基于有限单元柔度法和刚度法的非线性梁柱单元比较研究

分别基于有限单元柔度法和有限单元刚度法理论,采用纤维模型梁柱单元编制了钢筋混凝土杆系结构非弹性分析程序。基于柔度法的梁柱单元模型的特点在于以单元截面力插值函数作为出发点,在不考虑几何非线性的前提下,总能保证单元内部截面力场分布满足平衡条件。通过构造的数值算例及钢筋混凝土双向弯曲柱反复加载试验结果与两种方法模拟分析结果的对比,对柔度法与刚度法的分析效果进行了比较研究,并对纤维模型梁柱单元解决空间杆系结构非弹性分析的有效性进行了验证。结果表明:对于结构处于强非线性阶段,尤其是对于处理下降段(软化)问题,基于柔度法的梁柱单元无论从计算效率还是计算效果上都明显优于基于刚度法的梁柱单元;纤维模型梁柱单元是目前处理空间杆系双向弯曲与变轴力耦合问题最为实用有效的单元分析模型。     

三种非线性梁柱单元的研究及单元开发

罕遇地震作用下混凝土梁柱构件易进入塑性阶段而发生弹塑性损伤,正确地模拟结构进入非线性状态后的力学行为对评价结构的抗震安全性具有重要的意义.通过面向对象语言编制了基于宏观单元的结构弹塑性分析软件平台MESAP,增加了三种非线性梁柱单元:基于刚度法纤维单元、基于柔度法纤维单元及基于柔度法的塑性铰单元.通过算例分析三种非线性...     

弹塑性纤维梁柱单元及其单元参数分析

基于柔度法且沿单元长度积分的弹塑性纤维梁柱单元是可以模拟复杂的截面双向滞回曲线和截面刚度沿杆长方向连续变化的单元模型。由于其计算工作量太大,这种复杂的单元自提出以来,一直没有得到推广应用。对弹塑性纤维梁柱单元模型进行了研究,在此基础上对其单元参数进行了分析,通过研究单元积分段以及截面上纤维的合理划分,使计算工作量适当减少而又不影响计算结果准确性,为纤维单元在大型结构中应用打下基础。     

基于共旋法与稳定函数的几何非线性平面梁单元

建立一个准确、高效的几何非线性梁单元对于描述杆系结构的非线性行为至关重要。该文基于共旋坐标法和稳定函数提出了一种几何非线性平面梁单元。该单元在形成中把变形和刚体位移分开,局部坐标系内采用稳定函数以考虑单元P-δ效应的影响,从局部坐标系到结构坐标系的转换则采用共旋坐标法以及微分以考虑几何非线性,给出了几何非线性平面梁单元在结构坐标系下的全量平衡方程和切线刚度矩阵;在此基础上根据带铰梁端弯矩为零的受力特征,导出了能考虑梁端带铰的单元切线刚度矩阵表达式。通过多个典型算例验证了算法与程序的正确性、计算精度和效率。     

基于混合单元法的预应力混凝土梁非线性分析

利用共旋坐标法提出了一种预应力钢筋混凝土梁非线性分析的混合单元模型,在随转坐标系内,采用分层梁单元来模拟混凝土结构,带初应变的杆单元来模拟预应力钢筋,预应力钢筋杆元和混凝土梁元的变形协调则通过非线性刚臂来实现,通过刚臂单元两端节点位移和力的关系形成预应力钢筋对混合单元刚度矩阵的贡献,从而导出随转坐标系下预应力混凝土梁考虑材料非线性的切线刚度矩阵,几何非线性则由单元随转坐标系到结构坐标系的转换矩阵及其微分来体现,从而获得结构坐标系下混合单元模型的几何与材料双非线性切线刚度矩阵。数个钢筋混凝土及预应力钢筋混凝土梁非线性分析算例表明:所提出的混合单元模型能较好地分析预应力钢筋混凝土梁非线性性能,具有一定的实用价值。     

改进共旋坐标法的Timoshenko梁单元非线性分析

为提高空间Timoshenko梁单元非线性问题的计算精度,在共旋坐标法的基础上,提出了一种改进的Timoshenko梁单元几何非线性分析方法。利用虚功原理得到改进空间梁单元的刚度矩阵;使用有限质点法中的逆向运动思路计算单元局部坐标系下的刚体旋转矩阵;根据整体坐标系与局部坐标系之间旋转角度的转化以及微分关系,求得空间梁单元的切线刚度矩阵;编制了相应的有限元程序,对多个经典的大变形结构进行几何非线性分析。计算结果印证了该文所提出改进方法的正确性,同时与传统共旋坐标法相比,具有更高的精度。     

基于等参公式的三节点梁单元

为了提高非线性分析的计算精度和效率,详细介绍了基于等参公式的三节点梁单元,推导了这种梁单元考虑几何非线性的切线刚度矩阵,并给出了高斯积分点的分布。在此基础上编制有限元程序,考虑了单元的大转角、大位移和剪切变形的影响,并采用von-Mises屈服准则和Zeigler随动硬化法则考虑了材料非线性的影响。与试验结果和通用程序的对比分析表明,这种方法具有较高的精度和效率,并且能方便地用于变截面杆系结构的空间双重非线性分析。     

变截面压杆稳定计算的有限单元法

本文在文「１」建立的三维退化梁单元的基础上，考虑几何非线性，推导出计算任竭尽为截面压杆稳定问题的有限元无式。计算结果表明，本文公式正确，力学概念清晰明了，计算效率较高，该单元三维梁、板、块单元的连接非常方便，很适合于工程结构的总体分析。     

基于静力凝聚的高精度变截面梁单元及其几何非线性分析研究

基于Euler-Bernoulli梁单元基本假定,通过静力凝聚获得截面特性沿单元轴向连续变化的变截面梁单元高精度刚度矩阵,并提出一种基于随动坐标法求解变截面梁杆结构大位移、大转动、小应变问题的新思路。首先依据插值理论和非线性有限元理论推导出三节点变截面梁单元的切线刚度矩阵,然后使用静力凝聚方法消除中间节点自由度,从而得到一种新型非线性两节点变截面梁单元。结合随动坐标法,在变形后位形上建立随动坐标系,得到变截面梁单元的大位移全量平衡方程。实例计算表明,该新型变截面梁单元具有较高的计算精度,可应用于变截面梁杆系统大位移几何非线性分析。     

基于有限质点法的结构动力非线性行为分析

有限质点法是以向量力学为基础的崭新的结构分析方法,该文将其应用到结构动力非线性行为分析中。该方法将结构离散为质点群,采用牛顿定律描述质点的运动,通过对质点行为的模拟和分析计算结构行为。该文介绍了有限质点法的基本思想,提出了该方法分析结构“动”与“静”,“线性”与“非线性”问题的独特思路。以杆系结构为例,推导了该方法求解结构动力反应,及几何、材料非线性问题的基本公式。通过三个数值算例,验证了该方法在结构动力非线性行为分析中的正确性和适用性。有限质点法在处理动力非线性问题时无需迭代求解和特殊修正,与传统方法相比在结构复杂行为分析中有明显的优势。     

A conformal decomposition finite element method for arbitrary discontinuities on moving interfaces

Interface capturing methods using enriched finite element formulations are well suited for solving multimaterial transport problems that contain weak or strong discontinuities. The conformal decomposition FEM decomposes multimaterial elements of a non‐conforming background mesh into sub‐elements that conform to material interfaces captured using a level set method. As the interface evolves, interfacial nodes move, and background nodes may change material. The present work describes approaches for handling moving interfaces in the context of the conformal decomposition FEM for both weakly and strongly discontinuous fields. Dynamic discretization methods using extrapolation and moving mesh approaches are considered and developed with first‐order and second‐order time integration methods. The moving mesh approach is demonstrated to be a stable method that preserves both weak and strong discontinuities on a variety of one‐dimensional and two‐dimensional test problems, while achieving the expected second‐order error convergence rate in space and time. Copyright © 2014 John Wiley & Sons, Ltd.     

Quadrilateral membrane elements with analytical element stiffness matrices formulated by the new quadrilateral area coordinate method (QACM‐II)

A novel strategy for developing low‐order membrane elements with analytical element stiffness matrices is proposed. First, some complete low‐order basic analytical solutions for plane stress problems are given in terms of the new quadrilateral area coordinates method (QACM‐II). Then, these solutions are taken as the trial functions for developing new membrane elements. Thus, the interpolation formulae for displacement fields naturally possess second‐order completeness in physical space (Cartesian coordinates). Finally, by introducing nodal conforming conditions, new 4‐node and 5‐node membrane elements with analytical element stiffness matrices are successfully constructed. The resulting models, denoted as QAC‐ATF4 and QAC‐ATF5, have high computational efficiency since the element stiffness matrices are formulated explicitly and no internal parameter is added. These two elements exhibit excellent performance in various bending problems with mesh distortion. It is demonstrated that the proposed strategy possesses advantages of both the analytical and the discrete method, and the QACM‐II is a powerful tool for constructing high‐performance quadrilateral finite element models. Copyright © 2008 John Wiley & Sons, Ltd.     

Use of higher‐order shape functions in the scaled boundary finite element method

The scaled boundary finite element method is a novel semi‐analytical technique, whose versatility, accuracy and efficiency are not only equal to, but potentially better than the finite element method and the boundary element method for certain problems. This paper investigates the possibility of using higher‐order polynomial functions for the shape functions. Two techniques for generating the higher‐order shape functions are investigated. In the first, the spectral element approach is used with Lagrange interpolation functions. In the second, hierarchical polynomial shape functions are employed to add new degrees of freedom into the domain without changing the existing ones, as in the p‐version of the finite element method. To check the accuracy of the proposed procedures, a plane strain problem for which an exact solution is available is employed. A more complex example involving three scaled boundary subdomains is also addressed. The rates of convergence of these examples under p‐refinement are compared with the corresponding rates of convergence achieved when uniform h‐refinement is used, allowing direct comparison of the computational cost of the two approaches. The results show that it is advantageous to use higher‐order elements, and that higher rates of convergence can be obtained using p‐refinement instead of h‐refinement. Copyright © 2005 John Wiley & Sons, Ltd.     

钢梁-钢筋混凝土柱梁柱中节点非线性有限元模拟

借助ANSYS有限元分析软件,对5个"梁贯通"式RCS梁柱中节点进行三维非线性有限元分析,并和试验结果相比较。分析中考虑材料非线性以及混凝土的开裂与压碎。对单元类型的选取、钢和混凝土材料模型的定义、整体有限元模型的建立、施加荷载、设置求解选项并求解等数值模拟技术进行了深入的研究。研究表明,通过合理设置参数,ANSYS有限元软件能够模拟RCS梁柱节点在静力荷载作用下的性能,并和试验结果吻合较好。     

钢筋混凝土结构空间有限元分析的体梁组合单元

本文提出了一种用于钢筋混凝土结构空间有限元分析的体梁组合单元模型。该模型将混凝土体元内的钢筋作为能承受轴力、剪力、弯矩和扭矩的梁元,根据钢筋和混凝土在单元内的位移协调条件和虚功原理将两者组合成一个单元。体梁组合单元模型能较全面地反映混凝土内钢筋的力学效应,能适应钢筋的任意布置方式,容许用较大的单元对结构进行离散,解决了大型钢筋混凝土结构有限元分析的单元划分问题。数值算例及其与解析解的比较演示了模型的可行性和精度。     

柔度法梁柱单元考虑损伤分布的高斯积分方法

分析了积分方案对基于柔度法梁-柱单元模型的影响,将高斯积分和钢筋混凝土梁、柱构件损伤特点结合起来,提出了考虑损伤分布的积分方法。将单元非线性区域划分为塑性铰区、开裂区、过渡区,一方面赋予高斯积分区域物理含义,另一方面使得塑性铰区域可以向相邻的开裂区、过渡区扩展,实现塑性铰长度动态变化。对钢筋混凝土框架结构进行静力非线性分析,结果表明:该积分方案更能反映梁、柱构件的实际损伤,具有较好的数值稳定性和收敛性。     

Lower‐dimensional interface elements with local enrichment: application to coupled hydro‐mechanical problems in discretely fractured porous media

In this study, we develop lower‐dimensional interface elements to represent preexisting fractures in rock material, focusing on finite element analysis of coupled hydro‐mechanical problems in discrete fractures–porous media systems. The method adopts local enrichment approximations for a discontinuous displacement and a fracture relative displacement function. Multiple and intersected fractures can be treated with the new scheme. Moreover, the method requires less mesh dependencies for accurate finiteelement approximations compared with the conventional interface element method. In particular, for coupled problems, the method allows for the use of a single mesh for both mechanical and other related processes such as flow and transport. For verification purposes, several numerical examples are examined in detail. Application to a coupled hydro‐mechanical problem is demonstrated with fluid injection into a single fracture. The numerical examples prove that the proposed method produces results in strong agreement with reference solutions. Copyright © 2012 John Wiley & Sons, Ltd.