钢筋混凝土矩形贮液结构的海固耦合晃动——弹性底板

针对小幅晃动的理想液体,根据钢筋混凝土矩形贮液结构的液-固耦合振动模型和数理方程理论,推导了结构内液体的速度势函数。针对winkler弹性地基的情况,应用能量原理推导了钢筋混凝土矩形贮液结构液-固耦合晃动频率的计算公式。为便于工程应用,给出了钢筋混凝土矩形贮液结构液-固耦合晃动基本频率的计算公式。结合数值算例,讨论了混凝土弹性模量、基床系数、液体密度和底板的相对厚度等对钢筋混凝土矩形贮液结构液-固耦合晃动基本频率的影响,从而为以后工程结构中钢筋混凝土矩形贮液结构的设计计算提供了理论依据。     

钢筋混凝土矩形贮液结构的液-固耦合晃动——弹性底板

针对小幅晃动的理想液体,根据钢筋混凝土矩形贮液结构的液-固耦合振动模型和数理方程理论,推导了结构内液体的速度势函数.针对Winkler弹性地基的情况,应用能量原理推导了钢筋混凝土矩形贮液结构液-固耦合晃动频率的计算公式.为便于工程应用,给出了钢筋混凝土矩形贮液结构液-固耦合晃动基本频率的计算公式.结合数值算例,讨论了混凝土弹性模量、基床系数、液体密度和底板的相对厚度等对钢筋混凝土矩形贮液结构液-固耦合晃动基本频率的影响,从而为以后工程结构中钢筋混凝土矩形贮液结构的设计计算提供了理论依据.     

非线性流体弹性力学研究进展

流体弹性力学理论是用来描述液体、气体的运动与弹性结构相互作用的学科.由于其交叉性质, 涉及到人类日常生活中的方方面面,致使在许多学科和工程领域中都成了主要的研究内容,并得到了广泛地应用.本文在阐述研究流体与弹性体相互作用的非线性问题的重要意义及分类方法的基础上,介绍了非线性流体弹性力学的特征、研究现状和非线性问题的研究方法,如理论分析法、实验分析法、数值分析法和半解析法等的进展;介绍了描述介质相互作用的任意拉格朗日-欧拉(ALE)法、相容拉格朗日-欧拉(ULE)法、单一拉格朗日(SL)法和单一欧拉(SE)法之间的关系,并且对这些研究方法的优缺点进行了比较;介绍了非线性流体弹性力学研究的内容和在气动弹性力学、水弹性力学、环境流体弹性力学、微尺度流体弹性力学和涡激振动等领域中的应用;阐述了非线性流体弹性力学的发展前景和所面临的任务.      

弹性梁式薄板在横向绕流中的大变形

采用相容拉格朗日-欧拉(ULE)法,给出了弹性薄板理想流体横向绕流条件下变形与应力的理论算法,其中:对固体采用拉格朗日法;对流体采用欧拉法;对相互接触面采用拉格朗日法和欧拉法.建立了不问断横向绕流条件下弹性梁式薄板的大弯曲变形的非线性微分方程.求解该方程时,将纵向位移分量和曲率的改变量用挠度表示.通过具体算例分析了各参数对悬臂梁式薄板挠度、纵向位移及应力大小的影响.理论解与数值解进行比较,验证了理论解的可靠性.     

载流圆形薄板的磁弹性应力与变形分析

本文在建立非定常电磁场和机械载荷作用下载流圆形薄板非线性变形状态下的磁弹性二维关系方程和运动方程的基础上，对其在非静态电磁场和机械载荷联合作用下的位移及应力进行了分析，获得了耦合场中一些参量的变化规律，通过具体算例，得出了载流圆形薄板在机械场和电磁场作用下的位移及应力与通电电流强度之间的关系，并解决了圆板中心处的奇异性问题，给出了在轴对称条件下的数值解，计算结果表明，改变通电电流及电磁感应强度的大小，可以改变载流薄板的应力和变形状态，达到控制薄板的受力和变形的目的。     

载流圆锥薄壳的磁弹性应力与变形分析

在建立旋转壳体的非线性磁弹性运动方程的基础上,研究了电磁场和机械载荷联合作用下载流圆锥薄壳的磁弹性效应通过算例,得到了载流圆锥薄壳的位移及应力与通电电流强度之间的关系,解决了圆锥薄壳顶点处的奇异性问题,给出了轴对称条件下的数值解.计算结果表明:改变通电电流强度,可以改变载流圆锥薄壳的应力与变形状态,达到控制圆锥薄壳的受力与变形的目的.     

可渗透圆柱壳流固耦合问题的流场与内力分析

在弹性薄壳的非线性理论和流体力学基本方程的基础上,研究了可渗透圆柱壳的流固耦合问题.假定壳体具有均布孔隙且孔的面积很小,不考虑其阻力,忽略对弯曲刚度和壳体腔内流体微小运动影响,应用相容欧拉--拉格朗日法建立了带孔的圆柱壳在流体中相互作用的基本方程.通过具体算例求解,给出了流场速度与压力的变化、圆柱壳的变形及内力分布,并对相关参数进行了讨论.     

具有约束层阻尼贮液圆柱容器的耦振与减振特性分析

该文在对空圆柱层合壳(不充液)振动分析研究的基础上,借助线性势流理论,进一步考虑液固耦合效应,导出了敷有CLD贮液圆柱层合壳谐耦振的一阶常微分矩阵方程,该方程右边多了液动压力项.由于它不能预先给定,导致方程中出现未知项.为了克服这一困难,文中研究了液动压力的解式,并采用新型齐次扩容精细积分技术,提出了一种高效率和高精度的半解析半数值解法.进而还求解了CLD贮液圆柱容器在地面谐运动激励下的响应;通过大量数值计算分析了CLD的厚度、长度、敷设位置以及粘弹芯的复剪切模量对减振效果的影响.计算还表明了有液体的存在,这些影响和空容器时是不一样的.文中方法为CLD贮液容器的控制优化提供了有力手段.     

锚胫侧倾角对拖曳锚在砂土中的下潜性能大变形数值分析

拖曳锚作为一种造价低、结构简单的系泊基础,在深海资源开发中得到了广泛的应用。拖曳锚的安装下潜性能与锚的自重、锚板厚度、锚胫与锚板夹角、土层条件等因素相关,锚胫对拖曳锚下潜性能的影响研究还不深入。提出了一种通过调整锚胫侧倾角来提高拖曳锚下潜性能的方法,并采用大变形有限元分析进行了验证。以MK5拖曳锚在砂土中的安装过程为例,分析了不同锚胫前倾角、锚胫侧倾角、拖曳锚密度、锚–土界面摩擦特性等因素对拖曳锚下潜深度的影响。结果表明,相较于传统的锚胫内倾的拖曳锚,拖曳锚锚胫直立以及向外侧倾斜时其嵌入深度有明显提高。

     

基于有限元模拟的SUS304奥氏体不锈钢摩擦耦合变形过程的应力分析

采用ANSYS/LS-DYNA软件对SUS 304奥氏体不锈钢薄板的摩擦耦合变形过程进行了数值模拟.采用隐式-显式序列求解法和分段线性塑性材料模型,分析了钢带摩擦耦合变形时的应力分布规律及载荷、下压量和滑动速度等因素对钢带剪应力、主应力及等效应力的影响.结果表明:摩擦耦合变形的试验参数显著影响钢带的应力分布,验证了钢带在低于其屈服强度的应力条件下发生塑性变形的摩擦诱发效应.对奥氏体不锈钢摩擦诱发马氏体转变行为的研究及其摩擦学性能的改善具有一定的指导意义.     

Dynamic response of liquid-filled rectangular tank with elastic appendages under pitching excitation

Nonlinear dynamics of liquid-filled rectangular tank with elastic appendages are studied. Based on the assumption of ideal fluid, the coupling dynamic equations of rigid tank, elastic appendages and liquid fuel are derived using H-O principle. In the case of pitch excitation, the modified potential function and wave height function are introduced to describe the moving boundary of fluid, then Galerkin's method is used to discretize the dynamic equations into ordinary differential equations. The natural frequencies of the coupling system are formulated in liquid depth, the length of the tank, etc. The formulae are confirmed by numerical simulations, which also show that the effects of liquid and elastic appendages on the attitude angular of rigid.     

Boundary element analysis of interaction between an elastic rectangular inclusion and a crack

The interaction between an elastic rectangular inclusion and a kinked crack inan infinite elastic body was considered by using boundary element method. The new complexboundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundaryintegral equation was obtained on interface and involves only singularity of order l/ r. Toverify the validity and effectiveness of the present boundary element method, some typicalexamples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easiernear a softer inclusion and the harder inclusion is helpful for crack arrest.     

3D dynamic stress intensity factors at three rectangular cracks in an infinite elastic medium subjected to a time-harmonic stress wave

Summary Dynamic stresses around three coplanar cracks in an infinite elastic medium are determined in the paper. Two of the cracks are equal, rectangular and symmetrically situated on either side of the centrally located rectangular crack. Time-harmonic normal traction acts on each surface of the three cracks. To solve the problem, two kind of solutions are superposed: one is a solution for a rectangular crack in an infinite elastic medium, and the other one is that for two rectangular cracks in an infinite elastic medium. The unknown coefficients in the combined solution are determined by applying the boundary conditions at the surfaces of the cracks. Finally, stress intensity factors are calculated numerically for several crack configurations. Received 14 July 1998; accepted for publication 2 December 1998     

Dynamic stress intensity factors around two rectangular cracks in an infinite elastic plate under impact load

A dynamic problem for two equal rectangular cracks in an infinite elastic plate is considered. The two cracks are placed perpendicular to the plane surfaces of the plate. An incoming shock tensile stress is returned by the cracks. In the Laplace transform domain, the boundary conditions at the two sides of the plate are satisfied using the Fourier transform technique. The mixed boundary conditions are reduced to dual integral equations. Crack displacement is expanded in a series of functions which are zero outside of the cracks. The unknown coefficients in the series are determined by the Schmidt method. The stress intensity factors are defined in the Laplace transform domain and these are inverted using a numerical method.     

Dynamic stress intensity factors of two 3D rectangular cracks in a transversely isotropic elastic material under a time-harmonic elastic P-wave

The dynamic stress intensity factors (DSIFs) of two 3D rectangular cracks in a transversely isotropic elastic material under an incident harmonic stress wave are investigated by generalized Almansi’s theorem and the Schmidt method in the present paper. Using 2D Fourier transform and defining the jumps of displacement components across the crack surface as the unknown functions, three pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement components across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the geometric shape of the rectangular crack, the characteristics of the harmonic wave and the distance between two rectangular cracks on the DSIFs of the transversely isotropic elastic material.     

DEFORMATION RIGIDITY OF ASSUMED STRESS MODES IN HYBRID ELEMENTS

The new methods to determine the zero-energy deformation modes in the hybrid elements and the zero-energy stress modes in their assumed stress fields are presented by the natural deformation modes of the elements. And the formula of the additional element deformation rigidity due to additional mode into the assumed stress field is derived. Based on, it is concluded in theory that the zero-energy stress mode cannot suppress the zero-energy deformation modes but increase the extra rigidity to the nonzero-energy deformation modes of the element instead. So they should not be employed to assume the stress field. In addition, the parasitic stress modes will produce the spurious parasitic energy and result the element behaving over rigidity. Thus, they should not be used into the assumed stress field even though they can suppress the zero-energy deformation modes of the element. The numerical examples show the performance of the elements including the zero-energy stress modes or the parasitic stress modes.     

Analytical solutions of steady vibration of free rectangular plate on semi-infinite elastic foundation

The method of double Fourier transform was employed in the analysis of the semi-infinite elastic foundation with vertical load.And an integral representations for the displacements of the semi-infinite elastic foundation was presented.The analytical solution of steady vibration of an elastic rectangle plate with four free edges on the semi-infinite elastic foundation was also given by combining the analytical solution of the elastic rectangle plate with the integral representation for displacements of the semi- infinite elastic foundation.Some computational results and the analysis on the influence of parameters were presented.     

冲击载荷作用下矩形薄板的弹性动力屈曲

为了研究冲击载荷作用下考虑应力波效应弹性矩形薄板的动力屈曲,根据动力屈曲发生瞬间的能量转换和守恒准则,导出板的屈曲控制方程和波阵面上的补充约束条件,真实的屈曲位移应同时满足控制方程和波阵面上的附加约束条件。满足上述条件,建立了该问题的完整数值解法,对屈曲过程中冲击载荷、屈曲模态和临界屈曲长度之间的关系进行研究,定量计算了横向惯性效应对提高薄板动力屈曲临界应力的贡献。研究表明：板的厚宽比一定时,临界屈曲长度随冲击载荷的增大而减小;由于屈曲时的横向惯性效应,应力波作用下薄板一阶临界力参数是相应边界板的静力失稳临界力参数的1.5倍;随着边界约束逐渐减弱,板临界力参数逐渐减小,动力特征参数逐渐增大。

     

横观各向同性弹性半空间地基上正交异性矩形中厚板弯曲解析解

对横观各向同性体通解进行双重傅里叶变换,获得了直角坐标系下横观各向同性弹性半空间地基受任意竖向荷载作用下的位移积分变换解;在此基础上建立了板与地基的变形协调方程,并与三个广义位移变量描述的弹性地基上四边自由正交各向异性矩形中厚板的弯曲控制方程相结合,用三角级数法,得出横观各向同性弹性半空间地基上四边自由正交异性矩形中厚板受任意竖向荷载作用的弯曲解析解。相关算例分析表明,本文方法是有效的。