热效应下梯度柱形壳的自由振动分析

对四组带平面内边界条件的简支梯度柱形壳进行自由振动分析。假设其材料特性随壳厚度方向逐渐变化的温度而变化。通过指定柱外表面的高温以及内表面的温度来研究温度升高的作用,壳厚度方向的温度分布是通过在该方向的定态热传导来实现的。根据Love壳理论和Von Karman Donnell-type运动学非线性特性确定运动方程。首先采用静力分析确定热荷载作用下产生的预应力状态,静力分析采用控制方程以及Galerkin法推导的运动等式进行分析。结果指出了幂律指数对热环境下壳体的自振频率及模态的影响作用。     

Buckling of fixed-roof aboveground oil storage tanks under heat induced by an external fire

This paper presents computational modeling and results of steel storage tanks under heat induced by an adjacent fire. In this research, modeling is restricted to the structural behavior of the tank, with emphasis on thermal buckling of the shell. Two tanks that buckled under a huge fire in Bayamón, Puerto Rico in 2009, are investigated in detail: a small tank with a self-supported conical roof, and a large tank in which the conical roof is supported by a set of rafters and columns. For a tank that is empty, the results show that a relatively low temperature is enough to produce static buckling of the shell. In pre-buckling states, the cylindrical shell has thermal expansion; at the critical state the displacements reverse and inwards displacements are observed at advanced post-buckling states. Parametric studies are performed to understand the influence of the shell thickness, the level of fluid stored in the tank, the area affected by fire in the circumferential direction, and the temperature gradient through the thickness. The buckling modes are compared with real deflection of tanks that were affected by fire.     

Thermal buckling of FGM shells resting on a two-parameter elastic foundation

This paper focuses on the thermal buckling analysis of FGM shells resting on the two-parameter elastic foundation. Material properties of the constituents are graded in the thickness direction according to the power-law distribution. The surrounding elastic medium is modeled as an elastic foundation of the Pasternak-type. After giving the fundamental relations, the stability and compatibility equations of an FGM truncated conical shell subjected to thermal load and resting on a two-parameter elastic foundation have been derived. Critical temperature differences of FGM truncated conical shells with or without elastic foundations subjected to non-linearly distributed temperature across the thickness of the shells are obtained by solving eigenvalue problems. The appropriate formulas for FGM cylindrical shells with or without elastic foundations are found as a special case. In order to assure the accuracy of the present study, convergence properties of the critical temperature are examined in detail.     

双参数弹性地基上的FGM壳体的热屈曲性能

分析双参数弹性地基上的FGM壳体的热屈曲性能。根据幂律分布,从厚度方向对各个构件的材料性能进行分级。周边的弹性介质被模拟为Pasternak弹性地基。在假定基本关系之后,对温度荷载下及位于双参数弹性地基上的FGM截顶圆锥壳体的稳定性和相容方程式进行分析。通过求解特征值,得到沿壳体厚度方向非线性分布的温度荷载下的基于或不基于弹性地基上的FGM截顶圆锥壳体临界温差。作为一个特殊案例,提出基于或不基于弹性地基上的FGM截顶圆锥壳体的方程。为了保证目前研究的正确性,详细地评价了临界温度的收敛性。     

Thermal analysis of FRP chimneys using consistent laminated shell element

Due to their high corrosion and chemical resistance, fiber reinforced plastic (FRP) materials are increasingly being used in the construction of industrial chimneys. The design of a chimney is governed by wind loads as well as thermal loads resulting from the differences among the ambient, the operating and the curing temperatures. This study involves an investigation for the thermal stresses induced in angle-ply laminated FRP chimneys, using an in-house developed laminated shell element model. The finite element model is verified by performing thermal analysis of a number of plate and shell problems and comparing the results to those available in the literature. An extensive parametric study is then conducted using the shell element model to identify the parameters which significantly affect thermal stresses induced in FRP chimneys.The study indicates that the thermal stresses are only affected by the inclination of the lamina plies, the percentage of fibers content and the through thickness temperature distribution. Analyses also show that localized cracks in the direction perpendicular to the fibers are expected to occur due to the thermal loads. Finally, thermal stress values that can be used in the design of FRP chimneys, when cracking is considered, are presented as function of the through thickness temperature distributions.     

Unsteady free convective boundary layer flow of a nanofluid past a stretching surface using a spectral relaxation method

ABSTRACT

An analysis is presented to study the unsteady, two-dimensional nanofluid flow of heat and mass transfer with vanishing nanoparticles flux at the wall in the presence of heat generation or absorption with viscous dissipation. In this analysis, it is assumed as nanoparticle flux is zero on the boundaries. The highly nonlinear differential equations governing the boundary layer flow, heat and mass transfer are numerically solved by spectral relaxation method and validated with MATLAB solver bvp4c. The results are obtained by some values of the physical parameters, namely, the Brownian motion parameter, the thermophoresis parameter, unsteadiness parameter, Eckert number, heat generation or absorption parameter, Prandtl number and Lewis number. Physical features for all relevant parameters on the dimensionless velocity, temperature, nanoparticles volume fraction and heat and mass transfer rates are analysed and discussed. The thermal boundary layer thickness increases with an increase in the thermophoretic parameter. The nanoparticle volume fraction profile significantly descends from the surface with an increase in Brownian motion parameter.     

Dynamic analysis of functionally graded truncated conical shells subjected to asymmetric moving loads

The dynamic behavior of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads is studied. The material properties are assumed to have continuous variations in the shell thickness direction. The equations of motion are derived based on the first-order shear deformation theory (FSDT) using Hamilton׳s principle. The finite element method (FEM) together with Newmark׳s time integration scheme is employed to discretize the equations of motion in the spatial and temporal domain, respectively. The formulation and method of solution are validated by studying their convergence behavior and carrying out the comparison studies in the limit cases with existing solutions in the literature. Then, the influences of material graded index, radius-to-length ratio, semi-vertex angle, thickness, boundary conditions and moving load velocity on the dynamic behavior of the FG truncated conical shells are studied. In addition, the difference between the responses of the FG shells under symmetric and asymmetric loadings is compared.     

Nonlinear mechanical,thermal and thermo-mechanical postbuckling of imperfect eccentrically stiffened thin FGM cylindrical panels on elastic foundations

This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FGM cylindrical panels on elastic foundations subjected to mechanical loads, thermal loads and the combination of these loads. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. Governing equations are derived basing on the classical shell theory incorporating von Karman–Donnell type nonlinearity, initial geometrical imperfection, the Lekhnitsky smeared stiffeners technique and Pasternak type elastic foundations. Explicit relations of load–deflection curves for FGM cylindrical panels are determined by applying stress function and Galerkin method. The effects of material and geometrical properties, imperfection, elastic foundations and stiffeners on the buckling and postbuckling of the FGM panels are discussed in detail. The obtained results are validated by comparing with those in the literature..     

Coupled thermoelasticity of functionally graded plates based on the third-order shear deformation theory

In this paper, the analytical solution is presented for a plate made of functionally graded materials based on the third-order shear deformation theory and subjected to lateral thermal shock. The material properties of the plate, except Poisson's ratio, are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The solution is obtained under the coupled thermoelasticity assumptions. The temperature profile across the plate thickness is approximated by a third-order polynomial in terms of the variable z with four unknown multiplier functions of (x,y,t) to be calculated. The equations of motion and the conventional coupled energy equation are simultaneously solved to obtain the displacement components and the temperature distribution in the plate. The governing partial differential equations are solved using the double Fourier series expansion. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Results are presented for different power law indices and the coupling coefficients for a plate with simply supported boundary conditions. The results are validated based on the known data for thermomechanical responses of a functionally graded plate reported in the literature.     

常量定常温度场作用下壳体热应力当量静载的试验研究

本文根据热弹性理论,求解了壳体在常量定常温度场作用下的热应力问题,并通过壳体相容方程给出与上述热应力相对应的当量静载,使壳体的热应力计算转化为静力分析问题,从而简化了壳体热应力的计算方法,这对各类受有温度作用的建筑屋盖、容器等具有一定实用意义。 文中还通过试验验证了上述当量静载与温度场的关系。     

Natural vibrations of loaded noncircular cylindrical shells containing a quiescent fluid

The paper deals with a solution of three-dimensional problems of natural vibrations and stability of loaded cylindrical shells with circular and arbitrary cross sections containing a quiescent ideal compressible fluid. A mathematical formulation of the problem has been developed based on the variational principle of virtual displacements taking into account the pre-stressed undeformed state caused by the action of static forces on the shell. The motion of potential compressible non-viscous fluid is described by a wave equation, which is transformed using the Bubnov–Galerkin method. The solution of the problem reduces to the computation of complex eigenvalues of a coupled system of two equations. Based on the developed finite element algorithm several numerical examples have been considered to analyze the influence of fluid levels, ratio of ellipse semi-axes, shell thickness and boundary conditions on the natural frequencies and vibration modes of circular and elliptical cylindrical shells loaded by mechanical forces. It has been found that the value of the external uniformly distributed pressure giving rise to instability does not depend on the level of fluid in the shell. The results allow us to conclude that the dynamic characteristics of the system are specified not only by the equivalent added mass of the fluid but also by hydroelastic interaction at the wetted surface.     

Thermal and mechanical instability of functionally graded truncated conical shells

Thermal and mechanical instability of truncated conical shells made of functionally graded material (FGM) is studied in this paper. It is assumed that the shell is a mixture of metal and ceramic that its properties changes as a function of the shell thickness. The governing equations are based on the first-order shell theory and the Sanders nonlinear kinematics equations. The results are obtained for a number of thermal and mechanical loads and are validated with the known data in the literature.     

三维横观各向同性层状地基任意点格林函数求解

提出了求解横观各向同性层状地基表面或内部任意点位移格林函数的混合数值算法。此算法利用Fourier变换将频率–空间域的波动方程转换到频率–波数域内的状态方程,采用高精度的精细积分算法进行求解,得到频率–波数域内的动力柔度矩阵,最后利用Fourier逆变换得到频率–空间域内任意点的位移格林函数。提出的算法适用于任意横观各向同性层状地基,对地基层数和单层的厚度均没有任何的限制。数值算例验证了算法的准确性,并针对层状地基的各向异性特性进行了参数分析。     

Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure

The solution of viscoplastic axisymmetrical buckling of a complete thin spherical shell subjected to radial pressure impulse is presented. Analytically, the problem is formulated as a superposition of small perturbations on the basic unperturbed motion. The amplitudes of perturbed motion are restricted to be so small that the homogeneous compressive deformation predominates over the local bending. This condition allows the constitutive equations to be linearized by the expansion into Taylor's series in the vicinity of unperturbed motion. As a result, a set of two linear partial differential equations of the fifth order is obtained for describing the perturbed motion of the shell. The functional coefficients of these equations are determined by the solution for the unperturbed motion. The governing set of equations is solved using the series of Legendre's functions. As a result, for the time-dependent amplitudes in the series, the set of two ordinary equations with variable coefficients is arrived at. It turns out that certain harmonics grow very rapidly and cause the shell to exhibit a characteristic wrinkled shape which is characterized by a critical mode number. This property of the amplitudes is used to determine the threshold impulse that a shell can tolerate without excessive deformation.The influence of the meridional displacement on the magnitude of radial displacement, buckling mode and critical impulse is investigated. Also, the influence of the viscosity and the initial imperfections of the geometry and loading is shown. The numerical results for a steel shell are presented diagrammatically.     

Local buckling in infinitely,long cylindrical shells subjected uniform external pressure

This paper presents a unique approach to analyze the buckling of an infinitely long cylindrical shell subjected to the external pressure. Buckling is considered to occur locally in the shell, spreading over a certain length along the longitudinal axis of the shell. A plausible function of the flexural displacement is created according to Timonshenko's ring solution of the transverse collapse mode. The governing equations based on Donnell–МУШТАРИ's shell theory are solved using Ritz method and the equilibrium conditions are educed. Numerical computations are performed for cases when shell thickness/radius ratios are 0.1, 0.05 and 0.03. In general, the pressure decreases sharply with a very slight increase of the normalized radial deflection just at the beginning of the initiation, then falls quite slowly till the two opposite points on the inner surface of the shell contact each other. It is found that the buckling pressure of the shell converges to the critical value given by Donnell–МУШТАРИ's shell theory and the span of the buckling mode in the longitudinal axis of the shell is independent of material properties. Solutions given in this paper can be used to address the problem of steady-state buckle propagation in the shells.     

Nonlinear thermomechanical post-buckling of circular FGM plate with geometric imperfection

Nonlinear thermomechanical post-buckling of an imperfect functionally graded material (FGM) circular plate, subjected to both mechanical load and transversely non-uniform temperature rise, is presented. The material properties of FGM plates are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. Based on von Kármán's plate theory, equilibrium equations governing a large axi-symmetric deformation of the FGM circular plate under thermomechanical loads are derived. In the analysis, the geometric imperfections of the plate are taken into account. By using a shooting method the nonlinear ordinary differential equations with immovably clamped boundary conditions are solved numerically. Responses for the nonlinear thermomechanical post-buckling responses of the FGM plate are obtained. Numerical examples are presented that relate to the performances of perfect and imperfect, homogenous and graded plates. Characteristic curves of the post-buckling deformation of the imperfect FGM circular plate varying with thermal loads, imperfection parameters and volume fraction index are plotted. And then effects of the load parameters, materials constitution, and the geometric imperfection of the plate on the deformation are discussed in detail.     

对带几何缺陷的FGM圆板的非线性热力学后屈曲现象的分析

带有几何缺陷FGM圆板的非线性热力学后屈曲现象是由力学荷载及横向不均匀温度升高导致的。基于组成材料的体积分数导致的能量分布法则,FGM板的材料特性假定在板厚度方向呈梯度变化。根据VonK偄rm偄n平板理论,推导出FGM板在温度荷载作用下的轴对称大变形的计算公式。在此分析中同时考虑了板的几何缺陷。通过运用目标法,解决了那些带有固定边界条件的非线性方程。数值算例中考虑了是否带有几何缺陷、均质或非均质的钢板。带缺陷FGM圆板的后屈曲变形特征曲线根据温度荷载、缺陷参数和体积分数的变化绘制而成。文中同时讨论了荷载参数、材料构成及板的几何缺陷对变形的影响。     

表面波度对线接触往复运动下热弹流润滑特性的影响

应用数值分析方法求解了表面波度对线接触往复运动工况下的热弹性流体动力润滑的影响.分析中假设所研究的润滑油服从Ree-Eyring流变模型,使用3种冲程长度,并使这3种冲程下冲程中心的卷吸速度值完全相等.表面波度扰乱了压力、膜厚和油膜中层温升的分布.由于表面波度的影响,一个周期的两个冲程内的油膜的变化不再一致.同光滑表面接触相比,表面波度在一个周期内提升了油膜中的最大压力和最大温升,降低了最小膜厚和摩擦因数.表面波度对油膜中最大压力的变化影响最大.     

Wrinkling of sandwich polymer matrix composite panels under transverse thermal gradients

This paper studies the effect of transverse thermal gradients on the wrinkling load of sandwich polymer matrix composite panels. Analytical solution of wrinkling load is obtained for the sandwich panels with continuous material property variations along the transverse direction induced by the transverse thermal gradients in fire damage. The wrinkling load is presented in terms of a single parameter that measures the geometrical lengths of the panel, the degraded material properties and material gradients at elevated temperature. The effects of the thickness of the core and the material gradients on wrinkling load are discussed. An alternative approach to use upper bound temperature fields in wrinkling analysis is discussed. The solution provides insights toward the development of a quantitative methodology for structural integrity in fire.