组合型扁壳的一种广义变分原理及对幕壳的应用

本文提出一个带边梁的组合型扁壳弹性动力学广义变分原理,对它与相应的基本方程、脊线条件及边界条件的等价性作了论证.然后将这一变分原理应用于幕壳结构,利用多重级数给出幕壳在常见的边界条件下的静动力学近似解析解,将本文解析解同有限元计算及试验值作了比较,结果表明我们的解析解收敛性好,精确性令人满意.     

带弹性附件充液矩形贮箱俯仰运动动态响应

首先建立了俯仰运动矩形贮箱刚-液-弹耦合系统在外力矩作用下的耦合动力学模型,给出满足边界条件的速度势函数和液面波高的级数表达式,采用伽辽金法离散,将动力学模型转化为常微分方程组,得到刚-液-弹耦合系统的固有频率,给出简单的近似表达式,分析了转动中心距静液面不同位置时刚-液-弹耦合系统各阶固有频率的变化规律,系统转动中心距静液面较近时,耦合后液体反对称模态和刚体的固有频率对比耦合前减小,较远时则增大,最后进行数值验证,比较分析了液体和弹性体对刚体姿态的影响．     

无锚固储液罐提离的流-固多种非线性耦合的三维移动边界问题统一分析格式*

本文建立了在地震作用下无锚固储液罐提离的流-固多种非线性耦合的移动边界问题的统一格式的三维分析方法,其中建立了任意四边形标薄板壳拟协调非线性有限元的列式和分析移动边界问题的线性互补方程;提出了在ALE标架下用带压力项的时间分裂步法求解储液罐内含自由液面大幅晃动(移动边界问题)的非定常的三维粘性流体(N-S)问题的方法;其中没有利用轴称性和梁式模态假定等条件及未曾利用势函数理论;该方法适用于一般板壳-流体多种非线性耦合的多种移动边界问题.     

计及表面波的圆环形贮液容器的弯曲自由振动*

本文研究考虑表面波作用的圆环形贮液容器的弯曲自由振动问题,导出了贮液容器与液体耦联振动的振型函数和固有频率的精确计算公式,结果可借助于计算机求解.分析表明,水对容器的振动效应可等效于在内外环体上分别附着一不同的广义分布质量.     

贮液圆筒在水中的弯曲自由振动

本文研究了贮液圆筒在水中的弯曲自由振动问题,液体和水的深度均可任意,导出了水中贮液圆筒的振型函数及固有频率的精确计算公式,结果可由计算机解出.分析表明,液体和水对简体振动的影响各自等效一附着于筒体的广义分布质量.     

小Bond数条件下圆柱贮箱中液体晃动的模部分析

运用模部分析方法考察了小Bond数条件下圆柱贮箱中弯曲静液面对液体晃动模态的重构作用.研究表明,圆柱贮箱中的液体作小幅晃动时,参与晃动的各阶基本模态的正交性若仅由Bessel模部来给出,则弯曲静液面将使各阶模态加权耦合,形成新的特征模态;参与晃动的各阶基本模态的正交性若由三角函数模部来给出,则弯曲静液面将独立改变各阶模态的固有频率,各阶模态之间不耦合.运用新的重构模态来研究圆柱贮箱中液体的横向受迫晃动,给出了其模态选择特征.     

横向剪变形对具有一小圆孔的浅壳应力集中系数的影响

本文导出了分析计及横向剪变形的浅壳小孔应力集中问题的简化方程.对浅球壳和圆柱壳带一小圆孔的情况,获得了方程的级数形式通解.对均匀内压作用下的圆柱壳,求得了小圆孔边上应力集中系数的近似显式解,并计算了数值结果.     

无锚固储液罐提离的流—固多种非线性耦合的三维移动边界问题统…

本文建立了在地震作用下无锚固储液罐提高的流－固多种非线性耦合的移动边界问题的统一格式的三维分析方法，其中建立了任意四边形标薄板壳拟协调非线性有限元的列式和分析移动边界问题的线性互补方程；提出了在ＡＬＥ标架下用带压力项的时间分裂步法求解储液罐内含自由液面大幅晃动（移动边界问题）的非定常的三维粘性流体（Ｎ－Ｓ）问题的方法；其中没有利用轴称性和梁式模态假定等条件及未曾利用势函数理论；该方法适用于一般板壳     

圆柱壳的轴对称平面应变弹性动力学解

给出一种圆柱壳的轴对称平面应变弹性动力学问题的解析方法。首先通过引入一特定函数将非齐次边界条件化为齐次边界条件,然后利用分离变量法将位移减去特定函数的量展开为关于贝塞尔函数和时间函数乘积的级数,并由贝塞尔函数的正交性,导出时间函数的方程,容易求得此方程的解。将两者叠加可得弹性动力学问题的位移解。运用此方法,可以避免积分变换,并适宜于各种载荷。文中给出了各向同性和柱面各向同性圆柱壳内表面和实心圆柱外表面受冲击荷载作用以及内表面固定的柱面各向同性圆柱壳外表面受冲击荷载作用的数值结果。     

万因斯坦-钱伟长法的应用——简支与固支混合边界矩形板基频上下限

本文将边界条件放松法[1][2]应用于简支与固支混合边界矩形板,求得此类板的基频下限值.文中还设计了一种能满足位移边界条件的多项式作为振型试函数,从而用里兹法得到相应的上限值.具体算例得到了满意的结果.最后本文指出,通常用力法迭加法得到的此类板的所谓精确解,若考虑实际计算的级数截断误差,本质上是一种下限解.     

Haar wavelet discretization approach for frequency analysis of the functionally graded generally doubly-curved shells of revolution

This paper aims to investigate the free vibrational analysis of the generally doubly-curved shells of revolution made of functionally graded (FG) materials and constrained with different boundary conditions by means of an efficient, convenient and explicit method based on the Haar wavelet discretization approach. The FG materials of the shell consist of a combination of ceramic and metal, which four parameter power-law distribution functions have chosen for modeling of the smoothly and gradually variation of the material properties in the thickness direction. The theoretical model of the shell is formulated by employing of the first-order shear deformation theory. The rotation and displacement components of each point of the shell are expanded in the form of product of the Haar wavelet series in meridional direction as well as trigonometric series in the circumferential direction. By adding the boundary condition equations to the main system of equations, the constants appeared from the integrating of the Haar wavelet series are satisfied. In addition, with solving the characteristic equation, the vibrational results including the natural frequencies and the corresponding mode shapes are achieved. Then, the present results have been compared with those available in the literature. The results indicate that this method has high accuracy, high reliability and also a higher convergence rate in attaining the frequencies of the FG doubly-curved shells of revolution. Also, the effects of the main parameters such as power-law exponent, geometrical parameters, material distribution profiles and different types of boundary conditions, on the vibrational behavior of the FG doubly-curved shells of revolution, are investigated. Finally, taking into account the effects of geometrical parameters and material distribution profiles, for FG doubly-curved shells of revolution with different boundary conditions such as classic, elastic restraints and their combination, a variety of new frequency studies are provided which can be considered as proof results for further researches in this field.     

A mixed finite element method for a shallow shell problem with a stress function

In this paper we consider the problem of a deflected mode of a shallow shell. The stress function and the normal component of the displacement of the median surface of the shell are unknown functions. We propose a mixed variational statement of the problem, where the second derivatives of the stress function and the normal component of the displacement of the median surface are additional unknowns. This enables us to construct the finite element approximation of the initial problem. We prove the existence of a unique solution of the approximating problem and estimate the rate of convergence of the discrete solution.     

弹性边界约束旋转功能梯度圆柱壳结构自由振动行波特性分析

对旋转功能梯度圆柱壳自由振动行波特性及边界约束影响进行了分析研究.将功能梯度材料的物理特性表示成沿壳体厚度方向指数变化的函数,基于Love壳体理论,将圆柱壳3个方向的振动位移场采用改进Fourier(傅立叶)级数方法展开, 进而改善位移函数在边界位置求导连续性,结合旋转圆柱壳结构能量原理描述与Rayleigh Ritz法,推导旋转功能梯度圆柱壳自由振动特征方程.通过将计算结果与现有文献结果对比验证了该文模型的正确性与收敛性.随后,通过算例讨论分析了功能梯度材料特性参数、几何参数、边界条件及约束弹簧刚度对旋转功能梯度圆柱壳自由振动行波振动特性的影响.结果表明:边界条件在环向波数n较小或长径比L/R较小的情况下对行波特性影响较为明显;随着厚径比H/R的增大,边界条件的影响逐渐减小;边界约束弹簧对行波特性影响程度取决于模态阶数情况;功能梯度材料特性参数对前后行波频率的影响随着模态序数的增大而逐渐增大.     

Free vibration analysis of FGM cylindrical shells surrounded by Pasternak elastic foundation in thermal environment considering fluid-structure interaction

This paper presents an investigation on partially fluid-filled cylindrical shells made of functionally graded materials (FGM) surrounded by elastic foundations (Pasternak elastic foundation) in thermal environment. Material properties are assumed to be temperature dependent and radially variable in terms of volume fraction of ceramic and metal according to a simple power law distribution. The shells are reinforced by stiffeners attached to their inside and outside in which the material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The formulations are derived based on smeared stiffeners technique and classical shell theory using higher-order shear deformation theory which accounts for shear flexibility through shell's thickness. Displacements and rotations of the shell middle surface are approximated by combining polynomial functions in the meridian direction and truncated Fourier series with an appropriate number of harmonic terms in the circumferential direction. The governing equations of liquid motion are derived using a finite strip element formulation of incompressible inviscid potential flow. The dynamic pressure of the fluid is expanded as a power series in the radial direction. Moreover, the quiescent liquid free surface is modeled by concentric annular rings. A detailed numerical study is carried out to investigate the effects of power-law index of functional graded material, fluid depth, stiffeners, boundary conditions, temperature and geometry of the shell on the natural frequency of eccentrically stiffened functionally graded shell surrounded by Pasternak foundations.     

Problem-Oriented Functionals in the Theory of Nonlinearly Elastic Composite Shells

Based on the Kirchhoff-Love or Timoshenko hypotheses and with regard for a possible membrane or shear degeneration, mixed linearized functionals for four variants of shell theory are presented. The convergence of numerical methods is improved by choosing small strain components as additional variable functions. New classes of problems for thin and nonthin shells are solved. The stress-strain state of shells is studied using different variants of this theory.     

A note on almost sure uniform and complete convergences of a sequence of random variables

The aim of this note is to introduce another way of defining the almost sure uniform convergence, which is necessary when studying some mathematical results on the existence of price bubbles in certain scenarios of trading securities. This mode of convergence of random variables' sequences is intermediate between the uniform and the almost sure ones, and, more specifically, between the uniform and the complete convergences. In this way, this paper presents some mathematical characterizations of both almost sure uniform and complete convergences, and shows that the almost sure uniform convergence is a particular case of complete convergence, when the number of summands in the series defining this mode of convergence is finite. Finally, this paper presents the relation of almost surely uniform convergence with convergence in mean when the random variable limit is integrable. Moreover, almost surely convergence and local boundedness of the sequence of random variables minus its limit are sufficient to derive convergence in mean.     

Justification of two dimensional model of shallow shells using gamma convergence

In this paper we derive the two dimensional model of elastic shallow shell using gamma convergence. We consider thin elastic shallow shells of “very small” thickness and we show that the sequence of functions minimizing the energy associated with the three-dimensional elastic shallow shells converges to the function which minimizes the energy associated with the two dimensional elastic shallow shell as the thickness of the shell goes to zero.     

An analytical solution for free liquid sloshing in a finite-length horizontal cylindrical container filled to an arbitrary depth

A general series-type theoretical formulation based on the linearized potential theory, the method of separation of variables, and the translational addition theorem for cylindrical Bessel functions is developed to study three-dimensional natural sloshing in a partially filled horizontally-mounted circular cylindrical tank of finite span. Assuming time-harmonic variations, the potential solutions associated with the Symmetric/Antisymmetric (S/A) modes of free liquid surface oscillations are first analytically expanded as series of bounded spatial functions with unknown modal coefficients. The impenetrability conditions of the rigid end-plates along with the free surface dynamic/kinematic boundary condition are then imposed. The zero-normal-velocity requirement of the lateral tank boundary is subsequently applied by innovative use of Graf's translational addition theorem for modified cylindrical Bessel functions. After truncation, four independent sets of homogeneous algebraic equations are obtained that are then numerically worked out for the natural sloshing eigen-frequencies and free surface oscillation mode shapes. Extensive numerical data include the first thirty six longitudinal/transverse Antisymmetric/Symmetric (AA, SA, AS, SS) dimensionless sloshing frequencies, for a wide range of liquid fill depths and container span to radius ratios. Also, the influence of fill depth on the free surface oscillation mode shapes is addressed through selected 2D images. Comprehensive numerical simulations illustrate the strong effects of container length and liquid fill depth on the calculated sloshing frequencies. It is revealed that the frequency branches with the same transverse mode number form a cluster that progressively merge together amid the tank fill-depth limits as the tank span ratio increases. On the other hand, when the tank length substantially decreases, the number of “frequency cross-overs” between various frequency clusters at certain liquid fill depths considerably increases. Moreover, primary advantages of proposed methodology in comparison to other approximate/numerical methods are explicitly pointed out, convergence of solution is tested, and accuracy/reliability of the results is demonstrated by comparisons with available data.     

Extrapolation Algorithms for Filtering Series of Functions,and Treating the Gibbs Phenomenon

In this paper, we study the application of some convergence acceleration methods to Fourier series, to orthogonal series, and, more generally, to series of functions. Sometimes, the convergence of these series is slow and, moreover, they exhibit a Gibbs phenomenon, in particular when the solution or its first derivative has discontinuities. It is possible to circumvent, at least partially, these drawbacks by applying a convergence acceleration method (in particular, the -algorithm) or by approximating the series by a rational function (in particular, a Padé approximant). These issues are discussed and some numerical results are presented. We will see that adding its conjugate series as an imaginary part to a Fourier series greatly improves the efficiency of the algorithms for accelerating the convergence of the series and reducing the Gibbs phenomenon. Conjugacy for series of functions will also be considered.