一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发,并假设横向剪切应变在单元内线性变化,提出了一种考虑横向剪切变形的具有15个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度,计算效率高,可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

一种考虑横向剪切变形的三角形板弯曲单元

本文从部分协调的三角形薄板弯曲单元出发，并假设横向剪切应变在单元内线性变化，提出了一种考虑横向剪切变形有具有１５个自由度的三角平板弯曲单元。该单元应用于薄板和中等厚度板分析均有较高的精度，计算效率高，可用于工程中具有复杂形状的薄板和中等厚度板结构的分析。     

一种提高薄板稳定分析精度的方法

在薄板稳定分析中，九参数三角形薄板单元因其形状简单，使用方便，在实际工程中得到了广泛应用。本文基于参数调正的几何刚度矩阵，对九参数三角形薄板单元的一致刚度矩阵进行了修正，为提高计算精度提供了一种有效方法。     

变厚度圆环板/圆板横向自由振动的动刚度法求解

分别基于经典薄板理论和一阶剪切理论研究了沿半径方向变厚度的圆板及圆环板的横向自由振动,将结构离散为若干个等厚度同心圆环单元,在得出圆环单元的精确解后,通过动刚度法组装单元。应用该方法将变厚度圆板退化至等厚度板,与解析解对比验证了计算方法的正确性;用于计算线性或非线性变厚度板,也能与有限元三维解吻合。计算结果表明:基于一阶剪切理论和薄板理论的动刚度法计算等厚度薄板的振动均能取得与解析解完全吻合的数值解;而计算变厚度薄板时则采用基于一阶剪切理论的动刚度法更准确;与有限元法相比,本文采用的动刚度法划分单元少,具有较高的计算效率,尤其在工程中的大型板结构振动方面有较好的应用前景。     

薄板小波有限元理论及其应用

利用样条小波尺度函数构造了常用的三角形和矩形薄板单元的位移函数,得到了利用小波函数表示的形函数。采用合理的局部坐标,对单元进行压缩,使单元在局部坐标区间上有其值,成功地推导出了分域的三角形和矩形薄板小波有限元列式。在此基础上,提出了弹性地基薄板的小波有限元求解方法。通过两个算例对薄板的挠度和弯矩进行了计算,数值结果表明,求解结果具有收敛快、精度高的特点。     

变厚度薄板、壳广义杂交元

本文基于胡海昌-鹫津久一郎广义杂交变分原理建立了一种三角形变厚度薄板、壳广义杂交元。给出提高杂交元实施效率的一种可能途径。这类单元与其他类型的杂交模型相比,精度高且能较好地避免矩阵求逆运算,具有较好的实用性。单元刚度矩阵常常给出显式,用于直接刚度法程序很方便。 本文还进一步指出,各种杂交模型都可以看成是一种广义直接刚度法。     

一个厚薄板通用的三角形板弯元

本文提出了一个新的厚薄板通用的三角形板弯元,根据Hellinger-Reissner变分原理推导出来的新单元具有独立的转角、位移、剪应变和弯曲应变的插入函数,它没有其它混合元所存在的一些缺点。一些典型例子表明这个新单元具有很好的特性,刚度矩阵简单,计算精度高,收敛速度快以及厚薄板通用性强。     

用张量分析进行薄壳混杂模型三角形单元的构式

一般常用薄板单元分析薄壳内力,但由于内部边界联接斜率的不连续性而影响到求解精度。本文首先从薄壳的基本理论着手,用张量分析法建立了薄壳的势能原理和混杂变分原理。其次,对任意形状的薄壳,提出了采用混杂模型进行三角形单元的构式方法。最后,以螺旋曲面薄壳为例,导出了性质矩阵的形式。     

线性变厚度粘弹性矩形板在随从力作用下的动力稳定性

利用粘弹性微分型本构关系和薄板理论,对线性变厚度粘弹性矩形薄板建立了在切向均布随从力作用下的运动微分方程,采用微分求积法研究了在随从力作用下线性变厚度粘弹性矩形薄板的稳定性问题,具体对对边简支对边固支和三边简支一边固支条件下体变为弹性、畸变服从Kelvin-Voigt模型的变厚度粘弹性矩形板在随从力下的广义特征值问题进行了求解,分析了薄板的长宽比、厚度比及材料的无量纲延滞时间的变化对随从力作用下矩形薄板的失稳形式及相应的临界荷载的影响.     

薄板几何非线性中的精化元方法及膜闭锁问题

基于放松单元间协调条件的大变形变分原理和全局拉格朗日方法，推导了几何非线性精化三角形薄板单元。对几何刚度矩阵，通过引入特殊的单元位移函数，有效地消除了薄板弯曲问题中伴生的膜闭锁现象。数值结果表明该单元在几何非线性分析中既能消除膜闭锁又具有较高精度。     

Static flexural analysis of elliptic Reissner–Mindlin plates on a Pasternak foundation by the triangular differential quadrature method

In this paper, static flexural analysis of elliptic Reissner–Mindlin plates resting on a Pasternak foundation is conducted using the triangular differential quadrature method (TDQM). A triangular serendipity transformation is proposed to map a curvilinear domain onto a unit isosceles right triangle. The applicability of the TDQM to problems on domains with curvilinear boundaries is improved significantly since no inner points are needed in the transformation. In the case of thin circular plates, the results of the present method are in excellent agreement with those of the available exact solution, demonstrating the effectiveness of the present method. Elliptic plates with various aspect ratios and thickness-to-width ratios under uniformly distributed load are studied.     

Discretized virtual internal bond model for nonlinear elasticity

The virtual internal bond (VIB) is a micro–macro constitutive model. Although this model is based on a postulated discrete microstructure, it ultimately returns to a continuum constitutive relation through a homogenization process. The homogenization process can reduce the internal degrees of freedom, but it omits the effect of the individual micro bond that may play an important role in the fracture process. The present research develops a discrete system to represent the nonlinear elasticity by discretizing the continuous VIB. This discrete system is composed of unit cells, which can adopt any geometry with any number of bonds. The system is characterized by the force–displacement, not the stress–strain constitutive relationship. The nonlinear properties of this discrete system are governed by the micro-bond potential. The micro bond properties are related to Young’s modulus of the material, the volume and the bond number of the unit cell. For a given material, the unit cell has a certain topological structure and configuration. A discussion of two specific cases (the 2D triangular and 3D tetrahedral unit cells) suggests that the discrete system converges with decreasing unit cell size. In the unstructured unit cell scheme, the discrete system can almost precisely represent the initial Young’s modulus and the Poisson ratio of a nonlinear continuum. A mixed fracture example demonstrates that the present method can efficiently simulate the fracture propagation. The present paper provides a theory for developing a lattice-type mechanical model for nonlinear elasticity and provides new method for the fracture simulation of a nonlinear elastic material.     

应力强度因子分析的三角形Williams单元

弹性断裂分析的Williams广义参数单元计算模型中忽略了紧邻裂尖的微区域,为了进一步完善该计算模型,本文提出并建立了三角形Williams单元。首先围绕裂尖将奇异区均匀分割为有限个三角形单元,利用改进的Williams级数建立该单元的整体位移场计算模型;其次沿径向将该三角形单元进一步离散为多个相似四边形微单元和裂尖三角形微单元,并利用经典有限元理论建立微单元的局部位移场计算模型;然后利用整体位移场控制各微单元结点位移,并在此基础上研究建立裂尖奇异区三角形Williams单元及其控制方程。该单元模型中含有与裂尖应力强度因子相关的参数,能够直接计算裂尖处的应力强度因子。最后结合算例详细分析了三角形Williams单元计算模型中径向离散因子、离散数、Williams级数项对计算结果的影响。算例分析表明,三角形Williams单元所得的应力强度因子具有对奇异区尺寸不敏感的优点,且收敛快,计算精度高。     

Bandgap calculation for mixed in-plane waves in 2D phononic crystals based on Dirichlet-to-Neumann map

In this paper, a method based on the Dirichlet-to-Neumann map is developed for bandgap calculation of mixed in-plane waves propagating in 2D phononic crystals with square and triangular lattices. The method expresses the scattered fields in a unit cell as the cylindrical wave expansions and imposes the Bloch condition on the boundary of the unit cell. The Dirichlet-to-Neumann (DtN) map is applied to obtain a linear eigenvalue equation, from which the Bloch wave vectors along the irreducible Brillouin zone are calculated for a given frequency. Compared with other methods, the present method is memory-saving and time-saving. It can yield accurate results with fast convergence for various material combinations including those with large acous- tic mismatch without extra computational cost. The method is also efficient for mixed fluid-solid systems because it considers the different wave modes in the fluid and solid as well as the proper fluid-solid interface condition.     

A study on flow resistance in the entrance region of isosceles triangular ducts

In the present paper the variational solution of velocity profile for anincompressible laminar and fully developed flow in isosceles triangular ducts is derivedby applying the Kantovorich method.The theoretical and experimental results ofpressure loss are also given.The velocity distribution model,additional pressure losscoefficient and calculating method of inlet length in the entrance region of isoscelestriangular ducts are also derived,which are suitable for various kinds of vertex angles.The calculations and experiments are also performed for two models:the isoscelestriangular channels with vertex angles2α=45.1°and2α=60°.Comparisons aremade between the theoretical analysis in this paper and those of the other authors.Itcan be seen that the present analytical result is of high.accuracy and widepracticability,and agrees well with the authors’experiment.     

基于非结构网格求解二维浅水方程的高精度有限体积方法

采用HLL格式,在三角形非结构网格下采用有限体积离散,建立了求解二维浅水方程的高精度的数值模型.本文采用多维重构和多维限制器的方法来获得高精度的空间格式以及防止非物理振荡的产生,时间离散采用三阶Runge-Kutta法以获得高阶的时间精度.基于三角形网格,底坡源项采用简单的斜底模型离散,为保证计算格式的和谐性,对经典的HLL格式计算的数值通量中的静水压力项进行了修正.算例证明本文提出的方法的和谐性并具有高精度的间断捕捉能力和稳定性.     

On the Green's Functions and Boundary Integral Formulation of Elastic Planes with Cutouts

ABSTRACT

The problem of an infinite elastic plane that contains a hole of arbitrary shape and is subjected to a concentrated unit load is considered. The Green's function (influence function) for the problem is formulated by means of two complex potential functions. This is accomplished by mapping the region that is exterior to the hole onto a unit circle. A class of closed contour hole shapes is analyzed. Green's functions for an elliptical hole and a class of triangular holes are determined. Green's functions for a class of rectangular holes are also discussed. In order to determine stress and displacement fields for the finite plane problem, Green's function is employed and an indirect boundary integral equation is formulated, with the integrand of the integral equation incorporating the effect of the hole. The contour of the hole is no longer considered a part of the boundary and only the contour of the region that is exterior to the hole is subdivided into boundary elements. Examples for elliptical and triangular holes are solved.     

Scattering of SH-waves on triangular hill joined by semi-cylindrical canyon

Scattering of SH-waves on the triangular hill joined by semi-cylindrical canyon in half-space is studied using the method of complex function and moving coordinates. The model being studied is divided into two domains. The wave functions satisfying the required condition at each wedge are constructed in each equation. The equations are solved with Fourier expansion. Numerical results are provided to discuss the influence of scattering of SH-waves.