4.6%. These values can be much larger than the values for a large scale copper sample, since polycrystalline microstructure was seen to decrease the system strength.

Mechanical properties of nanoscale copper under shear

We study the effects of shear strain and stress in several nanoscale copper systems consisting of about 200,000 atoms with the effective-medium theory and molecular dynamics method. Both single and polycrystal systems are studied. In single crystals, we concentrate on dislocation initiation and propagation and briefly discuss, what happens under oscillatory loading. In case of polycrystals, we study the validity of the Hall–Petch relation under shear. The results indicate that both sub- and super-sonic dislocations may be present in copper. The minimum stress and strain, at which a dislocation initiated in a single crystal was 1.2 GPa and 4.6%. These values can be much larger than the values for a real copper sample, since polycrystalline microstructure was seen to decrease the system strength.

Shear-induced changes of the potential energy landscape underlying n -butane liquids and glasses

The effects of shear strain on n-butane liquids and glasses are examined with molecular simulations. The simulations focus on the nonlinear mechanical properties and the transport properties of these systems. These properties are analyzed in terms of the changes in the potential energy landscape with strain, which is quantified by the curvature of the energy minima and the height, position, and curvature of barriers between minima. Shear strain is shown to cause local minima to disappear and barrier heights to decrease to zero, which renders the system mechanically unstable and forces the system toward alternate local minima. These disappearances of energy minima and barriers lead to plastic deformation in mechanically stressed n-butane glasses, and enhanced diffusion and molecular alignment in flowing n-butane liquids.

Strain effects on physical gelation of crystallizing isotactic polypropylene

Early stages of crystallization of polymers may be viewed as thermoreversible physical gelation in which molecular connectivity is introduced by crystallization. Effects of shear strain on the early stages of crystallization of a commercial isotactic polypropylene are studied by dynamic mechanical experiments. Shear creep with large strains (up to γ = 300) on the undercooled melt for short times (the time did not exceed 100 s) was followed by small amplitude oscillatory shear (SAOS) at a strain amplitude (γ a = 0.01) for gel-point detection. The imposed shear strongly accelerates gelation; gel times decrease in a power law with increasing strain. Strain applied during the crystal growth stage enhances gelation much stronger than strain applied in the earlier nucleation stage. For rapid gelation, frequency sweeps are not possible and new methods for gel-point detection need to be explored; here, we propose to estimate the gel point from the storage modulus growth at a single frequency. A value of 10% of the total growth of G' was found to be a good estimate for the gel point. High strain experiments show the complexity of underlying mechanisms of strain-enhanced crystallization and reveal at least two sequential stages in the structure development under shear: at the first stage, crystalline regions connect molecules into a loose network; at the second, stage-intense crystallinity growth within the network proceeds. Results have industrial importance in predicting/tuning structure development and connectivity growth during nonisothermal processing. Morphological study of the early stages of crystallization under strain is underway to explore molecular mechanisms, which govern the gelation process.

Shear strain effects on flexure and torsion of thin-walled pultruded composite beams

The paper presents a theoretical study on the static structural response of thin-walled composite open-section beams. Based on a Vlasov-type linear hypothesis, a beam theory is formulated in terms of in-plane elastic properties to analyze composite I and channel section pultruded beams which includes the transverse shear deformation of the beam cross section. The importance of the shear influence on the total vertical deflection is reported. Symmetric lay-up composite beams result in a bending-twisting structural coupling. The optimal fibre orientation for minimizing vertical displacements and twist angle is also investigated.Key words: pultruded, shear strain, composite beams, twist.

SHEAR AND NORMAL STRAIN EFFECTS OF CORE LAYERS IN VIBRATION OF SQUARE SANDWICH PLATES UNDER CLAMPED BOUNDARY CONDITIONS

The authors previously investigated the effects of both shear and normal strains in the viscoelastic core layer on modal properties of sandwich plates under hinged boundary conditions. For such boundary conditions, analytic formulation of characteristic equations was possible. Agreeing that most real boundary conditions must lie somewhere between hinged and clamped, it is naturally worthwhile to solve for the clamped boundary conditions, for which, however, analytic formulation of the characteristic equations is not possible. In this study, hence, the finite difference method is utilized as a tool for numerical analysis. The effects of neglecting the extensional or compressional strain in the core material for the clamped boundary conditions are studied and compared with the case of simply supported boundary conditions.