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.

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.

KRMN-TYPE EQUATIONS FOR A HIGHER-ORDER SHEARDEFORMATION PLATE THEORY AND ITS USE IN THE THERMAL POSTBUCKLING ANALYSIS

arman-type nonlinear large deflection equations are derived occnrding to theReddy's higher-order shear deformation plate theory and used in the thermal postbuckling analysis The effects of initial geometric imperfections of the plate areincluded in the present study which also includes th thermal effects.Simply supported,symmetric cross-ply laminated plates subjected to uniform or nomuniform parabolictemperature distribution are considered. The analysis uses a mixed GalerkinGolerkinperlurbation technique to determine thermal buckling louds and postbucklingequilibrium paths.The effects played by transverse shear deformation plate aspeclraio, total number of plies thermal load ratio and initial geometric imperfections arealso studied.

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.

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。

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.

Bending and stress analysis of polymeric composite plates reinforced with functionally graded graphene platelets based on sinusoidal shear-deformation plate theory

The bending and stress analysis of a functionally graded polymer composite plate reinforced with graphene platelets are studied in this paper.The governing equations are derived by using principle of virtual work for a plate which is rested on Pasternak’s foundation.Sinusoidal shear deformation theory is used to describe displacement field.Four different distribution patterns are employed in our analysis.The analytical solution is presented for a functionally graded plate to investigate the influence of important parameters.The numerical results are presented to show the deflection and stress results of the problem for four employed patterns in terms of geometric parameters such as number of layers,weight fraction and two parameters of Pasternak’s foundation.

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.

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.

Higher-order electroelastic modelling of piezoelectric cylindrical nanoshell on elastic matrix

This paper develops electro-elastic relations of functionally graded cylindrical nanoshell integrated with intelligent layers subjected to multi-physics loads resting on elastic foundation.The piezoelectric layers are actuated with external applied voltage.The nanocore is assumed in-homogeneous in which the material properties are changed continuously and gradually along radial direction.Third-order shear deformation theory is used for the description of kinematic relations and electric potential distribution is assumed as combination of a linear function along thickness direction to show applied voltage and a longitudinal distribution.Electro-elastic size-dependent constitutive relations are developed based on nonlocal elasticity theory and generalized Hooke’s law.The principle of virtual work is used to derive governing equations in terms of four functions along the axial and the radial directions and longitudinal electric potential function.The numerical results including radial and longitudinal displacements are presented in terms of basic input parameters of the integrated cylindrical nanoshell such as initial electric potential,small scale parameter,length to radius ratio and two parameters of foundation.It is concluded that both displacements are increased with an increase in small-scale parameter and a decrease in applied electric potential.

Buckling analysis of shear deformable composite conical shells reinforced by CNTs subjected to combined loading on the two-parameter elastic foundation

The main objective of this study is to investigate the buckling analysis of CCSs reinforced by CNTs subjected to combined loading of hydrostatic pressure and axial compression resting on the twoparameter elastic foundation(T-P-EF).It is one of the first attempts to derive the governing equations of the CCSs reinforced with CNTs,based on a generalized first-order shear deformation shell theory(FSDST)which includes shell-foundation interaction.By adopting the extended mixing rule,the effective material properties of CCSs reinforced by CNTs with linear distributions are approximated by introducing some efficiency parameters.Three carbon nanotube distribution in the matrix,i.e.uniform distribution(U)and V and X-types linear distribution are taken into account.The stability equations are solved by using the Galerkin procedure to determine the combined buckling loads(CBLs)of the structure selected here.The numerical illustrations cover CBLs characteristics of CCSs reinforced by CNTs in the presence of the T-P-EF.Finally,a parametric study is carried out to study the influences of the foundation parameters,the volume fraction of carbon nanotubes and the types of reinforcement on the CBLs.

POSTBUCKLING OF PRESSURE-LOADED SHEAR DEFORMABLE LAMINATED CYLINDRICAL PANELS

A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with von Krmn_Donnell_type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, cross_ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied.

On the higher-order thermal vibrations of FG saturated porous cylindrical micro-shells integrated with nanocomposite skins in viscoelastic medium

Since the multi-layered structures are widely used nowadays, and due to interesting applications of cylindrical shells, this study is dedicated to analyzing free vibrational behaviors of functionally graded saturated porous micro cylindrical shells with two nanocomposite skins. Based on Biot's assumptions, constitutive relations for the core are presented and effective properties of the skins are determined via the rule of mixture. A sinusoidal theory is used to capture the shear deformation effects, and to account for the scale effects, the modified couple stress theory is employed which suggests a material length-scale parameter for predicting the results in small-dimension. With the aid of extended form of Hamilton's principle for dynamic systems, differential equations of motion are extracted. Fourier series functions are used to obtain natural frequencies and after validating them, a set of parametric studies are carried out. The results show the significant effects of porosity and Skempton coefficient, pores placement patterns, CNTs addition and distribution patterns, temperature variations, material length-scale parameter and viscoelastic medium on the natural frequencies of the microstructure. The outcomes of this work could be used to design and manufacture more reliable micro cylindrical structures in thermo-dynamical environments.

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.

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。

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。

功能梯度石墨烯增强多孔复合材料阶梯圆柱壳的振动特性

对功能梯度石墨烯增强多孔复合材料(FG-GPLRPC)阶梯圆柱壳的振动特性进行了研究。首先,采用Halpin-Tsai微观力学模型以及开胞体理论得到FG-GPLRPC阶梯圆柱壳的有效材料属性。其次,基于一阶剪切变形理论和惩罚参数法推导出壳体结构的能量表达式。最后,采用Jacobi-Ritz法建立壳体结构的振动控制方程,并求得结构的无量纲频率,验证了方法的有效性和正确性。结果表明,石墨烯质量分数、孔隙系数和边界弹簧刚度值对振动特性的影响显著,层数对振动特性的影响较小,尺寸参数对振动特性的影响不同,并得到了壳体频率随周向波数先减小后增大的变化规律。

复合材料环支撑圆柱壳结构振动特性分析研究

该文基于一阶剪切变形理论,结合波动法,构建了不同边界条件下环支撑复合材料圆柱壳结构振动特性分析模型。结合波函数形式为位移变量,对位移比例参数、位移矩阵和力参数矩阵进行设置。通过结合边界条件矩阵,对环支撑条件下复合材料圆柱壳结构的总体控制方程进行推导。通过与现有文献结果进行对比,验证所建立的振动特性分析模型的准确性。开展了相关参数化分析研究,探讨了材料参数、几何参数以及环支撑位置的影响情况。

基于n阶剪切变形理论的表面梯度脱碳汽车前轴弯曲分析

汽车前轴在热锻和热处理过程中,材料的表面会发生一定深度的脱碳,脱碳层的力学性能随脱碳深度呈梯度变化,影响了前轴在载荷下的弯曲性能。利用分段函数构建两侧表面功能梯度变化、内部性能均匀的简支夹芯梁,根据n阶剪切变形理论研究梁在两点载荷作用下的弯曲行为。利用虚功原理推导出位移场控制方程,采用Navier解析方法得到简支边界条件下梁的弯曲行为,并与相关文献中的实例进行比较。结果表明:n阶剪切变形理论具有良好的精度与可靠性;梁的挠度与转角随脱碳指数k的增大而增大,并于k≈10处达到准稳态;脱碳深度大于5 mm时,脱碳层厚度对梁弯曲时产生应力的影响比梁的高度变化带来的影响更大;两侧脱碳深度不对称时,物理中性面发生迁移;梁的弯曲挠度与转角随梁的厚度、宽度的增大而减小,但梁的厚度变化的影响更大。

弹性约束下变厚度蜂窝夹层板的隔声特性

基于一阶剪切变形理论,研究了变厚度蜂窝夹层板在不同边界条件下的自由振动和隔声性能。从能量角度,利用改进的瑞利-里兹法和流固边界耦合条件,建立并求解了蜂窝夹层板的隔声理论模型。将理论计算的蜂窝夹层板固有频率、传声损失与相关文献结果和仿真结果对比,验证了所建立变厚度蜂窝夹层板隔声理论模型的准确性。此外,对比分析了特征角、厚度变化系数和边界条件对蜂窝夹层板隔声性能的影响。研究表明,厚度变化系数和边界条件对蜂窝夹层板隔声性能影响较大。