用于光滑/非光滑壳的稳定化新型协同转动4节点四边形壳单元

该文发展了一种适用于光滑壳和非光滑壳的新型协同转动4节点四边形壳单元。在单元中每个节点采用了3个平动自由度和2/3个矢量型转动自由度,每个光滑壳的节点或非光滑壳的非交界节点采用壳中性面法向矢量的2个最小分量作为矢量型转动变量,在非光滑壳中性面交界线上的节点采用3个矢量型转动变量,他们分别是节点定向矢量组中一个定向矢量的较小或最小分量和另一定向矢量的2个最小分量。在非线性增量求解过程中,这些矢量型转动变量可以采用简单的加法将增量累加到原矢量中直接进行更新,且采用了协同转动框架的单元在局部和整体坐标系下得到的切线刚度矩阵都是对称的,结构整体切线刚度矩阵可以采用一维线性存储,可节省大量的计算机存储资源和计算时间。为消除膜闭锁和剪切闭锁的不利影响,采用单点积分方案计算单元内力矢量和切线刚度矩阵,并借鉴Belytschko提出的物理稳定化零能模态控制法来消除可能出现的零能模态。通过对2个光滑壳和2个非光滑壳进行非线性分析,检验了单元的可靠性、计算效率与计算精度。     

复合材料板壳结构的杂交/混合有限元分析

本文建立了一个9节点Lagrange退化壳杂交/混合有限元模型,以用于复合材料板壳结构的有限元分析。该有限元模型基于修正的Hellinger-Reissner原理,位移和应力均采用分离法思想,使得这一单元不仅具有下列优点:1.位移和应力计算精度都比较高;2.消除了多余零能变形模式;3.具有厚薄通用性;4.具有几何不变性,并且较之一般杂交/混合单元计算工作量进一步降低。单元还考虑了横向剪切影响。计算实例表明,本单元关于复合材料浅壳和深壳的解都与参考解吻合很好,且收敛很快。      

新型协同转动六节点三边形复合材料壳单元

为分析复合材料层合板壳结构,提出了一种协同转动六节点三边形复合材料曲壳单元。不同于现有的其它协同转动有限单元:1) 该单元中采用了增量可加的矢量型转动变量,因而在非线性增量求解过程中更新节点转动变量非常简单;2) 在计算应变能对局部节点变量的二阶偏微分时,微分的次序是可以交换的,并且通过链式微分计算应变能对整体节点变量的二阶偏微分时,微分的次序也是可以交换的,因此,得到的局部和整体坐标系下的切线刚度矩阵都是对称的;3) 在此有限单元公式中引入了混合公式法,以减轻膜闭锁和剪切闭锁的不利影响。对4个典型算例进行了分析,并与其他文献的结果进行对比,该文提出的单元的可靠性和计算效率得到了验证。     

基于三维有限元法的层合圆柱壳应力分析

针对空间结构中常见的蜂窝夹芯壳体提出了一种32节点相对自由度三层壳元,以及一种精确计算层间应力的后处理方案。这种32节点壳元可以更好地反映结构固有的特性,易与三维实体单元相连接,使变厚度、带有补强的蜂窝夹芯复合材料壳体等复杂结构问题得以正确建模。本文作者的后处理方案克服了位移有限元层间应力不连续的缺点,保证了应力精确满足边界条件。综合运用以上方法的典型算例表明:计算精度是令人满意的。     

一种非线性显式分层壳单元及其GPU并行计算实现

通用有限元程序ABAQUS的钢筋混凝土显式分层壳单元被广泛应用于剪力墙抗震性能分析,但存在两个缺陷:①只能得到混凝土受压损伤和受拉损伤,无法反映混凝土剪切损坏,因此不易根据损伤类型对结构进行优化;②基于CPU并行计算,大规模计算效率较低。基于平面应力条件下的混凝土弹塑性损伤本构模型,根据混凝土损伤发展时的受力状态和工程实践需要将损伤分为受拉损伤、受压损伤和受剪损伤。结合可损伤分类的塑性损伤模型,给出了非线性壳元物理沙漏力和面内旋转力的构造方法,进而得到一种含面内旋转自由度的4节点24自由度四边形非线性显式分层壳单元。将该研究壳元在自主研发的基于CPU+GPU异构并行计算的非线性分析软件中完成开发实现;通过与ABAQUS benchmark算例结果对比,验证了开发内容的正确性;通过与剪力墙单调加载试验对比,验证了该研究壳元的合理性。分别采用自主研发软件和ABAQUS对上海地区某框架核心筒体系的超高层结构进行了罕遇地震非线性时程分析,结果表明:①自主研发软件与ABAQUS结果基本一致,而计算效率为ABAQUS计算效率的5.69倍;②自主研发软件得到的受拉损伤、受压损伤和受剪损伤损伤可更清晰地揭示核心筒在罕遇地震作用下的损坏演化规律和破坏模式。     

大型油罐桩筏基础有限元分析

对变厚度油罐筏板采用16节点实体退化单元进行有限单元法分析.计算结果证明,应用16节点退化实体单元能大大减少了单元数目,大幅度提高了计算效率,并能达到相当高的精度.该研究结果适合大型油罐桩筏基础的计算,具有广泛的应用前景.     

新型协同转动3节点三边形壳单元

发展了一种新型3节点三边形壳单元。计算单元在局部坐标系下的节点变量时,通过采用协同转动法,预先扣除节点整体变量中的刚体转动成分,从而简化了单元的计算公式。不同于现有的其他协同转动单元,在该单元中采用了增量可以直接累加的矢量型转动变量,单元的切线刚度矩阵可以通过直接计算能量泛函对节点变量的二阶偏微分得到,且对节点变量的偏微分次序是可以互换的,因而在局部和整体坐标系下都得到了对称的单元切线刚度矩阵。为消除单元中可能出现的闭锁现象,引入了MacNeal提出的线积分法,分别用沿单元边线方向的膜应变和剪切应变构造新的假定应变场。最后,通过对几个产生了大位移与大转角变形的板壳问题进行分析,检验了该单元的可靠性、计算精度和计算效率。     

混杂CFRP/GFRP筋HPC梁的非线性梁壳组合单元研究

对于混杂CFRP/GFRP筋高性能混凝土（HPC）梁, 研究一种新的三维非线性梁壳组合单元, 对HPC梁进行了全过程分析。引入实体退化壳单元理论, 利用空间梁单元模拟预应力CFRP筋, 并根据CFRP筋单元节点线位移和转角位移的协调性, 推导CFRP筋单元对梁壳组合单元刚度矩阵的贡献, 同时对GFRP筋和HPC梁采用分层壳单元模拟。并运用Jiang屈服准则、 Madrid强化准则等描述混凝土的材料非线性, 提出一种新的非线性梁壳组合单元, 研制相应的三维非线性计算程序。计算结果与试验数据吻合良好, 说明本文构造的非线性梁壳组合单元的正确性和研制程序的可靠性, 以及混凝土材料非线性描述的合理性; 采用组合单元能准确模拟CFRP筋的几何构形, 能综合考虑其拉压弯剪性能, 利于全面地反映配筋对结构的增强作用。      

考虑应变依赖性的硬涂层圆柱壳振动特性有限元分析

硬涂层材料的应变依赖性使分析硬涂层圆柱壳的振动特性成为一项具有挑战性的研究任务。通过自编有限元程序来解决考虑应变依赖性的硬涂层圆柱壳振动特性计算问题;在用多项式表征硬涂层材料应变依赖性的前提下,研发出一种4节点36自由度的复合单元来描述硬涂层圆柱壳结构,并确定了该单元的质量、刚度矩阵以及基础激励作用下的单元所受的载荷向量;在确定等效应变的基础上,提出了利用Newton-Raphson法求解硬涂层圆柱壳非线性振动响应及共振频率的计算流程;以Ni Co Cr Al Y+YSZ硬涂层圆柱壳为对象进行了实例研究,对其线性和非线性振动特性进行求解,其中将线性计算结果与ANSYS求解结果进行了比对以初步说明研发程序的合理性。硬涂层圆柱壳的非线性计算结果显示:随着激励幅度的增加,硬涂层圆柱壳显示软式非线性特点。     

考虑主材节点刚域影响的钢管输电塔变截面梁单元有限元模型

为了准确、快捷地计算加劲板和连接板形成的主材节点刚域对输电塔受力的影响,将考虑节点刚域影响的主材视为若干段段不同截面梁单元的组合。首先,推导了主材两端节点刚域横截面转动惯量和面积的公式;然后,根据能量原理,推导了变截面梁单元的单元刚度矩阵,并采用C++语言将它引入开源有限元软件OpenSees;最后,将主材及节点刚域采用变截面梁单元,常截面梁单元,变弹性模量梁单元及壳单元离散的有限元模型计算结果和塔架试验的实测结果进行对比。结果表明:常截面梁单元会低估主材的弯矩和最大正应力,而变弹性模量梁单元会低估输电塔的挠度,均会使设计偏于不安全;变截面梁单元和壳单元的计算结果均实测结果很接近,但前者计算量远小于后者。可见:变截面梁单元有限元模型兼顾了计算效率和精度。     

基于共旋三角形厚薄通用壳元的几何非线性分析

基于共旋列式方法发展了一种用于复合材料层合板结构几何非线性分析的简单高效的三结点三角形平板壳元。该壳元由具有面内转动自由度的广义协调膜元GT9与假设剪切应变场和假设单元转角场的广义协调厚薄通用板元TMT组合而成。为避免薄膜闭锁而采用单点积分计算与薄膜应变有关的项, 同时增加一个稳定化矩阵以消除单点积分导致的零能模式。基于层合板一阶剪切变形理论, 给出了考虑层合板具体铺层顺序的修正的横向剪切刚度, 使该壳元可用于中厚层合板结构的分析。由于共旋列式大转动小应变的假设, 共旋列式内核的几何线性的单元刚阵可仅计算一次而保存下来用于整个几何非线性求解的过程以提高计算效率。数值算例表明提出的壳元进行包括复合材料层合板结构的厚薄壳结构的几何非线性分析的精度高且效率高。     

Degenerated shell element with composite implicit time integration scheme for geometric nonlinear analysis

A degenerated shell element with composite implicit time integration scheme is developed in the present paper to solve the geometric nonlinear large deformation and dynamics problems of shell structures. The degenerated shell element is established based on the eight‐node solid element, where the nodal forces, mass matrices, and stiffness matrices are firstly obtained upon virtual velocity principle and then translated to the shell element. The strain field is modified based on the mixed interpolation of tensorial components method to eliminate the shear locking, and the constitutive relation is modified to satisfy the shell assumptions. A simple and practical computational method for nonlinear dynamic response is developed by embedding the composite implicit time integration scheme into the degenerated shell element, where the composite scheme combines the trapezoidal rule with the three‐point backward Euler method. The developed approach can not only keep the momentum and energy conservation and decay the high frequency modes but also lead to a symmetrical stiffness matrix. Numerical results show that the developed degenerated shell element with the composite implicit time integration scheme is capable of solving the geometric nonlinear large deformation and dynamics problems of the shell structures with momentum and energy conservation and/or decay. Copyright © 2015 John Wiley & Sons, Ltd.     

A finite element formulation with stabilization matrix for geometrically non-linear shells

An assumed strain finite element formulation with a stabilization matrix is developed for analysis of geometrically non-linear problems of isotropic and laminated composite shells. The present formulation utilizes the degenerate solid shell concept and assumes an independent strain as well as displacement. The assumed independent strain field is divided into a lower order part and a higher order part. Subsequently, the lower order part is set equal to the displacement-dependent strain evaluated at the lower order integration points and the remaining higher order part leads to a stabilization matrix. The strains and the determinant of the Jacobian matrix are assumed to vary linearly in the thickness direction. This assumption allows analytical integration through thickness, independent of the number of plies. A nine-node element with a judiciously chosen set of higher order assumed strain field is developed. Numerical tests involving isotropic and composite shells undergoing large deflections demonstrate the validity of the present formulation.     

A hybrid stress nine-node degenerated shell element for geometric nonlinear analysis

A stabilized nine-node degenerated shell element, previously derived for linear analysis by the admissible matrix formulation, is extended to geometrically nonlinear analysis. The assumed stress modes pertinent to stabilization matrix are contravariant in nature and their energy products with the displacement-derived covariant strain can be programmed without resorting to numerical integration and the Gram-Schmidt orthogonalization. Numerical tests show that its accuracy is virtually identical to the uniformly reduced integration element.     

A sixteen node shell element with a matrix stabilization scheme

A sixteen node shell element is developed using a matrix stabilization scheme based on the Hellinger-Reissner principle with independent strain. Initially the assumed independent strain is divided into a lower order part and a higher order part. The stiffness matrix corresponding to the lower order assumed strain is equivalent to the stiffness matrix of the assumed displacement model element with the reduced integration scheme. The spurious kinematic modes of the element are suppressed by introducing a stabilization matrix associated with a judiciously chosen set of higher order assumed strain fields. Numerical results show that this element is free of locking even for very thin plates and shells.     

An eight‐node hybrid‐stress solid‐shell element for geometric non‐linear analysis of elastic shells

This paper presents eight‐node solid‐shell elements for geometric non‐linear analysis of elastic shells. To subdue shear, trapezoidal and thickness locking, the assumed natural strain method and an ad hoc modified generalized laminate stiffness matrix are employed. A selectively reduced integrated element is formulated with its membrane and bending shear strain components taken to be constant and equal to the ones evaluated at the element centroid. With the generalized stresses arising from the modified generalized laminate stiffness matrix assumed to be independent from the ones obtained from the displacement, an extended Hellinger–Reissner functional can be derived. By choosing the assumed generalized stresses similar to the assumed stresses of a previous solid element, a hybrid‐stress solid‐shell element is formulated. Commonly employed geometric non‐linear homogeneous and laminated shell problems are attempted and our results are close to those of other state‐of‐the‐art elements. Moreover, the hybrid‐stress element converges more readily than the selectively reduced integrated element in all benchmark problems. Copyright © 2002 John Wiley & Sons, Ltd.     

高性能碳-玻璃纤维布加固混凝土梁的非线性响应

针对高性能碳-玻璃-环氧树脂(CF-GF-EP)混杂纤维布加固钢筋混凝土(RC)梁,研究了一种三维非线性混杂组合单元,并推导了统一单元模式,对RC梁的刚度退化、应力重分布等进行了分析。首先根据实体退化单元理论,研究了组合单元模拟RC梁,并利用选择积分技术推求了高性能CF-GF-EP纤维布单元对混杂组合单元刚度矩阵的贡献。运用Jiang屈服准则、Hinton压碎准则和Madrid强化准则等描述混凝土材料非线性,研制了相应的三维非线性分析程序。与试验资料对比分析可知,计算结果与试验数据吻合良好,表明本文构造的非线性单元模式的正确性和研制程序的可靠性,推导的混杂组合单元能准确用于混杂CF-GF-EP纤维布加固RC梁的非线性响应分析。加载初期高性能CF-GF-EP纤维布加固梁未有明显的刚度折减,其后达到屈服荷载和极限荷载时,加固梁刚度折减系数分别约为0.6和0.9。在开裂荷载前,高性能CF-GF-EP纤维布应力发展较为平缓且应力重分布系数变化较小,其后应力重分布系数逐渐增大直至结构失效。     

热冲击下的复合材料壳刚柔耦合动力学研究

研究了在热冲击下任意形状(仅一个方向有曲率)复合材料壳的非线性刚柔耦合动力学响应。根据Mindlin理论,建立了任意形状的复合材料壳的非线性应变-位移关系。借助于数学理论以及几何关系,描述了壳上任意点的变曲率。用虚功原理建立了动力学变分方程,并采用等参单元对壳的连续动力学方程进行离散,建立了中心刚体-复合材料壳的刚-柔耦合动力学方程。用高斯积分计算常值阵,为了提高计算效率,采用广义-α法结合Newton-Raph-son迭代法对动力学方程进行积分。将采用该方法计算得到的频率与ANSYS软件计算得到的作对比,验证了模型的正确性。通过算例分析了在热冲击作用下复合材料壳的线性、非线性的动力学特性,以及曲率、材料特性对动力学响应的影响。     

A new efficient mixed formulation for thin shell finite element models

A nine node shell element is developed by a new and more efficient mixed formulation. The new shell element formulation is based on the Hellinger–Reissner principle with independent strain and the concept of a degenerate solid shell. The new formulation is made more efficient in terms of computing time than the conventional mixed formulation by dividing the assumed strain fields into a lower order part and a higher order part. Numerical results demonstrate that the present nine node element is free of locking even for very thin plates and shells and is also kinematically stable. In fact the stiffness matrix associated with the higher order assumed strain plays the role of a stabilization matrix.     

The geometric stiffness of thick shell triangular finite elements for large rotations

This paper is concerned with the development of the geometric stiffness matrix of thick shell finite elements for geometrically nonlinear analysis of the Newton type. A linear shell element that is comprised of the constant stress triangular membrane element and the triangular discrete Kirchhoff Mindlin theory (DKMT) plate element is ‘upgraded’ to become a geometrically nonlinear thick shell finite element. Perturbation methods are used to derive the geometric stiffness matrix from the gradient, in global coordinates, of the nodal force vector when stresses are kept fixed. The present approach follows earlier works associated with trusses, space frames and thin shells. It has the advantage of explicitness and clear physical insight. A special procedure, tailored to triangular elements is used to isolate pure rotations to enable stress recovery via linear elastic constitutive relations. Several examples are solved. The results compare well with those available in the literature. Copyright © 2005 John Wiley & Sons, Ltd.