面向对象的钢筋混凝土有限元非线性分析程序设计

采用面向对象的程序设计方法，结合钢筋混凝土有限元非线性分析模型，利用MFC(Microsoft Foundation Class Library)建立了有关描述钢筋混凝土有限元非线性分析的类，包括混凝土单元类、钢筋单元类、粘结单元类、非线性计算类，并给出了这些类的描述和它的实现方法，并为钢筋混凝土有限元非线性分析程序采用更合理的面向对象的方法提供了思路。     

无限元方法及其应用

限元是几何上趋于无穷的单元,它是一种特殊的有限元,也是对有限元在求解无界域 问题上的有效补充, 并可实现与有限元间的无缝连接.无限元分为映射无限元和非映射 无限元:映射无限元需要引入几何映射,在局部坐标系中构造插值形状函数,如Bettess 元和Astley元;非映射无限元则直接在整体坐标系中构造插值形状函数,如Burnett元. 本文评述求解无界域问题的无限元方法的研究现状和最新发展.首先介绍无限单元的概念 和无限元方法的特点;围绕求解以Helmholtz方程控制的波动问题,评述几种常规无限单 元的优劣,这些单元包括Bettess元、Astley元和Burnett元.然后介绍新近提出的广义 无限元方法,以及与常规无限元方法的区别与联系.最后对无限元方法在各种问题中的 应用做了总结.     

A catenary element for the analysis of cable structures

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组合单元法在砂井地基有限元分析中的应用

针对砂井地基的平面应变有限元分析，本文首次将组合单元法引入到砂井地基的分析中，提出砂墙组合单元。该单元对常规等参元进行改进，在单元内部同时考虑砂井的涂抹作用和井阻作用，从而克服了常规有限元法在计算砂井地基时单元数和节点数过多的缺点。将砂墙组合单元加入USAP有限元计算软件，工程算例分析结果表明：与已有的各砂井地基的平面应变解答和荷兰的基础工程有限元分析软件PLAXIS相比，解答合理并有效地考虑砂井的涂抹作用和井阻作用；与常规有限元法相比，在保证计算精度的前提下，减少了可观的单元数和节点数，降低了计算的工作量。     

面向对象的无单元法

介绍了一种用C 进行的面向对象无单元方法程序设计;定义了一些关键的类并将有些类设计成类等级,从而建立了包含权函数、基函数和形函数在内的面向对象无单元法程序类库,在此过程中考虑了无单元法与有限元法的某些联系,保留并重用了面向对象有限元法程序中的一些类。本文提供了一种无单元法大型分析软件开发新途径。     

A reconstructed edge-based smoothed DSG element based on global coordinates for analysis of Reissner–Mindlin plates

A reconstructed edge-based smoothed triangular element, which is incorporated with the discrete shear gap(DSG) method, is formulated based on the global coordinate for analysis of Reissner–Mindlin plates. A symbolic integration combined with the smoothing technique is implemented to calculate the smoothed finite element matrices,which is integrated along the boundaries of each smoothing cell. Numerical results show that the proposed element is free from shear locking, and its results are in good agreement with the exact solutions, even for very thin plates with extremely distorted elements. The proposed element gives more accurate results than the original DSG element without smoothing, and it can be taken as an alternative element for analysis of Reissner–Mindlin plates. The prominent feature of the present element is that the integration scheme is unified in the smoothed form for all of the finite element matrices.     

用拟协调元直接构造平面任意四边形单元——进入有限元的禁区

利用拟协调元方法,在直角坐标系下直接构造了一族平面任意四边形单元,对其收敛性进行了分析,并与平面等参元进行了对比研究.结果证明平面任意四边形单元可采用多项式基函数直接列式,并可以保障单元的收敛性;拟协调元列式可以使平面问题的有限元方法得到统一.与平面等参元相比,单元列式简单,性能稳定,具有显式的刚度阵,计算量小,这说明对于有限元平面问题拟协调元是一个更正确、有效的做法.      

A decomposed Crouzeix-Raviart element for the finite element solution of the Navier-Stokes equation

A methodology for the decomposition of the Crouzeix-Raviart finite element into six linear subelements is described. The resulting element is shown to satisfy the Brezzi-Babu?ka compatibility condition. The error bounds are also established. A comparison in accuracy between this and the standard Crouzeix-Raviart element is presented for driven cavity flows. Other results include the execution time for the DCR element and the Crouzeix-Raviart element along with both analytical and numerical integration. It is shown that the decomposed element results in shorter execution times with only marginal changes in accuracy.     

Using co-rotational method for cracked frame analysis

A cracked element is formulated using the two-filed Hellinger–Reissner functional. Due to utilization of the linear elastic fracture mechanics, only geometrical nonlinearities can be considered for the cracked element. A clear step-by-step algorithm for the element state determination is also presented. The element flexibility matrix is derived in a basic coordinate system. Co-rotational approach is used to transform the element stiffness matrix and the resisting force vector from the basic system to the global one. The suggested element is applicable for static and dynamic analysis, as well as, the stress intensity factor calculation, and also inverse crack detection. Various numerical problems verify accuracy of the proposed element for linear and nonlinear structural analysis.     

Corotational nonlinear analyses of laminated shell structures using a 4-node quadrilateral flat shell element with drilling stiffness

A new 4-node quadrilateral flat shell element is developed for geometrically nonlinear analyses of thin and moderately thick laminated shell structures. The fiat shell element is constructed by combining a quadrilateral area co- ordinate method （QAC） based membrane element AGQ6- II, and a Timoshenko beam function （TBF） method based shear deformable plate bending element ARS-Q12. In order to model folded plates and connect with beam elements, the drilling stiffness is added to the element stiffness matrix based on the mixed variational principle. The transverse shear rigidity matrix, based on the first-order shear deformation theory （FSDT）, for the laminated composite plate is evaluated using the transverse equilibrium conditions, while the shear correction factors are not needed. The conventional TBF methods are also modified to efficiently calculate the element stiffness for laminate. The new shell element is extended to large deflection and post-buckling analyses of isotropic and laminated composite shells based on the element independent corotational formulation. Numerical re- sults show that the present shell element has an excellent numerical performance for the test examples, and is applicable to stiffened plates.     

US-FE-LSPIM四边形单元及其在几何非线性问题中的应用

为了提高在网格畸变时的数值计算精度,基于非对称有限单元的概念,提出US-FE-LSPIM四边形单元。该单元是利用传统的四节点等参元形函数集和FE—LSPIM四边形单元形函数集分别作为检验函数和试函数而构成。前者用于满足单元间和单元内的位移连续性要求,后者用于满足位移完备性要求。该单元结合了有限单元法和无网格法的优点,能...     

等参元——修改等参元——最佳等参元

本文以二维问题为模型,建立了等参元、修改等参元和最佳等参元间的相互关系.给出了最佳等参元附加节点方程的解法.其数值解与理论分析一致.显示出修改等参元的许多良好特性.     

压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

A precise singular finite element for crack analysis

The multi-variable finite element algorithm based on the generalized Galerkin’smethod is more flexible to establish a finite element model in the continuum mechanies.Byusing this algorithm and numerical tests a new singular finite element for elasto-plasticfracture analysis has been formulated.The results of numerical tests show that the newelement possesses high accuracy and good performance.Some rules for formulating amulti-variable singular finite element are also discussed in this paper.     

一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

框架结构屈曲的精确有限元求解

基于屈曲微分控制方程的一般解,构造了Euler梁在轴力作用下的精确形函数,建立了用于框架结构屈曲分析的精确有限单元,得到了单元刚度矩阵和几何刚度矩阵的显式表达,并提出了基于常规特征值计算的迭代算法以确定屈曲载荷及相应失稳模态的精确解. 研究表明, 对于线性稳定性分析而言,常规框架有限单元可视为精确有限单元的一种近似. 若采用精确单元,无需进行网格细分就可以获得精确的屈曲载荷和失稳模态. 数值算例证明了新单元和算法的效率和精度.      

Formulations of a hydromechanical interface element

A hydromechanical interface element is proposed for the consideration of the hydraulic-mechanical coupling effect along the interface.The fully coupled governing equations and the relevant finite element formulations are derived in detail for the interface element.All the involved matrices are of the same form as those of a solid element,which makes the incorporation of the model into a finite element program straightforward.Three examples are then numerically simulated using the interface element.Reasonable results confirm the correctness of the proposed model and motivate its application in hydromechanical contact problems in the future.     

四边形等参单元温度场有限元分析中的混合边界条件

在温度场有限元分析中，边界条件的合理确定是一个非常重要的问题。本文以四边形等参单元为基本单元，采用基于微分方程等效积分原理的Galerkin加权余量法，建立了热传导问题的有限元方程，推导出混合边界条件的有限元计算公式。最后，根据求得的温度场可得截面温度应力分布。     

A cubic quadrilateral spline element with concave shapes

Basic requirement for applying isoparametric element is that the element has to be convex and no violent distortion is allowed. In this paper, a cubic quadrilateral spline element with 12 nodes has been developed using the triangular area coordinates and the B-net method, which can exactly model the cubic field for quadrilateral element with both convex and concave shapes. Neither mapping nor coordinate transformation is required and the spline element can obtain high accuracy solutions and insensitive to mesh distortions.