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).

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.

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。

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.

Dynamic stability analysis of porous functionally graded beams under hygro-thermal loading using nonlocal strain gradient integral model

We present a study on the dynamic stability of porous functionally graded(PFG)beams under hygro-thermal loading.The variations of the properties of the beams across the beam thicknesses are described by the power-law model.Unlike most studies on this topic,we consider both the bending deformation of the beams and the hygro-thermal load as size-dependent,simultaneously,by adopting the equivalent differential forms of the well-posed nonlocal strain gradient integral theory(NSGIT)which are strictly equipped with a set of constitutive boundary conditions(CBCs),and through which both the stiffness-hardening and stiffness-softening effects of the structures can be observed with the length-scale parameters changed.All the variables presented in the differential problem formulation are discretized.The numerical solution of the dynamic instability region(DIR)of various bounded beams is then developed via the generalized differential quadrature method(GDQM).After verifying the present formulation and results,we examine the effects of different parameters such as the nonlocal/gradient length-scale parameters,the static force factor,the functionally graded(FG)parameter,and the porosity parameter on the DIR.Furthermore,the influence of considering the size-dependent hygro-thermal load is also presented.

Shear wave elastography results correlate with liver fibrosis histology and liver function reserve

AIM: To evaluate the correlation of shear wave elastography (SWE) results with liver fibrosis histology and quantitative function reserve. METHODS: Weekly subcutaneous injection of 60% carbon tetrachloride (1.5 mL/kg) was given to 12 canines for 24 wk to induce experimental liver fibrosis, with olive oil given to 2 control canines. At 24 wk, liver condition was evaluated using clinical biochemistry assays, SWE imaging, lidocaine metabolite monoethylglycine-xylidide (MEGX) test, and histologic fibrosis grading. Clinical biochemistry assays were performed at the institutional central laboratory for routine liver function evaluation. Liver stiffness was measured in triplicate from three different intercostal spaces and expressed as mean liver stiffness modulus (LSM). Plasma concentrations of lidocaine and its metabolite MEGX were determined using high-performance liquid chromatography repeated in duplicate. Liver biopsy samples were fixed in 10% formaldehyde, and liver fibrosis was graded using the modified histological activity index Knodell score (F0-F4). Correlations among histologic grading, LSM, and MEGX measures were analyzed with the Pearson linear correlation coefficient. RESULTS: At 24 wk liver fibrosis histologic grading was as follows: F0, n = 2 (control); F1, n = 0; F2, n = 3; F3, n = 7; and F4, n = 2. SWE LSM was positively correlated with histologic grading (r = 0.835, P < 0.001). Specifically, the F4 group had a significantly higher elastic modulus than the F3, F2, and F0 groups (P = 0.002, P = 0.003, and P = 0.006, respectively), and the F3 group also had a significantly higher modulus than the control F0 group (P = 0.039). LSM was negatively associated with plasma MEGX concentrations at 30 min (r = -0.642; P = 0.013) and 60 min (r = -0.651; P = 0.012), time to 1/2 of the maximum concentration (r = -0.538; P = 0.047), and the area under the curve (r = -0.636; P = 0.014). Multiple comparisons showed identical differences in these three measures: significantly lower with F4 (P = 0.037) and F3 (P = 0.032) as compared to F0 and significantly lower with F4 as compared to F2 (P = 0.032). CONCLUSION: SWE LSM shows a good correlation with histologic fibrosis grading and pharmacologic quantitative liver function reserve in experimental severe fibrosis and cirrhosis.

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

In this pap er, a novel size-dep endent functionally graded (FG) cylindrical shell model is develop ed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory . The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical typ es of size e ects simultaneously , which are the nonlocal stress ef- fect, the strain gradient e ect, and the surface energy e ects. With the help of Hamilton’s principle and rst-order shear deformation theory , the non-classical governing equations and related b oundary conditions are derived. By using the prop osed model, the free vibra- tion problem of FG cylindrical nanoshells with material prop erties varying continuously through the thickness according to a p ower-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various b oundary conditions are obtained. After verifying the reliability of the prop osed model and analytical method by comparing the degenerated results with those available in the literature, the in uences of nonlocal parameter, material length scale parameter, p ower-law index, radius-to-thickness ratio, length-to-radius ratio, and surface e ects on the vibration characteristic of func- tionally graded cylindrical nanoshells are examined in detail.

Metallurgical analysis of a failed maraging steel shear screw used in the band separation system of a satellite launch vehicle

Maraging steels have excellent combination of strength and toughness and are extensively used for a variety of aerospace applications. In one such critical application, this steel was used to fabricate shear screws of a stage separation system in a satellite launch vehicle. During assembly preparations, one of the shear screws which connected the separation band and band end block has failed at the first thread. Microstructural analysis revealed that the crack originated from the root of the thread and propagated in an intergranular mode. The failure is attributed to combined effect of stress and corrosion leading to stress corrosion cracking.

Size-dependent shear buckling response of FGM skew nanoplates modeled via different homogenization schemes

The size effects on the shear buckling behaviors of skew nanoplates made of functionally graded materials(FGMs)are presented.The material properties are supposed to be changed uniformly from the ceramic phase to the metal one along the plate thickness.To estimate the associated effective material properties,various homogenization schemes including the Reuss model,the Voigt model,the Mori-Tanaka model,and the Hashin-Shtrikman bound model are used.The nonlocal elasticity theory together with the oblique coordinate system is applied to the higher-order shear deformation plate theory to develop a size-dependent plate model for the shear buckling analysis of FGM skew nanoplates.The Ritz method using Gram-Schmidt shape functions is used to solve the size-dependent problem.It is found that the significance of the nonlocality in the reduction of the shear buckling load of an FGM skew nanoplate increases for a higher value of the material property gradient index.Also,by increasing the skew angle,the critical shear buckling load of an FGM skew nanoplate enhances.This pattern becomes a bit less significant for a higher value of the material property gradient index.Furthermore,among various homogenization models,the Voigt and Reuss models in order estimate the overestimated and underestimated shear buckling loads,and the difference between them reduces by increasing the aspect ratio of the skew nanoplate.

Interfacial behavior of a thermoelectric film bonded to a graded substrate

To improve the thermoelectric converting performance in applications such as power generation,reutilization of heat energy,refrigeration,and ultrasensitive sensors in scramjet engines,a thermoelectric film/substrate system is widely designed and applied,whose interfacial behavior dominates the strength and service life of thermoelectric devices.Herein,a theoretical model of a thermoelectric film bonded to a graded substrate is proposed.The interfacial shear stress,the normal stress in the thermoelectric film,and the stress intensity factors affected by various material and geometric parameters are comprehensively studied.It is found that adjusting the inhomogeneity parameter of the graded substrate,thermal conductivity,and current density of the thermoelectric film can reduce the risk of interfacial failure of the thermoelectric film/graded substrate system.Selecting a stiffer and thicker thermoelectric film is advantageous to the reliability of the thermoelectric film/graded substrate system.The results should be of great guiding significance for the present and upcoming applications of thermoelectric materials in various fields.

Thermo-mechanical Behaviors of Functionally Graded Shape Memory Alloy Timoshenko Composite Beams

This paper focuses on the thermo-mechanical behaviors of functionally graded(FG)shape memory alloy(SMA)composite beams based on Timoshenko beam theory.The volume fraction of SMA fiber is graded in the thickness of beam according to a power-law function and the equivalent parameters are formulated.The governing differential equations,which can be solved by direct integration,are established by employing the composite laminated plate theory.The influences of FG parameter,ambient temperature and SMA fiber laying angle on the thermo-mechanical behaviors are numerically simulated and discussed under different boundary conditions.Results indicate that the neutral plane does not coincide with the middle plane of the composite beam and the distribution of martensite is asymmetric along the thickness.Both the increments of the functionally graded parameter and ambient temperature make the composite beam become stiffer.However,the influence of the SMA fiber laying angle can be negligent.This work can provide the theoretical basis for the design and application of FG SMA structures.

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.

Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the thickness direction of the beam. By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material （FGM）, certain vibration characteristics are affected. Results are presented to demonstrate the effects of shear deformation, fiber volume fraction, and boundary conditions on the natural frequencies and mode shapes of composite beams.

Effect of different geometrical non-uniformities on nonlinear vibration of porous functionally graded skew plates: A finite element study

This article presents the investigation of nonlinear vibration analysis of tapered porous functionally graded skew(TPFGS)plate considering the effects of geometrical non-uniformities to optimize the thickness in the structural design.The TPFGS plate is analyzed considering linearly,bi-linearly,and exponentially varying thicknesses.The plate’s effective material properties are tailor-made using a modified power-law distribution in which gradation varies along the thickness direction of the TPFGS plate.Incorporating the non-linear finite element formulation to develop the kinematic equation’s displacement model for the TPFGS plate is based on the first-order shear deformation theory(FSDT)in conjunction with von Karman’s nonlinearity.The nonlinear governing equations are established by Hamilton’s principle.The direct iterative method is adopted to solve the nonlinear mathematical relations to obtain the nonlinear frequencies.The influence of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the TPFGS plate for different skew angles and variable thicknesses are studied for various geometrical parameters.The influence of taper ratio,variable thickness,skewness,porosity distributions,gradation,and boundary conditions on the plate’s nonlinear vibration is demonstrated.The nonlinear frequency analysis reveals that the geometrical nonuniformities and porosities significantly influence the porous functionally graded plates with varying thickness than the uniform thickness.Besides,exponentially and linearly variable thicknesses can be considered for the thickness optimizations of TPFGS plates in the structural design.

Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory

This manuscript presents the comprehensive study of thickness stretching effects on the free vibration,static stability and bending of multilayer functionally graded(FG)carbon nanotubes reinforced composite(CNTRC)nanoplates.The nanoscale and microstructure influences are considered through a modified nonlocal strain gradient continuum model.Based on power-law functions,four different patterns of CNTs distribution are considered in this analysis,a uniform distribution UD,FG-V CNTRC,FG-X CNTRC,and FG-O CNTRC.A 3D kinematic shear deformation theory is proposed to include the stretching influence,which is neglected in classical theories.Hamilton's principle is applied to derive the governing equations of motion and associated boundary conditions.Analytical solutions are developed based on Galerkin method to solve the governing equilibrium equations based on the generalized higher-order shear deformation theory and the nonlocal strain gradient theory and get the static bending,buckling loads,and natural frequencies of nanoplates.Verification with previous works is presented.A detailed parametric analysis is carried out to highlight the impact of thickness stretching,length scale parameter(nonlocal),material scale parameter(gradient),CNTs distribution pattern,geometry of the plate,various boundary conditions and the total number of layers on the stresses,deformation,critical buckling loads and vibration frequencies.Many new results are also reported in the current study,which will serve as a benchmark for future research.

Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shells

This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, the linear distribution of electric potential across the thickness of the piezoelectric layer and five different types of carbon nanotube(CNT) distributions through the thickness direction are considered. Based on the four-variable shear deformation refined shell theory, governing equations are obtained by applying Hamilton's principle. Navier's solution for the shell panels with the simply supported boundary condition at all four edges is derived. Several numerical examples validate the accuracy of the presented solution. New parametric studies regarding the effects of different material properties, shell geometric parameters, and electrical boundary conditions on the free vibration responses of the hybrid panels are investigated and discussed in detail.

弹性支撑功能梯度压电多孔微圆柱壳的自由振动分析

旨在研究热-力-电载荷下弹性支撑功能梯度压电多孔微圆柱壳的自由振动。首先,建立弹性支撑功能梯度压电多孔微圆柱壳动力学模型;然后,应用三阶剪切变形壳体理论和修正的偶应力理论,推出弹性支撑功能梯度压电多孔微圆柱壳模态频率的解析解;最后,通过数值算例分析了微圆柱壳模态频率的影响因素。结果表明:Pasternak弹性支撑比Winkler弹性支撑更有利于提高微圆柱壳的模态频率;改变弹性支撑的刚度系数、轴向力、外加电压、孔隙分布、材料体积分数指数和结构尺寸可调节微圆柱壳的模态频率;孔隙体积分数越大,温度或轴向力对模态频率的影响越大,而电压对模态频率的影响则越小;不同材料指数下,增大孔隙体积分数对模态频率的影响趋势不同;弹性支撑会减弱温度、轴向力和电压对模态频率的影响,对薄圆柱壳或短圆柱壳模态频率的影响较为显著。

压电集成石墨烯增强功能梯度多孔板的等几何建模与分析

基于等几何分析方法和一种仅含有4自由度的简化一阶剪切变形理论(simple first-order shear deformation theory,S-FSDT)建立了压电集成石墨烯增强功能梯度多孔(piezoelectric integrated graphene platelets reinforced functionally graded porous,P-GPLs-FGP)板的数值分析模型。利用Halpin-Tsai微观力学模型、闭胞体高斯随机场理论和混合定律得到了石墨烯增强功能梯度多孔板的有效材料属性;基于等几何分析方法、S-FSDT和哈密顿原理推导了P-GPLs-FGP板的运动控制方程,并通过与已有算例对比验证了模型的准确性和有效性;利用所建模型分析了孔隙分布形式、孔隙系数、石墨烯分布形式、石墨烯质量分数、边界条件和宽厚比对P-GPLs-FGP板固有频率和机-电载荷作用下静态弯曲响应的影响。研究结果表明:板的刚度与孔隙系数成反比,而在基体材料中添加少量的石墨烯可以有效地增强结构的刚度;与其他组合形式相比,板的刚度在孔隙PD-S分布和石墨烯GPL-S分布时最大。

海陆交互相软土固结抗剪强度指标变化规律研究

以珠三角地区海陆交互相淤泥质软土为研究对象,通过室内直剪试验探究不同固结压力和固结度下抗剪强度及抗剪强度指标的变化规律,提出抗剪强度及对应指标-固结度-固结压力三维Logistic数学模型。研究结果表明,当固结压力P≥200 kPa、固结度U≥40%时,软土黏聚力(c)和内摩擦角(φ)增长较为明显;当U=100%时,各级固结压力作用下的软土抗剪强度(τ)相较于初始状态分别提高了7.89、12.73、13.50、18.20、22.38 kPa;所给出的三维数学模型可直接计算出某一固结压力和固结度下的抗剪强度指标c、φ、τ。研究成果能够更为准确地评价该地区软土地基逐级加载过程中的整体稳定性。

功能梯度多孔磁电弹板的等几何建模与自由振动分析

针对功能梯度多孔磁电弹(functional graded porous-magneto electro elastic,FGP-MEE)板结构,该文基于等几何分析法(isogeometric analysis,IGA),采用一阶剪切变形理论(first-order shear deformation theory,FSDT)建立了等几何数值分析模型。首先,根据修正幂律(modified power law,MPL)方法得到了具有4种不同孔隙分布形式(V_(u),V_(o),V_(x),V_(v))功能梯度多孔磁电弹结构的等效材料参数;然后,利用磁-电-弹耦合本构方程、哈密顿变分原理以及等几何分析方法推导了FGP-MEE板的控制方程,并通过与已有文献对比,验证了所建模型的有效性和准确性;最后,研究了孔隙系数、功能梯度指数、孔隙分布形式、结构的几何参数(宽厚比、长宽比)以及边界条件对FGP-MEE板自由振动的影响。研究结果表明,材料中孔隙分布形式、孔隙系数以及功能梯度指数的变化对FGP-MEE板的固有频率有较大影响,且在孔隙呈V_o型分布时板的固有频率最大。