A model of composite laminated Reddy beam based on a modified couple-stress theory

In this paper, a new anisotropic constitutive relation based on a modified couple-stress theory is defined for composite laminated Reddy beam. The theory contains only one material length-scale parameter in each ply of the composite laminated beam. The example of a cross-ply simply supported beam subjected to transverse load q₀sin(πx/L) is presented. Numerical results show that the proposed beam model can capture the scale effect of the microstructure. The proposed model can be reduced to several models of the modified couple-stress theory by adopting the assumptions in Timoshenko beam, Bernoulli–Euler beam and material isotropy. It can be seen that the deflections and stresses obtained by the proposed beam model are smaller than those based on Timoshenko and Bernoulli–Euler beam assumptions.     

A UNIFIED TIMOSHENKO BEAM B-SPLINE RAYLEIGH–RITZ METHOD FOR VIBRATION AND BUCKLING ANALYSIS OF THICK AND THIN BEAMS AND PLATES

First, the shear-locking phenomenon in the wψB_kSRRM^1–3 is investigated and the shear-locking terms are identified in both one-dimensional beam and two-dimensional plate analyses. Subsequently the shear-locking free conditions are proposed and under the guidance of these conditions the Timoshenko beam B-spline Rayleigh–Ritz method, designated as TB_kSRRM, is formulated for vibration analysis of beams based on Timoshenko beam theory and vibration and buckling analysis of isotropic plates or fibre-reinforced composite laminates based on the first-order shear deformation plate theory (SDPT). In TB_kSRRM the number of degrees of freedom is exactly the same as that when the Bernoulli–Euler beam theory or classical plate theory (CPT) is used. However, the TB_kSRRM includes the through-thickness shearing and rotary inertia effects in full. Several numerical applications are presented and they show that this unified approach is extremely efficient for both thick and thin beams and plates. © 1997 by John Wiley & Sons, Ltd.     

A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates

In this paper, a nth-order shear deformation theory is proposed to analyze the free vibration of laminated composite plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third-order theory can be considered as a special case of present nth-order theory (n = 3). Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties are computed by present nth-order theory and a meshless radial point collocation method based on the thin plate spline radial basis function. The results are compared with available published results which demonstrate the accuracy and efficiency of present nth-order theory.     

Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams

A class of higher-order continuum theories, such as modified couple stress, nonlocal elasticity, micropolar elasticity (Cosserat theory) and strain gradient elasticity has been recently employed to the mechanical modeling of micro- and nano-sized structures. In this article, however, we address stability problem of micro-sized beam based on the strain gradient elasticity and couple stress theories, firstly. Analytical solution of stability problem for axially loaded nano-sized beams based on strain gradient elasticity and modified couple stress theories are presented. Bernoulli–Euler beam theory is used for modeling. By using the variational principle, the governing equations for buckling and related boundary conditions are obtained in conjunctions with the strain gradient elasticity. Both end simply supported and cantilever boundary conditions are considered. The size effect on the critical buckling load is investigated.     

A new FE model based on higher order zigzag theory for the analysis of laminated sandwich beam with soft core

A new finite element (FE) model has been developed based on higher order zigzag theory (HOZT) for the static analysis of laminated sandwich beam with soft core. In this theory, the in-plane displacement variation is considered to be cubic for both the face sheets and the core. The transverse displacement is assumed to vary quadratically within the core while it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the beam. The nodal field variables are chosen in an efficient manner to overcome the problem of continuity requirement of the derivatives of transverse displacements. A C₀ quadratic beam finite element is implemented to model the HOZT for the present analysis. Numerical examples covering different features of laminated composite and sandwich beams are presented to illustrate the accuracy of the present model. Many new results are also presented which should be useful for future research.     

基于新修正偶应力理论的Mindlin层合板自由振动分析

该文基于各向异性修正偶应力理论建立一个Mindlin层合板（跨厚比10~20的中厚板）自由振动模型。该理论偶应力曲率张量不对称,但偶应力弯矩对称。利用Hamilton原理推导振动微分方程和边界条件。新模型可退化为修正偶应力层合薄板振动模型和经典Mindlin层合板振动模型。以正交铺设简支方板为例计算了偶应力模型的自振频率,分析偶应力Mindlin层合板的自由振动尺度效应。算例表明,该文建立的新修正偶应力层合板模型能够用于分析细观尺度下Mindlin层合板的自由振动及尺度效应。     

修正偶应力理论层合薄板稳定性模型及尺度效应

该文将各向同性修正偶应力理论推广到各向异性,提出各向异性的细观尺度的复合材料层合板的本构方程,基于虚功原理建立了各向异性修正偶应力理论并用于建立复合材料层合薄板偶应力理论稳定性模型。该理论的偶应力部分的转角不是独立变量(称为C1理论),对于各单层引入纤维和基体材料的不同的两个材料细观参数,建立了适用于层合板/夹层板的偶应力理论模型。该理论的应变不对称,但是,用于各向同性材料与修正偶应力理论等价。为了便于工程应用,忽略基体材料的细观长度参数,建立了各单层只含一个材料细观参数的偶应力层合薄板理论稳定性模型。算例表明建立的偶应力层合板模型能用于分析层合板稳定性的尺度效应。     

Spectral element model for axially loaded bending–shear–torsion coupled composite Timoshenko beams

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide extremely accurate solutions, while reducing the total number of degrees-of-freedom to resolve the computational and cost problems. Thus, in this paper, the spectral element model is developed for an axially loaded bending–shear–torsion coupled composite laminated beam which is represented by the Timoshenko beam model based on the first-order shear deformation theory. The high accuracy of the spectral element model is then numerically verified by comparing with exact theoretical solutions or the solutions obtained by conventional finite element method. For the numerical verification, the finite element model is also provided for the composite laminated beam.     

A theory of one-dimensional fracture

A completely analytical theory is developed for the mixed mode partition of one-dimensional fracture in laminated composite beams and plates. Two sets of orthogonal pure modes are determined first. It is found that they are distinct from each other in Euler beam or plate theory and coincide at the Wang-Harvey set in Timoshenko beam or plate theory. After the Wang-Harvey set is proved to form a unique complete orthogonal pure mode basis within the contexts of both Euler and Timoshenko beam or plate theories, it is used to partition a mixed mode. Stealthy interactions are found between the Wang-Harvey pure mode I modes and mode II modes in Euler beam or plate theory, which alter the partitions of a mixed mode. The finite element method is developed to validate the analytical theories.     

A model of composite laminated Reddy plate based on new modified couple stress theory

Based on new modified couple stress theory a model for composite laminated Reddy plate is developed in first time. In this theory a new curvature tensor is defined for establishing the constitutive relations of laminated plate. The characterization of anisotropy is incorporated into higher-order laminated plate theories based on the modified couple stress theory by Yang et al. in 2002. The form of new curvature tensor is asymmetric, however it can result in same as the symmetric curvature tensor in the isotropic elasticity. The present model of thick plate can be viewed as a simplified couple stress theory in engineering mechanics. Moreover, a more simplified model for cross-ply composite laminated Reddy plate of couple stress theory with one material’s length constant is used to demonstrate the scale effects. Numerical results show that the present plate model can capture the scale effects of microstructure. Additionally, the present model of thick plate model can be degenerated to the model of composite cross-ply laminated Kirchhoff plate and Mindlin plate of couple stress theory.     

Electrical resistivity of the hole doped La0.8Sr0.2MnO3 manganites: Role of electron–electron/phonon/magnon interactions

In this work, a quantitative analysis of reported metallic and insulating behaviour of resistivity in perovskite manganites La_0.8Sr_0.2MnO₃ is established. An effective inter-ionic interaction potential (EIoIP) with the long-range Coulomb, van der Waals (vdW) interaction and short-range repulsive interaction up to second-neighbour ions within the Hafemeister and Flygare approach was employed to estimate the Debye and Einstein temperature and was found to be consistent with the available experimental data. The electrical resistivity data in low temperature regime (T < T_MI) were theoretically analyzed within the framework of the classical electron–phonon model of resistivity, for example, the Bloch–Gruneisen (BG) model. The Bloch–Gruneisen (BG) model and terms T², T^4.5 simplify the electron–phonon, electron–electron and electron–magnon scattering processes. On the other hand, in high temperature regime (T > T_MI) the insulating nature is discussed with Mott's variable range hopping (VRH) model and small polaron conduction (SPC) model. For T > T_MI SPC model is more appropriate than the VRH model. The SPC model consistently retraces the higher temperature resistivity behaviour (T > θ_D/2). The metallic and semiconducting resistivity behaviours of La_0.8Sr_0.2MnO₃ manganites are analyzed, to the knowledge, for the first time highlighting the importance of electron–phonon, electron–electron, electron–magnon interactions and small polaron conduction.     

Shear coefficients for thin-walled composite beams

The shear coefficient in Timoshenko beam theory is obtained for thin-walled beams constructed of laminated panels of composite material using a variation of the method due to Cowper. Formulae are presented for a class of such composite beams. Comparisons are made with Cowper's original formulae for the case of an isotropic beam. The effect of shear deformation under static loading of typical composite beams is investigated. A procedure is outlined for the distribution of plies in the laminated panels to achieve optimal response under static or dynamic loading.     

Experimental design in the electrodeposition process of porous composite Ni–P + TiO2 coatings

In this paper, an environmentally friendly electroplating process of the composite Ni–P + TiO₂ coatings was developed. Such coatings were prepared by in situ codeposition of Ni–P with TiO₂ powder (anatase) on a polycrystalline copper substrate from the nickel-plating bath in which titanium dioxide particles were held in suspension. The codeposition was carried out under galvanostatic conditions on a rotating disc electrode. To optimize the production conditions of the Ni–P coatings modified with TiO₂ by the method of mathematical statistics, the Hartley's polyselective quasi D optimum plan of experiments was used. The relationship between the percentage content in the electrodeposited composite Ni–P + TiO₂ coatings (z) and the electrodeposition parameters like cathodic current density (j_dep), bath temperature (T) as well as content of TiO₂ powder suspended in the galvanic bath (c), has been described by the adequate cubic polynomial equation and illustrated graphically. Based on the Hartley's plan it can be stated that the maximal TiO₂ content of 28.7 at.% in the Ni–P + TiO₂ coating can be obtained for the following optimal parameters of the electrodeposition process: j_dep = 0.05 A cm⁻², c = 99 g dm⁻³ and T = 40 °C. The chemical and physical characteristics of the coating obtained under such optimum conditions, have been presented. The deposit exhibits the presence of TiO₂ particles embedded into the amorphous Ni–P matrix. It has been ascertained that embedding of TiO₂ powder to the amorphous Ni–P matrix leads to the production of deposits with large surface area. Such electrochemical codeposition method may be a good alternative in the field of porous composite coatings used in gas evolution.     

On dynamic-vibration analysis of temperature-dependent Timoshenko microbeam possessing mutable nonclassical length scale parameter

Abstract

In this research paper, lateral vibration analysis of simply-supported microbeam under thermal stress is investigated. Microbeam model is presented based on the modified couple stress theory and Timoshenko beam theory. Thermo-mechanical properties of the microbeam are assumed variable by temperature shifts. This means that any shift in the temperature leads to different thermo-mechanical properties. Thermal stress is induced to the system due to the temperature difference between the lateral surfaces and the system itself. Major novelty of the current research includes the variable nonclassical length scale parameter. The mentioned parameter derived from the modified couple stress theory is assumed variable based on the power law. Hamilton’s approach is taken to derive the system of governing equations of motion. The mentioned coupled system of equations is solved using the Navier method. For verification, current results are compared with those available at benchmark. This research implies the importance of temperature, distribution profile of nonclassical length scale parameter, and slenderness ratio upon dynamic responses of the present model based on both classical and modified couple stress theories.     

Structure and magnetic property of CoFe2−xSmxO4 (x = 0–0.2) nanofibers prepared by sol–gel route

CoFe_2−xSm_xO₄ (x = 0–0.2) nanofibers with diameters about 100–300 nm have been prepared using the organic gel-thermal decomposition method. The composition, structure and magnetic properties of the CoFe_2−xSm_xO₄ nanofibers were investigated by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, inductive coupling plasma mass analyzer and vibrating sample magnetometer. The CoFe_2−xSm_xO₄ (x = 0–0.2) nanofibers obtained at 500–700 °C are of a single spinel structure. But, at 800 °C with a relatively high Sm content of 0.15–0.2 the spinel CoFe_2−xSm_xO₄ ferrite is unstable and the second phase of perovskite SmFeO₃ occurs. The crystalline grain sizes of the CoFe_2−xSm_xO₄ nanofibers decrease with Sm contents, while increase with the calcination temperature. This grain reduction effect of the Sm³⁺ ions doping is largely owing to the lattice strain and stress induced by the substitution of Fe³⁺ ions with larger Sm³⁺ ions in the ferrite. The saturation magnetization and coercivity increase with the crystallite size in the range of 8.8–57.3 nm, while decrease with the Sm content from 0 to 0.2 owing to a smaller magnetic moment of Sm³⁺ ions. The perovskite SmFeO₃ in the composite nanofibers may contribute to a high coercivity due to the interface pinning, lattice distortion and stress in the ferrite grain boundary fixing and hindering the domain wall motion.     

Dielectric properties of Poly(vinylidene fluoride)/CaCu3Ti4O12 composites

The possibility of obtaining relatively high dielectric constant polymer–ceramic composite by incorporating the giant dielectric constant material, CaCu₃Ti₄O₁₂ (CCTO) in a Poly(vinylidene fluoride) (PVDF) polymer matrix by melt mixing and hot pressing process was demonstrated. The structure, morphology and dielectric properties of the composites were characterized using X-ray diffraction, Thermal analysis, scanning electron microscope, and impedance analyzer. The effective dielectric constant (ε_eff) of the composite increased with increase in the volume fraction of CCTO at all the frequencies (100 Hz–1 MHz) under study. The dielectric loss did not show any variation up to 40% loading of CCTO, but showed an increasing trend beyond 40%. The room temperature dielectric constant as high as 95 at 100 Hz has been realized for the composite with 55 vol.% of CCTO, which has increased to about 190 at 150 °C. Theoretical models like Maxwell’s, Clausius–Mossotti, Effective medium theory, logarithmic law and Yamada were employed to rationalize the dielectric behaviour of the composite and discussed.     

Compressive and impression creep behavior of a cast Mg–Al–Zn–Si alloy

Creep behavior of an Mg–6Al–1Zn–0.7Si cast alloy was investigated by compression and impression creep test methods in order to evaluate the correspondence of impression creep results and creep mechanisms with conventional compression test. All creep tests were carried out in the temperature range 423–523 K and under normal stresses in the range 50–300 MPa for the compression creep and 150–650 MPa for impression creep tests. The microstructure of the AZ61–0.7Si alloy consists of β-Mg₁₇Al₁₂ and Mg₂Si intermetallic phases in the α-Mg matrix. The softening of the former at high temperatures is compensated by the strengthening effect of the latter, which acts as a barrier opposing recovery processes. The impression results were in good agreement with those of the conventional compressive creep tests. The creep behavior can be divided into two stress regimes, with a change from the low-stress regime to the high-stress regime occurring, depending on the test temperature, around 0.009 < (σ/G) < 0.015 and 0.021 < (σ_imp/G) < 0.033 for the compressive and impression creep tests, respectively. Based on the steady-state power-law creep relationship, the stress exponents of about 4–5 and 10–12 were obtained at low and high stresses, respectively. The low-stress regime activation energies of about 90 kJ mol⁻¹, which are close to that for dislocation pipe diffusion in the Mg, and stress exponents in the range of 4–5 suggest that the operative creep mechanism is pipe-diffusion-controlled dislocation viscous glide. This behavior is in contrast to the high-stress regime, in which the stress exponents of 10–12 and activation energies of about 141 kJ mol⁻¹ are indicative of a dislocation climb mechanism similar to those noted in dispersion strengthening mechanisms.     

Experimental assessment of mixed-mode partition theories

The propagation of mixed-mode interlaminar fractures is investigated using existing experimental results from the literature and various partition theories. These are (i) a partition theory by Williams (1988) based on Euler beam theory; (ii) a partition theory by Suo (1990) and Hutchinson and Suo (1992) based on 2D elasticity; and (iii) the Wang–Harvey partition theories of the authors based on the Euler and Timoshenko beam theories. The Wang–Harvey Euler beam partition theory seems to offer the best and most simple explanation for all the experimental observations. No recourse to fracture surface roughness or new failure criteria is required. It is in excellent agreement with the linear failure locus and is significantly closer than other partition theories. It is also demonstrated that the global partition of energy release rate when using the Wang–Harvey Timoshenko beam or averaged partition theories or 2D elasticity exactly corresponds with the partition from the Wang–Harvey Euler beam partition theory. It is therefore concluded that the excellent performance of the Wang–Harvey Euler beam partition theory is either due to the failure of materials generally being based on global partitions or that for the specimens tested, the through-thickness shear effect is negligibly small. Further experimental investigations are definitely required.     

An alternative numerical solution of 900/00/900 cross-ply laminated composite plate using displacement potential approach

Conventional loading with a composite plate has a very small moment of inertia due to its low height, and it was solved by shear deformation and other approaches. In the present study, a thin cross-ply 90⁰/0⁰/90⁰ laminated composite plate is erected to increase its height, which increases its moment of inertia with load; increased moments of inertia of the plate increase its load-carrying capacity in a real structure. Finite difference solutions of a cross-ply 90⁰/0⁰/90⁰ laminated plate made of T-300 carbon/epoxy are obtained using displacement potential approach. The plate behaves like a cantilever beam; one end of the plate is rigidly fixed and a uniformly distributed load is applied on its top span. The displacement potential approach is extended using the lamination theory of composite materials and plane stress concept. The different equivalent displacement, strain, and stress components at different sections of the plate with its deformed shape are discussed. Using the concept of the classical theory of laminations, different stress components along the lamina and inter-laminar regions are obtained. Besides to verify the reliability and soundness of the present numerical approach, the solutions of the present problem are compared with those of the finite element method.     

Hydrogen absorption/desorption properties of Li–Al–N–H composite

Li₃AlH₆ and LiNH₂ at a 1:3 molar ratio were mechanically milled to yield a Li–Al–N–H composite. The hydrogen storage properties of the composite were studied using thermogravimetry, differential scanning calorimetry, mass spectrometry, and X-ray diffraction. Addition of LiNH₂ lowered the decomposition temperature of Li₃AlH₆. The Li–Al–N–H composite began to release hydrogen at around 110 °C, which was 90 °C lower than the initial desorption temperature of Li₃AlH₆. About 7.46 wt% of hydrogen was released from the composite after heating from room temperature to 500 °C. A total hydrogen desorption capacity of 8.15 wt% was obtained after accounting for hydrogen released in the ball-milling process. The resulting dehydrogenated composite absorbed 3.56 wt% of hydrogen at 400 °C under a hydrogen pressure of 110 bar. The hydrogen absorption capacity and kinetic properties of the Li–Al–N–H composite significantly improved when CeF₃ was added to the composite. A maximum hydrogen absorption capacity of 4.8 wt% was reached when the composite was doped with 2 mol% CeF₃.