基于遗传算法和复合二次径向基函数的复合材料层合板自由振动分析

为了提高复合材料层合板自由振动分析的精度,采用无网格径向基配点法分析复合材料材料层合板的自由振动问题,径向基函数的形状参数对计算精度有很大影响。利用遗传算法对复合二次径向基函数的形状参数进行优化,用优化后的形状参数的复合二次径向基函数计算复合材料层合板的固有频率,计算结果与文献中的结果具有较好的一致性。遗传算法在形状参数优化方面具有很大的潜力,所提出的方法具有较高的计算精度。     

基于径向基点插值函数的弹性力学Hamilton正则方程无网格法

结合径向基点插值函数和弹性材料修正后的H-R(Hellinger-Reissner)变分原理,推导了Hamilton正则方程的无网格列式。以Multiquadric(MQ)、Gaussian(EXP)和薄板样条(TPS)为基函数,研究了Hamilton体系下无网格方法的收敛性、精确性以及基函数无量纲形状参数对计算结果的影响规律。该文的工作使得无网格有限元法的优越性与弹性力学Hamilton正则方程的半解析法得到了有机的结合,为Hamilton正则方程提出了一种无网格半解析方法。     

Hamilton体系下含弱粘接复合材料层合板的无网格求解方法

该文结合径向基点插值函数、弹簧层模型和弹性材料修正后的H-R（Hellinger-Reissner）变分原理,推导了含弱粘接复合材料层合板控制方程的无网格列式。利用典型径向基函数Multiquadric（MQ）,计算了含弱粘接复合材料层合板的应力与位移。通过与精确法的对比,证明了控制方程无网格列式的正确性,并研究了弱粘...     

Hermite径向基函数点插值配点法求解消声器横向模态

为了避免划分网格,应用Hermite径向基函数点插值配点法(HRPIC)求解消声器横向本征方程,应用该方法计算的圆形和跑道圆横截面本征波数分别与解析结果和有限元计算结果吻合较好。进而分析影响域尺寸,问题域内计算点数目以及径向基函数的形状参数对本征波数计算误差的影响。结果表明,本征波数的计算误差在一定范围内会随着影响域尺寸和问题域内节点数目的增大而减小,但是不会一直减小,存在最优的数值,无量纲的形状参数直接影响本征波数的计算精度。最后比较Hermite径向基函数点插值配点法与有限元法的计算速度。     

正交各向异性和各向同性方板自由振动的三维无网格解

推导了正交各向异性和各向同性弹性体自由振动的三维控制微分方程,利用基于逆复合二次径向基函数的无网格配点法对三维控制微分方程和边界条件进行离散,通过数值算例选取了逆复合二次径向基函数的形状参数,结果表明:形状参数(是x方向的节点数)时计算结果收敛最快。计算了不同边界条件的正交各向异性和各向同性板的固有频率,该文中的结果与文献中的结果具有较好的一致性。     

全局弱式无网格方法求解消声器横向模态

应用全局弱式无网格方法求解消声器的横向模态,使用径向基函数点插值法离散本征方程,使用伽辽金加权残数法进行数值积分。分别应用全局弱式无网格方法计算了圆形截面,不规则截面以及含有穿孔截面的本征值和本征向量,计算结果与解析方法和二维有限元方法计算结果吻合较好,并且与二维有限元方法相比,全局弱式无网格方法比较节省计算时间。进而分析了支持域的尺寸以及径向基函数中形状参数对计算精度的影响。     

层合板分析的无网格局部Petrov-Galerkin方法

基于Kirchhoff均匀各向异性板控制方程的等效积分弱形式和对挠度函数采用移动最小二乘近似函数进行插值, 进一步研究无网格局部Petrov-Galerkin方法在纤维增强对称层合板弯曲问题中的应用。该方法不需要任何形式的网格划分, 所有的积分都在规则形状的子域及其边界上进行,其问题的本质边界条件采用罚因子法来施加。通过数值算例和与其他方法的结果比较, 表明无网格局部Petrov-Galerkin法求解层合薄板弯曲问题具有解的精度高、收敛性好等一系列优点。      

复合材料层合板力学性质分析及角铺设层优化设计

基于Kirchhoff经典理论,用样条有限元法以三次B样条函数构成的样条基对反对称多层角铺设层合板的三个独立位移进行插值,推导了复合材料层合板刚度阵,质量阵列式,阻尼阵列式,并由Lagrange方程导出了层合板的动力学方程,通过瑞利一李兹法建立了特征方程。分析了层合板的固有频率及不同层数和不同约束条件下的基频变化等力学特性,在Kirchhoff假设的基础上,对层合板的非线性弯曲的力学特性进行了探讨。基于样条有限元法和遗传算法进行复合材料层合板的角铺设层的优化设计,数值算列验证了算法的有效性。     

点载静力梁函数在求解矩形薄板自振特性中的应用

本文选择一组点载静力梁函数作为基函数，应用李兹法近似求解矩形薄板的自振特性，计算了多种边界条件下各种长宽比的矩形薄板的自振频率，与其它方法相比，本文方法具有很好的精度和收敛性，且计算非常简单直接。     

样条函数配点法分析薄板的压曲及自由振动与薄壳的稳定问题

本文采用单五次B一样条函数配点分析了薄板的压曲以及自由振动,用九次样条函数配点分析了几种薄壳的稳定问题。计算了不同的例题并与解析解进行比较,证明样条函数配点法是分析板、壳稳定问题的简便、有较的方法。     

Thin plate spline radial basis function for the free vibration analysis of laminated composite shells

In this paper, the free vibration characteristics of laminated composite cylindrical and spherical shells are analyzed by the first-order shear deformation theory and a meshless global collocation method based on thin plate spline radial basis function. The singularity of thin plate spline radial basis function is eliminated by adding infinitesimal to the zero distance. Several numerical examples are used to show convergence of the present method and choose the proper shape parameter. It is found that the natural frequencies computed by thin plate spline radial basis function with shape parameter m = 4 converge most rapidly. In the comparison study, the present results are in good agreement with the results of Reddy and Liu [8] and Ferreira et al. [21].     

A nth-order meshless generalization of Reddy’s third-order shear deformation theory for the free vibration on laminated composite plates

In this paper, a nth-order shear deformation theory is proposed to analyze the free vibration of laminated composite plates. The present nth-order shear deformation theory satisfies the zero transverse shear stress boundary conditions on the top and bottom surface of the plate. Reddy’s third-order theory can be considered as a special case of present nth-order theory (n = 3). Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, material properties are computed by present nth-order theory and a meshless radial point collocation method based on the thin plate spline radial basis function. The results are compared with available published results which demonstrate the accuracy and efficiency of present nth-order theory.     

Local Collocation Method for Prediction of Natural Frequency of Functionally Graded Cylindrical Shells

In this article, the local thin plate spline collocation method and first-order shear deformation shell theory are used to predict the natural frequency of functionally graded cylindrical shells. The local collocation method does not require special treatment for essential boundary condition nor time-consuming integration of weak form. Natural frequency of functionally graded cylindrical shells with clamped and simply supported boundary conditions are solved and compared with available published results to assess the performance of the present method.     

A local radial basis functions—Finite differences technique for the analysis of composite plates

Radial basis functions are a very accurate means of solving interpolation and partial differential equations problems. The global radial basis functions collocation technique produces ill-conditioning matrices when using multiquadrics, making the choice of the shape parameter a crucial issue. The use of local numerical schemes, such as finite differences produces much better conditioned matrices. However, finite difference schemes are limited to special grids. For scattered points, a combination of finite differences and radial basis functions would be a possible solution. In this paper, we use a higher-order shear deformation plate theory and a radial basis function—finite difference technique for predicting the static behavior of thin and thick composite plates. Through numerical experiments on square and L-shaped plates, the accuracy and efficiency of this collocation technique is demonstrated, and the numerical accuracy and convergence are thoughtfully examined. This technique shows great potential to solve large engineering problems without the issue of ill-conditioning.     

A meshless local radial point collocation method for free vibration analysis of laminated composite plates

In this paper, a meshless local radial point collocation method based on multiquadric radial basis function is proposed to analyze the free vibration of laminated composite plates. This method approximates the governing equations based on first-order shear deformation theory using the nodes in the support domain of any data center. Natural frequencies of the laminated composite plates with various boundary conditions, side-to-thickness ratios, and material properties are computed by present method. The choice of shape parameter, effect of dimensionless sizes of the support domain on accuracy, convergence characteristics are studied by several numerical examples. The results are compared with available published results which demonstrate the accuracy and efficiency of present method.     

A two-dimensional adaptive nodes technique in irregular regions applied to meshless-type methods

We propose a two-dimensional (2D) adaptive nodes technique for irregular regions. The method is based on equi-distribution principle and dimension reduction. The mesh generation is carried out by first producing some adaptive nodes in a rectangle based on equi-distribution along the coordinate axes and then transforming the generated nodes to the physical domain. Since the produced mesh is applied to the meshless-type methods, the connectivity of the points is not used and only the grid points are important, though the grid lines are utilized in the adapting process. The performance of the adaptive points is examined by considering a collocation meshless method which is based on interpolation in terms of a set of radial basis functions. A generalized thin plate spline with sufficient smoothness is used as a basis function and the arc-length is employed as a monitor in the equi-distribution process. Some experimental results will be presented to illustrate the effectiveness of the proposed method.     

A meshless method for Kirchhoff plate bending problems

In this work a meshless method for the analysis of bending of thin homogeneous plates is presented. This meshless method is based on the use of radial basis functions to build an approximation of the general solution of the partial differential equations governing the Kirchhoff plate bending problem. In order to obtain a symmetric and non‐singular linear equation system the Hermite collocation method is used. To assess the formulation a series of plates with different boundary conditions are analysed. Comparisons are made with other results available in the literature. Copyright © 2001 John Wiley & Sons, Ltd.     

An analysis for the elasto-plastic problem of the moderately thick plate using the meshless local Petrov–Galerkin method

A meshless local Petrov–Galerkin method for the analysis of the elasto-plastic problem of the moderately thick plate is presented. The discretized system equations of the moderately thick plate are obtained using a locally weighted residual method. It uses a radial basis function (RBF) coupled with a polynomial basis function as a trial function, and uses the quartic spline function as a test function of the weighted residual method. The shape functions have the Kronecker delta function properties, and no additional treatment to impose essential boundary conditions. The present method is a true meshless method as it does not need any grids, and all integrals can be easily evaluated over regularly shaped domains and their boundaries. An incremental Newton–Raphson iterative algorithm is employed to solve the nonlinear discretized system equation. Numerical results show that the present method possesses not only feasibility and validity but also rapid convergence for the elasto-plastic problem of the moderately thick plate.     

Radial point interpolation collocation method (RPICM) for the solution of nonlinear poisson problems

This paper applies radial point interpolation collocation method (RPICM) for solving nonlinear Poisson equations arising in computational chemistry and physics. Thin plate spline (TPS) Radial basis functions are used in the work. A series of test examples are numerically analysed using the present method, including 2D Liouville equation, Bratu problem and Poisson-Boltzmann equation, in order to test the accuracy and efficiency of the proposed schemes. Several aspects have been numerically investigated, namely the enforcement of additional polynomial terms; and the application of the Hermite-type interpolation which makes use of the normal gradient on Neumann boundary for the solution of PDEs with Neumann boundary conditions. Particular emphasis was on an efficient scheme, namely Hermite-type interpolation for dealing with Neumann boundary conditions. The numerical results demonstrate that a good accuracy can be obtained. The h-convergence rates are also studied for RPICM with coarse and fine discretization models.