基于滑动Kriging插值的无网格MLPG法求解结构动力问题

利用基于滑动Kriging插值的无网格局部Petrov-Galerkin (MLPG) 法来求解二维结构动力问题,Heaviside分段函数作为局部弱形式的权函数并采用精细积分法来离散时间域。基于滑动Kriging插值构造的形函数满足Kronecker Delta性质,因此可以直接施加本质边界条件。刚度矩阵形成过程中只涉及到边界积分,而没有涉及到区域积分和奇异积分。计算结果表明：基于滑动Kriging插值的MLPG法具有模拟简单、计算精度高等优点。     

压电集成碳纳米管CNT增强功能梯度结构非线性建模与仿真

将碳纳米管(carbon nanotube,CNT)以梯度形式分布与基体材料结合,形成功能梯度(functionally graded,FG)结构。为了实现FG-CNT增强复合板在发生大变形时的准确计算,考虑四种典型的CNT分布形式,均匀分布、V型分布、O型分布和X型分布,建立基于Reissner-Mindlin板壳假设的大变形几何非线性有限元模型。该模型不仅包含了几何全非线性应变位移关系,还考虑了薄板结构法向发生大转角的情形。该研究与文献结果进行比较,验证模型的准确性;对FG-CNT增强复合板进行几何大变形非线性计算,分析CNT分布形式、CNT增强角度等因素对FG-CNT增强复合板刚度的影响。研究结果表明,CNT分布形式及增强角度对FG-CNT复合板的力学特征有显著的影响。     

几何非线性扩展有限元法及其断裂力学应用

该文将扩展有限元方法应用到几何非线性及断裂力学问题中,并研制开发了扩展有限元Fortran程序。扩展有限元法其计算网格与不连续面相互独立,因此模拟移动的不连续面时无需对网格进行重新剖分。该文推导了几何非线性扩展有限元法的公式,在常规有限元位移模式中,基于单位分解的思想加进一个阶跃函数和二维渐近裂尖位移场,反映裂纹处位移的不连续性,并用2个水平集函数表示裂纹;采用拉格朗日描述方程建立了有限变形几何非线性扩展有限元方程;采用多点位移外推法计算裂纹应力强度因子并通过最小二乘法拟合得到更精确的结果。最后给出的大变形算例表明该文提出的几何非线性的断裂力学扩展有限元方法和相应的计算机程序是合理可行的,而且对于含裂纹及裂纹扩展的问题,扩展有限元法优于传统的有限元法。     

考虑几何非线性效应的大展弦比机翼气动弹性分析

针对飞机飞行过程中因受气动载荷作用、机翼几何非线性效应影响气动弹性稳定性,提出考虑结构大变形几何非线性效应的大展弦比机翼气动弹性特性分析方法。通过对MSC.Nastran软件二次开发实现该方法的计算流程。考虑大展弦比机翼几何大变形对气动面网格构型影响,在每个迭代步对气动面网格进行更新,求出大展弦比机翼在给定飞行状态下的静气动弹性变形,获得考虑机翼结构几何非线性效应的刚度矩阵,并进行机翼颤振特性分析。对大展弦比机翼模型进行气动弹性特性分析计算表明,与线性气动弹性分析结果相比,考虑机翼结构大变形几何非线性效应,机翼静气动弹性变形会影响机翼动力学特性,使机翼扭转频率明显下降,导致机翼几何非线性颤振速度低于线性颤振速度。     

无网格MLPG法求解轴对称弹性力学问题

为了解决实际应用中复杂轴对称弹性力学问题的求解困难,对无网格局部彼得洛夫-伽辽金法(MLPG)应用于此类问题进行了研究,并发展了相应的计算方法。通过一些数值算例,对所提方法进行了检验。结果表明:建议的方法对轴对称弹性力学问题表现为较好的适应性,而且能达到较为满意的计算精度。     

采油井架钢结构非线性力学行为分析

本文对采油井架钢结构进行了非线性有限元分析。采用空间梁单元,通过包含单元几何刚度阵和变形刚度阵的增量切线刚度法考虑大变形问题;用杆端集中塑性法来简化材料非线性;采用弧长法迭代计算,最终可得到考虑几何和材料双重非线性情况下,井架钢结构的极限承载力。文中最后给出了A型采油井架的算例。     

圆柱壳几何大变形非线性频率求解的渐近摄动法

为解决圆柱壳在工作状态中由几何大变形而引起的弱非线性振动问题，将渐近摄动法引入求解考虑几何非线性的薄壁圆柱壳振动频率。首先，应用Donnell＇s简化壳理论获得了考虑几何大变形情况下具有位移三次项的非线性频率方程，把位移及频率以非线性参数的幂级数形式展开，并令同次幂的非线性项系数相等，由此得到非线性频率一次近似值与初始振幅的一系列耦合代数方程，引入Galerkin＇s方法对非线性频率方程进行解耦正交并忽略其中的永年项，考虑了对应实数根，各阶频率对应的振幅间不存在相互耦合的内共振现象，最终在引入小参数后用摄动法求出了非线性频率的一次近似解。计算结果表明，几何非线性使薄壁圆柱壳产生硬化，其非线性频率升高，并同时讨论了线性、非线性频率与节径数及初始位移之间的关系。     

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CFD/CSD耦合的结构几何非线性静气动弹性数值方法研究

柔性飞行器在气动力作用下会发生大变形,产生结构几何非线性,线性小变形方法难以获得准确的气动弹性分析结果。基于RANs的三维N-S流场控制方程耦合非线性结构静力学方程时域分析方法,用于考虑结构几何非线性的静气动弹性分析。该方法在结构静力学方程求解上采用非线性增量有限元方法进行迭代求解,考虑结构刚度矩阵随结构位形的变化,采用径向基函数方法实现气动/结构界面的数据交换和动网格变形。在建立某型宽体客机复材机翼三维有限元模型的基础上,对其静气动弹性进行了数值仿真,分析了线性结构和考虑结构几何非线性的结构在静气动弹性作用下翼面扭转、展向位移、垂向位移以及升力系数等物理量。算例结果表明,与线性结果相比,非线性结构由于结构几何非线性的影响,在展向和垂向变形上两者存在显著差异。为准确进行柔性结构的气动弹性分析,必须考虑结构几何非线性的影响。     

高层钢框架的非线性分析模型

本文提出了对高层钢框架考虑材料非线性和几何非线性的分析方法。几何非线性分析模型包括考虑杆件大变形和框架结构在受力状态下的任意大变形平衡。杆件大变形效应包括轴向力弯曲刚度,杆端大侧移,杆端大转角,杆件大应变以及它们之间的相关作用。本文还讨论了切线刚度矩阵中非线性项的几何意义。并利用考虑了几何非线性和材料非线性的分析模型编制了电算程序,该程序能追踪位移与外力关系的全过程。     

Topology optimization of geometrically nonlinear structures using an evolutionary optimization method

The topology optimization using isolines/isosurfaces and extended finite element method (Iso-XFEM) is an evolutionary optimization method developed in previous studies to enable the generation of high-resolution topology optimized designs suitable for additive manufacture. Conventional approaches for topology optimization require additional post-processing after optimization to generate a manufacturable topology with clearly defined smooth boundaries. Iso-XFEM aims to eliminate this time-consuming post-processing stage by defining the boundaries using isovalues of a structural performance criterion and an extended finite element method (XFEM) scheme. In this article, the Iso-XFEM method is further developed to enable the topology optimization of geometrically nonlinear structures undergoing large deformations. This is achieved by implementing a total Lagrangian finite element formulation and defining a structural performance criterion appropriate for the objective function of the optimization problem. The Iso-XFEM solutions for geometrically nonlinear test cases implementing linear and nonlinear modelling are compared, and the suitability of nonlinear modelling for the topology optimization of geometrically nonlinear structures is investigated.     

有限元线法求解非线性模型问题——Ⅰ.薄膜大挠度

本研究将新近发展起来的有限元线法应用于非线性问题,分析求解了若干具有代表性的模型问题,探讨了统一的求解模式及相应的处理手段。作为这一系列工作的首例,本文将该法应用于薄膜大挠度这一几何非线性模型问题,对任意形状的薄膜作了理论公式推导,通过对几种典型形状薄膜的具体数值计算,揭示了该类问题存在极限变形状态这一重要特性。数值算例的精确性与可靠性以及求解的高效性表明,本法是求解这类几何非线性问题的高效能的方法。     

A VDQ-based multifield approach to the 2D compressible nonlinear elasticity

A numerical multifield methodology is developed to address the large deformation problems of hyperelastic solids based on the 2D nonlinear elasticity in the compressible and nearly incompressible regimes. The governing equations are derived using the Hu-Washizu principle, considering displacement, displacement gradient, and the first Piola-Kirchhoff stress tensor as independent unknowns. In the formulation, the tensor form of equations is replaced by a novel matrix-vector format for computational purposes. In the solution strategy, based on the variational differential quadrature (VDQ) technique and a transformation procedure, a new numerical approach is proposed by which the discretized governing equations are directly obtained through introducing derivative and integral matrix operators. The present method can be regarded as a viable alternative to mixed finite element methods because it is locking free and does not involve complexities related to considering several DOFs for each element in the finite element exterior calculus. Simple implementation is another advantage of this VDQ-based approach. Some well-known examples are solved to demonstrate the reliability and effectiveness of the approach. The results reveal that it has good performance in the large deformation problems of hyperelastic solids in compressible and nearly incompressible regimes.     

The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics

The finite cell method (FCM) combines the fictitious domain approach with the p‐version of the finite element method and adaptive integration. For problems of linear elasticity, it offers high convergence rates and simple mesh generation, irrespective of the geometric complexity involved. This article presents the integration of the FCM into the framework of nonlinear finite element technology. However, the penalty parameter of the fictitious domain is restricted to a few orders of magnitude in order to maintain local uniqueness of the deformation map. As a consequence of the weak penalization, nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries, leading to a low algebraic rate of convergence. Therefore, the FCM approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp‐d method, which synergetically uses the h‐adaptivity of the integration scheme. Numerical experiments show that the hp‐d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation map. The hp‐d‐adaptive FCM is thus able to restore high convergence rates for the geometrically nonlinear case, while preserving the easy meshing property of the original FCM. Accuracy and performance of the present scheme are demonstrated by several benchmark problems in one, two, and three dimensions and the nonlinear simulation of a complex foam sample. Copyright © 2011 John Wiley & Sons, Ltd.     

高层结构几何非线性分析的QR法

本文利用ＱＲ法分析高层建筑结构几何非线性问题，建立了新的计算格式。该法不仅未知量的数目少，精度高，而且输入简单，计算速度快，可以用微机分析复杂问题。     

Meshless local Petrov–Galerkin (MLPG) method in combination with finite element and boundary element approaches

The meshless local Petrov–Galerkin (MLPG) method is an effective truly meshless method for solving partial differential equations using moving least squares (MLS) interpolants. It is, however, computationally expensive for some problems. A coupled MLPG/finite element (FE) method and a coupled MLPG/boundary element (BE) method are proposed in this paper to improve the solution efficiency. A procedure is developed for the coupled MLPG/FE method and the coupled MLPG/BE method so that the continuity and compatibility are preserved on the interface of the two domains where the MLPG and FE or BE methods are applied. The validity and efficiency of the MLPG/FE and MLPG/BE methods are demonstrated through a number of examples. Received 6 June 2000     

钢管混凝土结构材料非线性的一种有限元分析方法

为了更简单地考虑梁单元的材料非线性受力性能,把断面广义力和广义应变的概念运用于单元分析中,将单元的弹塑性刚度矩阵分离为弹性刚度矩阵和塑性刚度矩阵。这样,梁单元的变形可以由弹性变形和塑性变形简单地迭加,结构内力可通过弹性应变能的斜率(弹性刚度矩阵)与位移的乘积求得,从而在增量-迭代计算时可较准确且较快地计算出结构变形后的不平衡力。应用这一计算方法,推导了基于纤维模型的三维梁单元的钢管混凝土结构的有限元基本公式,并将其植入能考虑几何非线性的三维梁单元非线性计算程序NL_Beam3D中以计算结构的双重非线性问题。算例分析表明该方法和程序能较准确地反映钢管混凝土结构的双重非线性特性。     

底部钻具组合的二重非线性有限元分析

本文将弯曲井眼中的底部钻具组合(英文名称为Bottom Hole Assembly,简称BHA)作为空间梁来处理,在考虑几何非线性因素的基础上,导出了相应的有限元切向刚度矩阵。然后,利用“施加”与“放松”约束的方法处理了钻柱与井壁之间的接触非线性问题,并且考虑了钻柱与井壁之间摩擦力的影响。在此基础上,建立了对大曲率弯曲井眼中的钻柱进行二重非线性有限元分析的基本方程,以及相应的牛顿－拉斐逊迭代求解技术。最后,通过数值算例和工程算例证明了本文方法的可靠性,所得结果为大曲率井眼轨迹控制提供了参考依据。