Nonlinear in-plane thermal buckling of rotationally restrained functionally graded carbon nanotube reinforced composite shallow arches under uniform radial loading

The nonlinear in-plane instability of functionally graded carbon nanotube reinforced composite (FG-CNTRC) shallow circular arches with rotational constraints subject to a uniform radial load in a thermal environment is investigated. Assuming arches with thickness-graded material properties, four different distribution patterns of carbon nanotubes (CNTs) are considered. The classical arch theory and Donnell’s shallow shell theory assumptions are used to evaluate the arch displacement field, and the analytical solutions of buckling equilibrium equations and buckling loads are obtained by using the principle of virtual work. The critical geometric parameters are introduced to determine the criteria for buckling mode switching. Parametric studies are carried out to demonstrate the effects of temperature variations, material parameters, geometric parameters, and elastic constraints on the stability of the arch. It is found that increasing the volume fraction of CNTs and distributing CNTs away from the neutral axis significantly enhance the bending stiffness of the arch. In addition, the pretension and initial displacement caused by the temperature field have significant effects on the buckling behavior.     

Modeling and analysis of functionally graded carbon nanotube reinforced composite structures: A review

功能梯度碳纳米管增强复合材料是一种新一代的先进复合材料.在这种材料中,碳纳米管作为增强体在空间位置上梯度排布.功能梯度碳纳米管增强复合材料的力学行为已成为近年来材料科学与工程科学的研究热点.本文对功能梯度碳纳米管增强复合材料结构的建模与分析的研究进展进行评述,集中讨论功能梯度碳纳米管增强复合材料梁、板、壳在各种载荷条件下,边界条件下和环境条件下的线性和非线性弯曲、屈曲和后屈曲、振动和动力响应.文中所列成果可以看作是进一步研究的基石.最后,提出需要进一步研究的方向.     

Influence of elastic foundations and carbon nanotube reinforcement on the hydrostatic buckling pressure of truncated conical shells

In this study, the effects of elastic foundations(EFs) and carbon nanotube(CNT) reinforcement on the hydrostatic buckling pressure(HBP) of truncated conical shells(TCSs) are investigated. The first order shear deformation theory(FOSDT) is generalized to the buckling problem of TCSs reinforced with CNTs resting on the EFs for the first time. The material properties of composite TCSs reinforced with CNTs are graded linearly according to the thickness coordinate. The Winkler elastic foundation(W-EF...     

SMA纤维复合材料梁振动半主动控制

分析了一类形状记忆合金(SMA)纤维混杂层合粱用于振动控制的动力学模型和作用机理．采用多胞模型、形状记忆合金一维本构关系分析方法，同时考虑横向剪切的影响，建立了层合梁的数学模型．半主动控制是通过改变受控结构的参数来减小结构振动的响应．根据开关控制原理确定可变刚度系统的控制律，进行SMA纤维混杂层合粱的半主动控制的数值仿真．结果表明，将半主动控制应用于梁的振动控制是一种有效的方法．     

含脱层损伤复合材料层合梁的冲击动力屈曲

针对含初始缺陷和脱层损伤的复合材料层合梁的轴向冲击动力屈曲问题进行了分析。基于Hamilton原理导出了考虑初始缺陷、轴向和横向惯性、横向剪切变形以及转动惯性影响时含脱层损伤复合材料梁的非线性动力屈曲控制方程;基于B-R准则,采用有限差分方法求解了受轴向冲击载荷作用下含脱层损伤复合材料梁的动力屈曲问题;讨论了冲击速度、初始几何缺陷、铺层角度以及脱层长度等因素对复合材料层合梁动力屈曲的影响。     

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction

The structural instability of multi-walled carbon nanotubes (MWCNTs) has captured extensive attention due to the unique characteristic of extremely thin hollow cylinder structure. The previous studies usually focus on the buckling behavior without considering the effects of the wall number and initial pressure. In this paper, the axial buckling behavior of MWCNTs with the length-to-outermost radius ratio less than 20 is investigated within the framework of the Donnell shell theory. The governing equations for the infinitesimal buckling of MWCNTs are established, accounting for the van der Waals (vdW) interaction between layers. The effects of the wall number, initial pressure prior to buckling, and aspect ratio on the critical buckling mode, buckling load, and buckling strain are discussed, respectively. Specially, the four-walled and twenty-walled CNTs are studied in detail, indicating the fact that the buckling instability may occur in other layers besides the outermost layer. The obtained results extend the buckling analysis of the continuum-based model, and provide theoretical support for the application of CNTs.     

Stress and buckling analysis of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC) face sheets

In this paper, the stresses and buckling behaviors of a thick-walled micro sandwich panel with a flexible foam core and carbon nanotube reinforced composite(CNTRC) face sheets are considered based on the high-order shear deformation theory(HSDT) and the modified couple stress theory(MCST). The governing equations of equilibrium are obtained based on the total potential energy principle. The effects of various parameters such as the aspect ratio, elastic foundation, temperature changes, and volum...     

非均匀Winkler弹性地基上变厚度矩形板自由振动的DTM求解

针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法（DTM）,研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。     

Nonlinear vibration of embedded single-walled carbon nanotube with geometrical imperfection under harmonic load based on nonlocal Timoshenko beam theory

Based on the nonlocal continuum theory, the nonlinear vibration of an embedded single-walled carbon nanotube (SWCNT) subjected to a harmonic load is investigated. In the present study, the SWCNT is assumed to be a curved beam, which is unlike previous similar work. Firstly, the governing equations of motion are derived by the Hamilton principle, meanwhile, the Galerkin approach is carried out to convert the nonlinear integral-differential equation into a second-order nonlinear ordinary differential equation. Then, the precise integration method based on the local linearzation is appropriately designed for solving the above dynamic equations. Besides, the numerical example is presented, the effects of the nonlocal parameters, the elastic medium constants, the waviness ratios, and the material lengths on the dynamic response are analyzed. The results show that the above mentioned effects have influences on the dynamic behavior of the SWCNT.     

开口复合材料柱壳屈曲与补救有限元分析

用有限元法对含有轴向裂纹的开口加强复合材料柱壳结构进行了补救研究;分析其压缩屈曲强度与模态情况,得到了裂纹长度与屈曲强度的关系,并与无裂纹的结构进行了对比.结果表明:裂纹长度在200mm以下时,对整个结构承载能力影响很小;当裂纹长度继续增大时,屈曲区域从开口上方转移到裂纹附近,屈曲强度开始急剧下降.为了加强裂纹所在区域结构的承剪能力,进行适当的修补后,可使屈曲模态与无裂纹柱壳相同,且屈曲强度稍有增加,从而证明了所提出补救方法的有效性.     

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.     

Vibration and damping analysis of a composite plate with active and passive damping layer

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Free vibration analysis of functionally graded material beams based on Levinson beam theory

Free vibration response of functionally graded material (FGM) beams is studied based on the Levinson beam theory (LBT). Equations of motion of an FGM beam are derived by directly integrating the stress-form equations of elasticity along the beam depth with the inertial resultant forces related to the included coupling and higherorder shear strain. Assuming harmonic response, governing equations of the free vibration of the FGM beam are reduced to a standard system of second-order ordinary differential equations associated with boundary conditions in terms of shape functions related to axial and transverse displacements and the rotational angle. By a shooting method to solve the two-point boundary value problem of the three coupled ordinary differential equations, free vibration response of thick FGM beams is obtained numerically. Particularly, for a beam with simply supported edges, the natural frequency of an FGM Levinson beam is analytically derived in terms of the natural frequency of a corresponding homogenous Euler-Bernoulli beam. As the material properties are assumed to vary through the depth according to the power-law functions, the numerical results of frequencies are presented to examine the effects of the material gradient parameter, the length-to-depth ratio, and the boundary conditions on the vibration response.     

基于并行计算和遗传算法的钢-UHPC华夫板组合梁优化设计

为实现钢-超高性能混凝土(UHPC)华夫板组合梁结构快速经济合理的设计,提出了基于并行计算与遗传算法的结构优化设计方法。通过Python建立了并行计算平台,使Abaqus和Python能够执行同步数值模拟和数据处理,以成本最小化为目标,采用遗传算法对钢-UHPC华夫板组合梁进行了优化,验证了所提方法的可行性。结果表明,遗传算法中密集的分析任务可以并行化并分配给不同的计算资源以提高计算效率;使用并行计算可以提高8.6倍的优化效率;并行计算和串行计算的CPU平均使用率分别为82%和18%。本文方法的成功应用可为其他类型结构的优化设计提供参考。     

Structure buckling hybrid reliability analysis of a supercavitating projectile using a model with truncated probability and multi-ellipsoid convex set uncertainties

Structure buckling problems for supercavitating projectiles are often observed in high underwater velocity operating conditions. As a result, it is necessary to perform a structure buckling reliability analysis. It is common that \hboxprobabilistic and nonprobabilistic uncertainty information exist simultaneously. Also, it is reasonable that probability distributions of most random variables in engineering are treated as truncated probability distributions. In this paper, a new hybrid model is proposed, which deals with structure performance function with both truncated probability distribution variables and multi-ellipsoid convex set variables. The model discussed here is adapted for two separate cases in the standard super-sphere space, i.e., limit state surface interferences with a unit super-sphere region or not. The hybrid reliability index is calculated using a modified limit step length iteration algorithm to ensure convergence. Good convergence and validity of the iteration algorithm are verified using numerical examples with highly nonlinear structure performance function. The hybrid model is applied to the structure buckling hybrid reliability analysis of a supercavitating projectile. Results show that structure buckling hybrid reliability index increases with the increase in the ratio of base diameter to cavitator diameter, and decreases with the increase of initial launch velocity. Also, uncertainty degree of cavitator drag coefficient and initial launch velocity should be controlled in demonstration for high structure buckling reliability of supercavitating projectiles.     

Free vibration of functionally graded beams based on both classical and first-order shear deformation beam theories

The free vibration of functionally graded material （FGM） beams is studied based on both the classical and the first-order shear deformation beam theories. The equations of motion for the FGM beams are derived by considering the shear deforma- tion and the axial, transversal, rotational, and axial-rotational coupling inertia forces on the assumption that the material properties vary arbitrarily in the thickness direction. By using the numerical shooting method to solve the eigenvalue problem of the coupled ordinary differential equations with different boundary conditions, the natural frequen- cies of the FGM Timoshenko beams are obtained numerically. In a special case of the classical beam theory, a proportional transformation between the natural frequencies of the FGM and the reference homogenous beams is obtained by using the mathematical similarity between the mathematical formulations. This formula provides a simple and useful approach to evaluate the natural frequencies of the FGM beams without dealing with the tension-bending coupling problem. Approximately, this analogous transition can also be extended to predict the frequencies of the FGM Timoshenko beams. The numerical results obtained by the shooting method and those obtained by the analogous transformation are presented to show the effects of the material gradient, the slenderness ratio, and the boundary conditions on the natural frequencies in detail.     

Analytical modeling and vibration analysis of fiber reinforced composite hexagon honeycomb sandwich cylindrical-spherical combined shells

Applied Mathematics and Mechanics - This study analyzes and predicts the vibration characteristics of fiber-reinforced composite sandwich (FRCS) cylindrical-spherical (CS) combined shells with...     

Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress,the modified couple stress theory(MCST),and the nonlocal elasticity theories using the differential quadrature method(DQM)is presented.Main advantages of the MCST over the classical theory(CT)are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter.Based on the nonlinear von K′arm′an assumption,the governing equations of equilibrium for the micro-classical plate considering midplane displacements are derived based on the minimum principle of potential energy.Using the DQM,the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained.Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature.A parametric study is conducted to show the effects of the aspect ratio,the side-to-thickness ratio,Eringen’s nonlocal parameter,the material length scale parameter,Young’s modulus of the surface layer,the surface residual stress,the polymer matrix coefficients,and various boundary conditions on the dimensionless uniaxial,biaxial,and shear critical buckling loads.The results indicate that the critical buckling loads are strongly sensitive to Eringen’s nonlocal parameter,the material length scale parameter,and the surface residual stress effects,while the effect of Young’s modulus of the surface layer on the critical buckling load is negligible.Also,considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate.The results show that the critical biaxial buckling load increases with an increase in G12/E2and vice versa for E1/E2.It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude.Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios,it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications.