滑移索结构分析的精确三维有限元法

针对现有滑移索结构分析方法适用范围有限、精度不高的缺点,提出了一种通用、高精度的三维滑移索单元法。基于悬链线理论和Euler-Eytelwein公式,同时考虑了温度效应和滑动摩擦,分别建立了已知单元无应力索长和已知张拉力的三维滑移索单元的基本方程组;利用矩阵微分从单元基本方程组导出了单元的切线刚度矩阵;建立了滑移索结构从张拉到后期加载的全过程精细化分析流程,可实现自动调用建立的各类索单元,准确分析各滑移点的摩擦;通过3个算例的计算及与现有理论解、数值解和试验结果的比较来验证该文所提出方法的可靠性和有效性。结果表明,该文提出的三维有限元法准确可靠,计算效率较高,适用于工程中各种滑移索结构的高精度非线性分析。     

解析试函数法分析平面切口问题

本文利用平面切口问题的基本解析解构造单元,分析平面切口问题。通过分析平面切口问题的Williams特征方程的有解区间,使用分区加速lleruM&&法依序无漏地计算了平面V型切口特征值。从Williams应力函数出发,推导了V型切口尖端的应力场基本解析解列式。并用此根据分区混合能量原理构造了含切口解析单元ATF-VN的刚度矩阵。文中还对含切口解析单元的单元尺寸和应力项数等因素对分析结果的影响进行了系统的讨论。     

位移型板单元内力解的杂交化后处理

本文针对如何提高位移型板弯曲单元内力解的问题进行了一些探讨,在总结位移型和杂交型有限元的特点基础之上,提出了利用杂交元原理对位移型单元内力解进行重算的后处理方案：首先由位移型板元求出单元结点位移;其次假设满足平衡方程的单元内力场,并利用杂交能量泛函原理确定其与单元位移之间的联系,进而求出单元内力解。数值算例表明,本文所提出的方法可以明显改善多种板弯曲单元内力解的性态,使单元在获得较精确的位移解的同时,又可获得较好的内力解,而且又不使单元列式过于复杂。本文为改善位移型有限元的内力和应力解提供了一条可行的新途径。     

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。     

基于遗传算法的有限元方法

本文将遗传算法应用于力学计算，目的是探求一种理想的并行计算方法，克服有限元法在形成和存储整体刚质阵时数据处理的困难。基本思想是设法将力学问题转化为优化问题，借用有限元法的离散技术，将结构离散成单元和节点，根据能量原理得到以节点位移为基本未知量的目标函数，然后利用遗传算法求其最优解，得各节点位移的近似值，再由几何物理关系求解单元应力，算例表明，该方法是可行的。     

圆管网格结构的自适应有限元分析方法研究

为了判断网格结构有限元模型中梁单元的长度和插值函数是否合理并对此进行调整,首先推导了梁在受拉、受压、纯弯3种情况下的挠曲微分方程,以有限元试算得到的梁单元两端节点力为边界条件,求出了梁单元广义力分布场的解析解;然后,根据Zienkiewicz-Zhu后验误差估计理论,以该解析解为广义力相对精确解,推导了广义力有限元解和广义力相对精确解的能量范数以确定梁单元的相对误差。在试算过程中,如果网格结构中每个梁单元的相对误差都满足精度要求,则终止试算过程,否则调整梁单元的插值函数或长度后再进行试算。以单层球面网壳的自适应有限元静力分析为例验证了该方法的正确性和可行性。     

一种无奇异积分的边界单元法

处理基本解的奇异性是边界单元法的难题之一。本文避开奇异基本解,用非奇异基本解建立边界积分方程。非奇异基本解取自齐次微分方程的一般解和完备系,使求解边界积分方程容易。文中对边界未知量采用样条插值函数,计算精度良好。     

悬索桥结构分析中索鞍的精确模拟

为在悬索桥结构分析中精确模拟索鞍,建立了索段一端固定于鞍座上的两节点“左鞍座单元”和“右鞍座单元”,以及索段中一点固定于鞍座上的三节点“鞍座单元”,此固定点为新单元的一个节点。它们通过自动调整索与鞍座的切点而处于平衡状态,从而简化了计算。单元算法的推导基于有限元分析的基本原理和弹性悬链线的精确解,并利用了处于平衡状态时索与鞍座之间的内力关系。新单元可以考虑鞍座重量的影响,鞍槽纵向曲线可为复合圆曲线。新单元可以同常规单元一样直接用于索结构的有限元分析,设计的算例验证了其正确性,工程算例显示了其在悬索桥结构分析中的应用。     

索结构静力分析的新型拉索单元研究

总结和分析不同工况下索结构中拉索的受力特点, 将拉索行为归纳为已知原长和已知索力两种典型受力情况。利用悬链线拉索解析解的线性展开, 并引入适当的约束条件, 建立两种新型的拉索单元, 给出单元切线刚度矩阵的显式表达。提出索结构非线性静力分析的一般迭代算法, 算法中利用等效线自重考虑弹性变形对拉索静力状态的影响。以斜拉悬臂结构的多阶段安装为例, 分别采用该文方法和传统方法针对不同工况进行了索结构分析, 对比计算结果证明了该文新型单元和算法的效率和精度。     

P(VA-co-VAc)共聚物组成及VAc单元分布的调控

以具有不同醇解活性的氯乙酸乙烯酯(VClAc)和乙酸乙烯酯(VAc)为单体,通过自由基共聚制备了具有选择性醇解特性的共聚物P(VClAc-co-VAc)。进一步通过优化醇解条件,选择性醇解共聚物中VClAc单元,获得具有预定组成和结构的部分醇解聚乙烯醇,即P(VA-co-VAc)。通过聚合转化率、凝胶渗透色谱和核磁共振氢谱分析,研究了共聚合反应动力学、P(VClAc-co-VAc)选择性醇解反应特性和选择性醇解反应产物P(VA-co-VAc)共聚物组成及VAc单元分布。结果表明,通过调节单体投料比可获得预定组成和结构的醇解前驱体P(VClAc-co-VAc),经选择性醇解后可得到P(VA-co-VAc);通过在共聚阶段调控P(VClAc-co-VAc)的组成与结构,能实现对P(VA-co-VAc)共聚物组成及VAc单元分布的调控。     

Extended displacement discontinuity Green's functions for three-dimensional transversely isotropic magneto-electro-elastic media and applications

A versatile method is presented to derive the extended displacement discontinuity Green's functions or fundamental solutions by using the integral equation method and the Green's functions of the extended point forces. In particular, the three-dimensional (3D) transversely isotropic magneto-electro-elastic problem is used to demonstrate the method. On this condition, the extended displacement discontinuities include the elastic displacement discontinuities, the electric potential discontinuity and the magnetic potential discontinuity, while the extended forces include the point forces, the point electric charge and the point electric current. Based on the obtained Green's functions, the extended Crouch fundamental solutions are derived and an extended displacement discontinuity method is developed for analysis of cracks in 3D magneto-electro-elastic media. The extended intensity factors of two coplanar and parallel rectangular cracks are calculated under impermeable boundary condition to illustrate the application, accuracy and efficiency of the proposed method.     

Analysis of elliptical cracks perpendicular to the interface of two joined transversely isotropic solids

This paper presents a boundary element analysis of elliptical cracks in two joined transversely isotropic solids. The boundary element method is developed by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of stress intensity factors (SIFs) are obtained by using crack opening displacements. The results of the proposed method compare well with the existing exact solutions for an elliptical crack parallel to the isotropic plane of a transversely isotropic solid of infinite extent. Elliptical cracks perpendicular to the interface of transversely isotropic bi-material solids of either infinite extent or occupying a cubic region are further examined in detail. The crack surfaces are subject to the uniform normal tractions. The stress intensity factor values of the elliptical cracks of the two types are analyzed and compared. Numerical results have shown that the stress intensity factors are strongly affected by the anisotropy and the combination of the two joined solids.     

Boundary element analysis of three-dimensional crack problems in two joined transversely isotropic solids

The present paper presents a boundary element analysis of penny-shaped crack problems in two joined transversely isotropic solids. The boundary element analysis is carried out by incorporating the fundamental singular solution for a concentrated point load in a transversely isotropic bi-material solid of infinite space into the conventional displacement boundary integral equations. The conventional multi-region method is used to analyze the crack problems. The traction-singular elements are employed to capture the singularity around the crack front. The values of the stress intensity factors are obtained by using crack opening displacements. The numerical scheme results are verified with the closed-form solutions available in the literature for a penny-shaped crack parallel to the plane of the isotropy of a homogeneous and transversely isotropic solid of infinite extent. The new problem of a penny-shaped crack perpendicular to the interface of a transversely isotropic bi-material solid is then examined in detail. The crack surfaces are subject to the three normal tractions and the uniform shear traction. The associated stress intensity factor values are obtained and analyzed. The present results can be used for the prediction of the stability of composite structures and the hydraulic fracturing in deep rock strata and reservoir engineering.     

The gauss-hermite numerical integration method for the solution of the plane elastic problem of semi-infinite periodic cracks

The problem of parallel semi-infinite periodic cracks subjected to a transversely directed load in an infinite isotropic and elastic medium under conditions of plane stress or plane strain can be reduced to the solution of a Cauchy-type singular integral equation along one of the cracks. This equation can be transformed into a system of linear equations by means of an approximation of the integrals through the Gauss-Hermite procedure and application of the equation to distinct points along the faces of the crack. Stress intensity factors thus determined for the crack tips under constant load along the cracks are in satisfactory agreement with corresponding values derived previously.     

Boundary integral equation solution of three‐dimensional elastostatic problems in transversely isotropic solids using closed‐form displacement fundamental solutions

The boundary integral equation method is used for the solution of three‐dimensional elastostatic problems in transversely isotropic solids using closed‐form fundamental solutions. The previously published point force solutions for such solids were modified and are presented in a convenient form, especially suitable for use in the boundary integral equation method. The new presentations are used as a basis for accurate numerical computations of all Green's functions necessary in the BEM process without inaccuracy and redundant computations. The validity of the new presentation is shown through three numerical examples. Copyright © 2000 John Wiley & Sons, Ltd.     

Elastostatic Green’s functions for an arbitrary internal load in a transversely isotropic bi-material full-space

The problem of a full-space which is composed of two half-spaces with different transversely isotropic materials with an internal load at an arbitrary distance from the interface is considered. By virtue of Hu-Nowacki-Lekhnitskii potentials, the equations of equilibrium are uncoupled and solved with the aid of Hankel transform and Fourier decompositions. With the use of the transformed displacement- and stress-potential relations, all responses of the bi-material medium are derived in the form of line integrals. By appropriate limit processes, the solution can be shown to encompass the cases of (i) a homogeneous transversely isotropic full-space, and (ii) a homogeneous transversely isotropic half-space under arbitrary surface load. As the integrals for the displacement- and stress-Green’s functions, for an arbitrary point load can be evaluated explicitly, illustrative results are presented for the fundamental solution under different material anisotropy and relative moduli of the half-spaces and compared with existing solutions.     

Three-dimensional extended displacement discontinuity method for vertical cracks in transversely isotropic piezoelectric media

The conventional displacement discontinuity method is extended to study a vertical crack under electrically impermeable condition, running parallel to the poling direction and normal to the plane of isotropy in three-dimensional transversely isotropic piezoelectric media. The extended Green's functions specifically for extended point displacement discontinuities are derived based on the Green's functions of extended point forces and the Somigliana identity. The hyper-singular displacement discontinuity boundary integral equations are also derived. The asymptotical behavior near the crack tips along the crack front is studied and the ordinary 1/2 singularity is obtained at the tips. The extended field intensity factors are expressed in terms of the extended displacement discontinuity on crack faces. Numerical results on the extended field intensity factors for a vertical square crack are presented using the proposed extended displacement discontinuity method.     

Dynamic crack problems in three-dimensional transversely isotropic solids

In this paper, a general boundary element approach for three-dimensional dynamic crack problems in transversely isotropic bodies is presented for the first time. Quarter-point and singular quarter-point elements are implemented in a quadratic isoparametric element context. The procedure is based on the subdomain technique, the displacement integral representation for elastodynamic problems and the expressions of the time-harmonic point load fundamental solution for transversely isotropic media. Numerical results corresponding to cracks under the effects of impinging waves are presented. The accuracy of the present approach for the analysis of dynamic fracture mechanics problems in transversely isotropic solids is shown by comparison of the obtained results with existing solutions.     

Boundary integral equation method for conductive cracks in two and three-dimensional transversely isotropic piezoelectric media

Using the fundamental solutions and the Somigliana identity of piezoelectric medium, the boundary integral equations are obtained for a conductive planar crack of arbitrary shape in three-dimensional transversely isotropic piezoelectric medium. The singular behaviors near the crack edge are studied by boundary integral equation approach, and the intensity factors are derived in terms of the displacement discontinuity and the electric displacement boundary value sum near the crack edge on crack faces. The boundary integral equations for two dimensional crack problems are deduced as a special case of infinite strip planar crack. Based on the analogy of the obtained boundary integral equations and those for cracks in conventional isotropic elastic material and for contact problem of half-space under the action of a rigid punch, an analysis method is proposed. As an example, the solution to conductive Griffith crack is derived.     

Three-dimensional steady-state general solution for transversely isotropic hygrothermopiezoelectric media and its application in fracture

The potential theory method is utilized to derive the steady-state, general solution for three-dimensional (3D) transversely isotropic, hygrothermopiezoelectric media in the present paper. Two displacement functions are introduced to simplify the governing equations. Employing the differential operator theory and superposition principle, all physical quantities can be expressed in terms of two functions, one satisfies a quasi-harmonic equation and the other satisfies a tenth-order partial differential equation. The obtained general solutions are in a very simple form and convenient to use in boundary value problems. As one example, the 3D fundamental solutions are presented for a steady point moisture source combined with a steady point heat source in the interior of an infinite, transversely isotropic, hygrothermopiezoelectric body. As another example, a flat crack embedded in an infinite, hygrothermopiezoelectric medium is investigated subjected to symmetric mechanical, electric, moisture and temperature loads on the crack faces. Specifically, for a penny-shaped crack under uniform combined loads, complete and exact solutions are given in terms of elementary functions, which serve as a benchmark for different kinds of numerical codes and approximate solutions.