Galerkin法求解弹性边界条件下圆板的流-固耦合振动特性

用干圆板振型作为基函数将圆板位移展开为级数形式,采用速度势函数描述流体运动,研究了弹性边界条件下圆板的流-固耦合振动特性。根据圆板的平衡微分方程和流-固耦合界面的速度连续条件,结合Galerkin法和Fourier-Bessel级数展开法,建立了系统的控制方程。求解了流体中圆板的固有振动特性,并将计算结果与数值仿真结果进行对比,验证了方法的正确性。通过改变弹簧刚度,分析了几种常见边界条件下圆板的振动特性,结果表明,自由和导向边界圆板的振型受流体的影响较小。研究了流体深度对圆板振动特性的影响,结果表明,当深度大于1.5倍圆板半径时,流体深度的改变对于圆板自由振动的影响可以忽略。     

敷设覆盖层圆板水下爆炸响应理论计算方法研究

为研究敷设覆盖层圆板水下爆炸响应,提出一种理论计算方法。敷设覆盖层对圆板水下爆炸响应影响包括两方面:一为对冲击载荷的影响,二为在冲击载荷作用下对响应的影响。该理论计算方法运用波在多层介质传播理论得到湿表面压力,并积分得到冲量,运用等效均一化理论得到覆盖层与钢板整体结构的等效参数,根据圆板振动理论得到圆板真空振动方程,通过考虑水附加质量的影响修正圆板振动频率,最后根据初始条件得到圆板的响应。将理论方法的结果与有限元结果通过实例进行对比,证明该理论计算方法可以很好地预测圆板振动的位移响应。     

基于格林函数法的封闭声腔的结构-声耦合分析

以封闭声腔为模型，在考虑流固耦合作用的基础上，结合流体格林函数和Helmholtz方程及其边界条件，导出了各阶声压模态对应的声压振幅响应公式；结合结构格林函数和板的振动方程及其边界条件，导出了各阶板模态对应的速度振幅响应公式。这两个公式物理意义明确，易于转化为矩阵形式直接进行数值仿真，可应用于任意几何形状的封闭声腔，为进一步研究封闭声腔的结构-声耦合问题提供了必要的理论基础。数值仿真部分首先对声压振幅和速度振幅的积分形式作了矩阵化。然后以长方体封闭声腔为模型，结合有限元法计算声压模态和弹性板的振动模态，合成耦合系数，并最终合成弹性板与声腔耦合作用下的的声压响应和弹性板的速度响应；将数值仿真结果与解析结果以及前人的试验结果进行比较，验证了本文在理论分析和数值仿真方面的正确性。最后将该方法应用于一个非规则封闭声腔模型，得到了结构-声耦合作用下的系统响应。     

受任意个同心弹性环支圆板横向自由振动的一个新的解析解法

本文研究受任意个同心弹性环支图板的横向自由振动问题，给出了一个新的解析解法。对弹性环支反力表示为作用于圆板上的待定外力，在求得圆板受迫振动的解析式后，由圆板的边界条件决定积分常数，利用环支处板位移与环支反力之间的线性关系得环支反力，并得频率方程。它是一阶数等于环支个数的行列式，可由行列式搜根法数值计算各阶固有频率，而振型函数则用一解析式表示，本文最后给出了一个算例，并与已有结果进行了比较。     

破片模拟弹侵彻钢板的有限元分析

根据破片模拟弹侵彻钢板的实验研究，采用MSC．Dytran对破片模拟弹侵彻钢板的侵彻过程、侵彻特性、钢板的破坏模式以及弹体的侵彻速度、靶板的侵彻阻力进行了有限元分析，并将分析结果与实验结果进行了比较．分析结果表明，破片模拟弹冲击钢装甲的侵彻过程可大致分为初始接触、弹体侵入、剪切冲塞和穿甲破坏4个阶段．有限元分析的破片模拟弹侵彻特性及靶板破坏模式与实验观测结果有较好的一致性，在靶板破口的正面，与弹体平面凸缘两端接触的部分，变形以剪切为主，而与切削面接触的部分，以挤压变形为主；靶板破口背面为剪切冲塞破坏；有限元模拟的弹体剩余速度与实验结果吻合较好，弹体侵彻过程中弹靶作用界面的速度和侵彻速度近似呈线性变化．有限元分析结果还表明，采用适当的模型，有限元法能较好地模拟破片模拟弹侵彻钢板的侵彻过程、侵彻特性以及钢板的破坏模式．     

饱和地基上含刚核弹性圆板的摇摆振动分析

基于饱和土弹性波动方程,研究了饱和地基上含刚核弹性圆板在摇摆谐和力矩作用下的振动特性。首先应用Hankel积分变换求解该饱和土波动方程,然后按混合边值条件建立起一组描述含刚核弹性圆板振动的对偶积分方程,并将其化为第二类Fredholm积分方程进行数值求解。此外,给出了含刚核弹性圆板在饱和地基上振动的阻抗函数随无量纲频率的变化曲线,并考察了土的渗透系数、弹性板含刚域的大小以及板的柔度等参数对阻抗函数的影响,得出了一些有意义的结论。     

制冷压缩机阀片的流体振荡可靠性分析

为了预测受流体冲击的制冷压缩机阀片可靠性，通过引入非线性流体振荡条件，建立流体结构耦合分析的边界积分方程及求解格式，采用等效均值和离差的线性化处理进行可靠度指标计算，提出了流体振荡可靠性分析边界元数值方法。针对B67-30G半封闭制冷压缩机进、排气阀片结构动力可靠性分析显示，该方法能快速、有效地预测阀片结构在流体振荡下的总体性能，为新型阀片的优化和可靠性设计提供依据。     

圆板大挠度新的样条积分方程法

本文提出了圆板大挠度新的样条积分方程法。根据圆板大挠度问题的二个平衡方程及环基本解,导出了一组积分方程,再利用样条函数法进行求解。由于采用了样条插值,只要划分少量单元就能获得精度很高的数值解。本文成果与精确解良好吻合。     

水介质对多种边界条件方板振动频率及辐射效率的影响

本提出了一种简便计算置于无限大障板上的方板水中振动频率以及辐射效率的计算方法。在假定流体不可压、方板作小振幅振动、水中模态挠度近似为真空模态挠度的条件下，利用瑞利积分得到了因流体压而引起的附加质量密度。进而应用瑞利方法得到了方板水中振动频率与真空中振动频率、无量纲附加虚质量增量之间的关系。在真空中模态的有限元方法分析数据以及采用适当方法处理奇点积分的基础上，应用离散积分计算了无量纲附加虚质量增量的值。从真空中模态特征频率出发用迭代法直到水中频率收敛为止而得到水中方板的特征频率，进而计算了方板的模态辐射效率。方法的有效性通过方板的无量纲附加虚质量增量与献[11]结果对比的一致性来验证。     

阻力伞锁滚柱梁冲击失效分析

滚柱梁是阻力伞锁传力路径上的主承力件之一。某型阻力伞锁滑车试验过程中,滚柱梁失效导致开伞失败,故障分析认为滚柱梁失效模式为冲击剪切失效。对滚柱梁冲击剪切失效机理进行了分析,认为阻力伞锁运动机构在牵引伞初始冲量作用下获得初始冲击速度,并与滚柱梁发生碰撞-接触-挤压,该过程导致滚柱梁剪切失效。通过建立阻力伞锁运动机构的动力学模型,获得了初始冲击速度和运动机构等效质量,并将滚柱梁模型化为在均匀冲击载荷作用下的两端固支圆截面梁。应用刚塑性材料模型,考虑剪切失效厚度系数和弯曲-剪切共同作用,进行剪切失效分析,推导得到临界失效冲击速度,解释了滚柱梁失效机理。进一步讨论了套筒与滚柱梁质量比对滚柱梁失效的影响,为结构改进设计提出了建议。     

Plane stress and plate bending coupling in BEM analysis of shallow shells

In this paper the shear deformable shallow shells are analysed by boundary element method. New boundary integral equations are derived utilizing the Betti's reciprocity principle and coupling boundary element formulation of shear deformable plate and two‐dimensional plane stress elasticity. Two techniques, direct integral method (DIM) and dual reciprocity method (DRM), are developed to transform domain integrals to boundary integrals. The force term is approximted by a set of radial basis functions. Several examples are presented to demonstrate the accuracy of the two methods. The accuracy of results obtained by using boundary element method are compared with exact solutions and the finite element method. Copyright © 2000 John Wiley & Sons, Ltd.     

Boundary element analysis of a plate on elastic foundations

The objective of this study is to examine the applicability of the boundary element method to analysing a plate on elastic foundation. The fundamental solution of the problem is presented as a Fourier-Bessel integral. For the computation of the values of the fundamental solution an algorithm was developed in which the Fourier-Bessel integral was decomposed into an alternative convergent sequence. Equations based on the direct and indirect boundary element method were derived for a plate situated on a one- or two-parametric elastic foundation. According to the theory presented, computer programs based on the direct and indirect boundary element method were developed. These programs can be used for examining the behaviour of a smooth-boundary plate on a one- or two-parametric elastic foundation. The computer programs were tested by several examples. The results obtained by using a small number of boundary elements compared favourably to the results obtained by a fine finite element mesh. The study shows that the boundary element method is applicable to the analysis of a plate on elastic foundation.     

Finite element solution to an elastica problem of beams

In this study, finite element solution procedures are developed for an elastica problem of inextensible beams. The element stiffness matrices are obtained by using Galerkin's method. Results of a numerical example compare reasonably well with those obtained by using the elliptical integral. Extensions of this research are currently being made to include membrane effects of beams and to develop plate element stiffness matrices for elastica problems of plate structures.     

用耦合有限元／边界元方法研究加筋板的声传输

采用耦合的有限元／边界元方法,建立了考虑流体结构耦合的加筋板结构声传输计算模型,并利用该模型计算研究了加筋板的声传输特性。数值计算表明：结构的传声损失与结构的固有频率和激励频率密切相关,避免共振仍是产要的;改变板厚或肋骨惯性矩后,由于结构固有频率发生了变化会使得结构传声损失曲线上极小值的位置发生改变;当声波从空气经结构向空气中传递时,增大板厚或肋骨惯性矩可明显增大结构的传声损失;而当声波从空气经结构向水中传递时,增大板厚或肋骨惯性矩也增大了结构的传声损失,但效果明显不如当声波从空气经结构向空气中传递时显著。     

Transformation of domain integrals to boundary integrals in BEM analysis of shear deformable plate bending problems

In this paper two techniques, dual reciprocity method (DRM) and direct integral method (DIM), are developed to transform domain integrals to boundary integrals for shear deformable plate bending formulation. The force term is approximated by a set of radial basis functions. To transform domain integrals to boundary integrals using the dual reciprocity method, particular solutions are employed for three radial basis functions. Direct integral method is also introduced in this paper to evaluate domain integrals. Three examples are presented to demonstrate the accuracy of the two methods. The numerical results obtained by using different particular solutions are compared with exact solutions. Received 27 January 1999     

饱和地基上弹性圆板的固结位移

 采用Laplace变换及Hankel变换研究弹性圆板在饱和地基上的固结位移．在Laplace变换域上建立了求解弹性圆板固结位移的第二类Fredholm积分方程，由数值反变换获得时域解，给出了对工程实践有参考价值的计算结果．计算结果表明，弹性板的固结位移随饱和土的排水泊松比的减少而增加，而弹性板的初始位移随饱和土的不排水泊松比的减少而增加．     

Numerical simulations of cracked plate using XIGA under different loads and boundary conditions

This article deals with the numerical simulation of cracked plate using extended isogeometric analysis (XIGA) under different loads and boundary conditions. The plate formulation is done using first-order shear deformation theory. The crack faces are modeled by the Heaviside function, whereas the singularity in stress field at the crack tip is modeled by crack tip enrichment functions. The stress intensity factors for the cracked plate are numerically computed using a domain-based interaction integral. The results obtained by XIGA for the center and edge crack plate are compared with extended finite element method and/or literature results for different types of loads and boundary conditions.     

The hybrid Laplace transform/finite element method applied to the quasi-static and dynamic analysis of viscoelastic Timoshenko beams

The quasi-static and dynamic responses of a linear viscoelastic beam are solved numerically by using the hybrid Laplace transform/finite element method. In the analysis, the Timoshenko beam theory, which includes the transverse shear and rotatory inertia effect and conventional beam theory, are used to solve this problem. The temperature field is assumed to be constant and homogeneous and that the relaxation modulus has the form of the Prony series. In the hybrid method, the Laplace transform with respect to time is applied to the coupled equations and the finite element model is developed by applying Hamilton's variational principle without any integral transformation. The numerical results of quasi-static and dynamic responses for the models of Maxwell fluid and three parameter solid types are presented and discussed.     

A note on the porous-wavemaker problem

Summary A complete analytical solution is obtained, by using an integral transform method, for the porous-wavemaker problem, when the effect of surface tension is taken into account on the free surface of water of finite-depth in which surface waves are produced by small horizontal oscillations of a porous vertical plate. The final results are expressed in the form of convergent integrals as well as series and known results are reproduced when surface tension is neglected.