共查询到20条相似文献,搜索用时 62 毫秒
1.
弹性动力学的双互易杂交边界点法 总被引:2,自引:0,他引:2
将双互易法同杂交边界点法相结合,提出了求解弹性动力问题的新型数值方法------双互易杂交边界点方法. 该算法在求解弹性动力问题时,将控制方程非齐次项的域内积分转化为边界积分. 该方法将问题的解分为通解和特解两部分,通解使用杂交边界点法求得,特解则使用局部径向基函数插值得到,从而实现了使用静力问题的基本解来求解动力问题. 计算时仅仅需要边界上离散点的信息,无论积分还是插值都不需要网格,域内节点仅用来插值非齐次项,因此该算法仍是一种边界类型的无网格方法. 数值算例表明,该方法后处理简单,计算精度高,适合于求解弹性动力问题. 相似文献
2.
该文利用杂交边界点法对简支薄板的热弹性弯曲进行了分析计算.采用薄板的热弹性理论,通过薄板的修正变分原理建立了各向同性薄板的边界局部积分方程,域内变量使用基本解插值,而边界上的变量则用移动最小二乘法近似.计算时仅需边界上离散点的信息,无论变量近似还是数值积分都不需要网格,因此该方法是一种纯边界类型无网格方法.数值算例表明,杂交边界点法在分析薄板的热弯曲问题时具有效率高、精度高和收敛性好等优点. 相似文献
3.
4.
本文首先基于理性力学非线性几何场理论,建立了等效速率形式的热弹性薄板的Karman方程,通过将热弹性薄板大挠度弯曲问题的看成平板弯曲问题与平面大变形问题的耦合,在固定坐标系及拖带坐标系上推导出两组边界积分方程,从而建立起新的分析热性薄板大挠度弯曲问题的边界元。本文的方法较双往分析此问题的边界法在理论上更准确,合理,算例表明本文的方法理论可靠,精度良好。 相似文献
5.
本文采用两套变量构造有限元试函数空间,在单元内部要求试函数精确满足平衡微分方程,在单元边界上对位移和转角分别用Peano升阶函数插值,然后利用广义变分原理建立了一种薄板弯曲问题的P型杂交解析有限方法,与常规有限元法相比,该方法不心进行过细的网格剖分,通过增加单元插值多项式的阶数P来提高精度,此外,该方法还具有积分计算只需在单元边界上进行、单元钢度矩阵和载荷向量具有嵌入结构、协调程度可以自动控制等优 相似文献
6.
7.
8.
给出了一个弹性薄板弯曲问题分区横向联结的泛函。并且证明,它的驻值条件等价于全部支配方程、外边界条件、分区公共边界处的内力平衡条件和位移连续条件。 相似文献
9.
基于小波微分求积法的薄板弯曲分析 总被引:1,自引:1,他引:1
利用小波微分求积法(WDQM)对任意荷载作用下的薄板弯曲问题进行了求解分析。数值算例表明,小波微分求积法与一般的DQ法相比具有很好的适用性,特别是薄板受集中荷载或不连续分布荷载作用时,由于小波基函数的紧支撑特性与其对突变信号良好的描述能力,WDQ法的精度明显优于一般的DQ法,具有良好的应用前景。 相似文献
10.
11.
IntroductionIt’swell_knownthatthecomplicatedfundamentalsolution[1,2 ]forHelmholtzequationΔu(x) +k2 u(x) =0 (x∈Ω:boundedopenregioninR2 )isu (x,y) =-iH(2 )0 (k x-y ) 4,thusit’snotconvenientfornumericalcomputation .IfapplyingthesimplefundamentalsolutionofLaplaceequationu 0 (x ,y) =-ln|x-y|(2π) ,theexpressionforthesolutionofequationintheclosedregion Ωisc(y)u(y) + ∫Γu(x) u 0 (x,y) nx -u 0 (x ,y) u(x) n dsx =-k2∫Ωu(x)u 0 (x,y)dΩx.Astherightsideappearstheregionalintegrationinclu… 相似文献
12.
Equivalent Boundary Integral Equations with indirect unknowns for thin elastic plate bending theory 总被引:4,自引:0,他引:4
Zhang Yao-ming Associate Professor Doctor Sun Huan-chun Yang Jia-xin 《应用数学和力学(英文版)》2000,21(11):1246-1255
Equivalent Boundary Integral Equations (EBIE) with indirect unknowns for thin elastic plate bending theory, which is equivalent
to the original boundary value problem, is established rigorously by mathematical technique of non-analytic continuation and
is fully proved by means of the variational principle. The previous three kinds of boundary integral equations with indirect
unknowns are discussed thoroughly and it is shown that all previous results are not EBIE.
Paper from SUN Huan-chun, Member of Editorial Commitee, AMM
Biography: ZHANG Yao-ming (1962-) 相似文献
13.
Thin structures are generally solved by the Finite Element Method (FEM), using plate or shell finite elements which have many
limitations in applications, such as numerical locking, edge effects, length scaling and the envergence problem. Recently,
by proposing a new approach to treating the nearly-singular integrals, Liu et al. developed a BEM to successfully solve thin
structures with the thickness-to-length ratios in the micro- or nano-scales. On the other hand, the meshless Regular Hybrid
Boundary Node Method (RHBNM), which is proposed by the current authors and based on a modified functional and the Moving Least-Square
(MLS) approximation, has very promising applications for engineering problems owing to its meshless nature and dimension-reduction
advantage, and not involving any singular or nearly-singular integrals. Test examples show that the RHBNM can also be applied
readily to thin structures with high accuracy without any modification. 相似文献
14.
15.
Some further results of the boundary element method for the Kirchhoff type plate bending problems are given. The direct boundary integral equation-boundary element scheme with higher conforming properties is used for several computation examples. The results of computation show that the numerical scheme seems to be more economical in computer time and with better accuracy in comparison with some previous results. 相似文献
16.
本文用边界元法研究非均质无限域弹性薄板弯曲问题.在数值实施过程中,对于夹杂和基体分别形成边界积分方程.通过离散边界积分方程,得到相应的方程组,然后结合界面条件,最终获得问题的求解方程组.在界面的相关量求得之后,可以根据需要来求解基体和夹杂中的有关位置的弯矩.数值结果与已有的解做了对比. 相似文献
17.
Research on the companion solution for a thin plate in the meshless local boundary integral equation method 总被引:1,自引:1,他引:0
The meshless local boundary integral equation method is a currently developed numerical method, which combines the advantageous features of Galerkin finite element method ( GFEM ), boundary element method (BEM) and element free Galerkin method (EFGM), and is a truly meshless method possessing wide prospects in engineeringapplications. The companion solution and all the other formulas required in the meshless local boundary integral equation for a thin plate were presented, in order to make this method apply to solve the thin plate problem. 相似文献
18.
DUAL RECIPROCITY BOUNDARY ELEMENT METHOD FOR FLEXURAL WAVES IN THIN PLATE WITH CUTOUT 总被引:2,自引:0,他引:2
The theoretical analysis and numerical calculation of scattering of elastic waves and dynamic stress concentrations in the thin plate with the cutout was studied using dual reciprocity boundary element method (DRM). Based on the work equivalent law, the dual reciprocity boundary integral equations for flexural waves in the thin plate were established using static fundamental solution. As illustration, numerical results for the dynamic stress concentration factors in the thin plate with a circular hole are given. The results obtained demonstrate good agreement with other reported results and show high accuracy. 相似文献
19.
MESHLESS ANALYSIS FOR THREE-DIMENSIONAL ELASTICITY WITH SINGULAR HYBRID BOUNDARY NODE METHOD 总被引:6,自引:0,他引:6
The singular hybrid boundary node method (SHBNM) is proposed for solving three-dimensional problems in linear elasticity. The SHBNM represents a coupling between the hybrid displacement variational formulations and moving least squares (MLS) approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the later. The rigid movement method was employed to solve the hyper-singular integrations. The 'boundary layer effect', which is the main drawback of the original Hybrid BNM, was overcome by an adaptive integration scheme. The source points of the fundamental solution were arranged directly on the boundary. Thus the uncertain scale factor taken in the regular hybrid boundary node method (RHBNM) can be avoided. Numerical examples for some 3D elastic problems were given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method were studied through the numerical examples. 相似文献
20.
An efficient dual reciprocity hybrid radial boundary node method is developed for the analysis of Winkler and Pasternak foundation thin plate, in which a hybrid displacement variational principle, radial point interpolation method (RPIM) and dual reciprocity method (DRM) are combined. Firstly, the hybrid displacement variational principle is developed, in which the domain variables are interpolated by two groups of symmetric fundamental solutions, while the boundary variables are interpolated by RPIM instead of the traditional moving least square, and the shape function obtained by RPIM satisfies the delta function property, so boundary conditions can be applied directly. Besides, DRM is exploited to evaluate the particular solutions of inhomogeneous terms, which can be used to transform the domain integrals arising from the inhomogeneous term into equivalent boundary integrals. Finally, some additional equations based on the DRM theory are proposed to overcome the problem that the boundary integral equations are not enough to solve all variables. This method has the advantages of both no element mesh of meshless method and dimensionality reduction of boundary element method. Numerical examples of Winkler and Pasternak foundation plates are given to illustrate that the present method is effective, accurate and it can be further expanded into practical engineering. 相似文献