几何非线性样条单元

 <正>结构的有限变形与稳定性分析具有重要意义。有限元法的应用,促进了几何非线性研究工作的开展。本文在线性样条单元C’〕的基础上提出一种几何非线性样条板壳单元,壳体的应变位移关系采用Von一K巨rmon方案,以分片样条Hermite插值构造单元的位移模式。对于弱非线性问题,采用修正的Newton一Raphson法解非线性方程组。对于极值点失稳情况,以固定弧长法追踪屈曲路径,并用曲线拟合的方法确定结构的临界载荷值。     

Stress-strain state analysis of shells of revolution based on the triangular discretization element with the Lagrange multipliers

The present paper sets forth an algorithm of analyzing thin shells with significant gradients of meridian curvature based on the Kirchhoff-Love hypothesis and finite element method. As a discretization element use is made of a triangular fragment of the middle surface with the Lagrange multipliers in additional nodes arranged in the triangle side middles. We apply the vector method of displacement interpolation that has a number of advantages over the conventional interpolation procedure. The high efficiency of the algorithm developed is confirmed by the numerical examples.     

The finite element analysis of shells of revolution with a branching meridian

We present an algorithm for calculating the shells of revolution with the branching meridian using the triangular finite elements, the rigidity matrices of which are formed based on the vector method of displacement interpolation [1]. The correct kinematic and static conditions of shell conjugation on the line of their coupling have been developed. The shell structure consisting of a cylinder and adjacent shells is calculated under various conditions of support.     

Analysis of an arbitrarily loaded shell of revolution based on the finite element method in a mixed formulation

The volume finite element in the form of hexahedron with nodal unknowns as components of the displacement vector and stress tensor has been developed to analyze the shells of revolution. The displacement vector components for the inner point of the finite element and the components of its stress tensor are expressed through the nodal unknowns using the method of vector and tensor fields interpolation by the trilinear shape functions; that provides taking into account the finite element displacement as a whole solid. The variational principle in a mixed formulation is applied to form the matrix of hexahedron deformation. The efficiency of the proposed method for approximating the values being sought as vector and tensor fields in comparison with the traditional method for approximating the values being sought as scalar fields is confirmed by a numerical example.     

Analysis of nonlinear deformation and stability of reinforced elliptic cylindrical shells under bending with internal pressure

A finite element statement of solving problems on stability of reinforced elliptic cylindrical shells taking into account momentness and nonlinearity of their subcritical stress strain state is presented. The explicit expressions for displacements of noncircular cylindrical shell elements as rigid bodies are determined by integrating the equations obtained by equating the components of linear strains to zero. These expressions were used to construct the form functions for an efficient quadrilateral finite element of natural curvature. An efficient numerical algorithm of nonlinear deformation and stability of shells was developed. The stability of reinforced elliptic cylindrical shells under combined loading by bending moment, transverse boundary force and internal pressure is analyzed. We also examine how the critical loads are affected by the strain nonlinearity and ellipticity of shell deformation at the subcritical stage.     

Analysis of nonlinear deformation and stability of oval cylindrical shells under combined loading by bending and torsion moments

A problem of geometrically nonlinear deformation and stability of cylindrical shells with noncircular cross-section contour is solved by the finite element method. The nonlinear system of algebraic equations to determine the nodal unknowns of finite elements is obtained with the use of the variational Lagrange principle. The system is solved by the method of successive loadings with the use of the Newton-Kantorovich method of linearization, the method of solving linear Craut’s equations and Sylvestor’s stability criterion. The nonlinear deformation and stability of shells with the oval and elliptical cross-sections under combined loading by bending and torsion moments are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity, shell ovality and ellipticity on the critical loads is clarified.     

Nonlinear deformation and stability of supported oval cylindrical shells under torsion and bending with internal pressure

A problem of geometrically nonlinear deformation and stability of supported cylindrical shells with the oval cross-section contour is solved by the finite element method. The nonlinear deformation and stability of shells under combined loading by bending, torsion moments, transverse force and internal pressure are analyzed. The critical loads and buckling modes of shells are determined. The influence of deformation nonlinearity and shell ovality on critical loads is clarified.     

叶间相位角对叶片颤振的影响

发展了一种基于能量法并计及叶间相位角(IBPA)影响的数值计算方法.建立了全环振荡叶栅模型,将每一个扇区分为叶片表面附近的可动域及其外围的固定域,采用有限元形函数将计算结构动力学(CSD)网格点位移的传递到计算流体动力学(CFD)的耦合面网格点上,求解了全环振荡叶栅由k-ε湍流模型封闭的Reynolds平均Navier-Stokes(RANS)方程.以NASA 67转子叶片为例,在设计转速下,基于能量法分析了叶间相位角对叶片颤振的影响.计算结果表明:叶间相位角对叶片颤振有显著影响.      

A technique for calculating large deflections of nonshallow elastoplastic shells of revolution under nonaxisymmetric loading

A technique for calculating the geometrically and physically nonlinear stress strain state of nonshallow shells of revolution under the nonaxisymmetric wind-like loading is proposed. The calculation results for a semispherical shell with the central hole and rigidly fixed edges depending on the loading nonaxisymmetry, material characteristics and thickness are presented. We demonstrate not only quantitative but also qualitative influence of taking into account the factor of joint nonlinearity on the process of shell deformation.     

Nonlinear deformation and stability of discretely reinforced elliptical cylindrical shells under transverse bending and internal pressure

A finite element formulation of solving the stability problems for the discretely reinforced noncircular cylindrical shells is presented taking into account that their subcritical stress strain state is instantaneous and nonlinear. The author-developed finite elements for a natural-curved shell and the beam elements of reinforcements are used. A numerical algorithm to study the nonlinear deformation and stability of shells was developed. The stability of a stringer-stiffened cylindrical shell with an elliptical cross-sectional contour under transverse bending and internal pressure is examined. We also investigate the effect of internal pressure, ellipticity and nonlinearity of deformation, as well as of reinforcement discreteness and heterogeneity.     

复合材料叠层板壳材料非线性有限元分析

 本文采用通用于复合材料叠层厚、薄板壳的Heferosis三维退化曲壳元,利用Hill屈服准则和层状模型法,研制了针对金属基复合材料叠层板壳进行弹塑性分析的超参元程序。算例结果表明,叠层板壳分析方法和所编程序是可靠的,精度良好。     

一种考虑截面任意变形模式梁的有限元模型

提出了一种考虑截面完整变形的截面插值梁模型,并用于机翼结构的建模与分析。首先引入截面插值函数——拉格朗日函数描述截面形状,以位移向量为未知变量描述截面位移,在此基础上依据插值理论构造梁单元位移场。不同于传统梁单元通过假定的中性轴的挠度和转角来确定梁截面各点位移,该梁模型摒弃了中性轴假设与平截面假设,通过截面插值函数得到梁截面面内、面外变形;然后通过有限元理论推导了梁单元刚度矩阵与质量矩阵;最后利用截面插值梁单元对机翼各部件进行有限元建模,并展开典型工况下的静力学分析以及动力学分析,与Nastran实体单元计算结果进行了对比分析,验证了该梁模型的有效性,为机翼的结构设计和强度分析提供了一种新的简化建模方法。     

Analysis of static loading for a helicopter tubular skid landing gear

We compare the results of analyzing the stress strain state for the tubular skid landing gear with regard for the physically and geometrically nonlinear scheme of deformation; the analysis is carried out by the finite element method and with the aid of a special beam-type design model. The analysis has been performed for a real helicopter design. The peculiarities of deforming the aircraft structures of the type under study are shown based on the comparison results.     

Solving a plane problem of elasticity theory with the use of a hybrid FEM formulation

In the framework of a plane problem of elasticity theory in strength analysis based on the finite element method in the hybrid formulation, we suggest that the approximation of displacements and stresses be used as magnitudes of vector and tensor fields, respectively. The quadrilateral finite element, the displacements and stresses of which are accepted as nodal unknowns is proposed. The mixed Reissner functional is applied to form a finite element deformation matrix.     

GH4169合金蠕变疲劳行为的有限元模拟及寿命预测

考虑蠕变-疲劳损伤,对部件材料进行合理的循环变形描述和准确的寿命预测,是保证航空发动机等高温设备长周期安全运行需要解决的关键问题之一。基于大型有限元软件ABAQUS,采用组合Chaboche随动强化准则和Voce各向同性硬化准则的循环弹塑性本构模型,叠加应变强化的蠕变本构模型,对GH4169合金在蠕变-疲劳载荷下伴有应力松弛的循环变形行为进行了准确的有限元模拟。同时,将Wang等最新修正的基于逐周次概念的蠕变-疲劳损伤模型进行了有限元移植,结合有限元模拟所得的循环应力、应变状态,实现了对GH4169合金蠕变-疲劳寿命的准确预测。研究结果将为进一步实现对航空发动机关键部件精确的寿命预测提供理论基础和技术手段。     

基于径向基函数的网格变形及非线性气动弹性时域仿真研究

为开展非线性气动弹性研究,基于非线性结构有限元软件NASTRAN和自主研制的多块结构化计算流体力学(CFD)求解器,开发了一套基于计算流体力学/计算结构动力学(CFD/CSD)耦合求解方法的气动弹性时域仿真程序.该程序采用径向基函数(RBF)交换两套求解器之间的数据并进行网格变形.为提高RBF方法的效率,构造了基于多次插值的空间待插值点精简算法.在多次插值过程中,每次插值的对象为上次插值的误差,并同时限制插值区域,以此实现了空间待插值网格数的精简.数个网格变形的算例表明该方法可支持大变形运动,并且具有较高的计算效率.采用此程序开展了AGARD 445.6机翼颤振计算、大展弦比机翼的静气动弹性计算与切尖三角翼极限环振荡(LCO)现象的动气动弹性仿真,结果揭示了当机翼展弦比较大或者响应幅值较大时,结构非线性对于气动弹性有显著影响.     

层合陶瓷基复合材料多尺度应力-应变计算模型

对层合陶瓷基复合材料(CMCs)的应力-应变行为进行了研究。基于多尺度分析方法,实现了由组分性能参数到层合陶瓷基复合材料整体应力-应变的计算。采用可实现单向纤维增强陶瓷基复合材料应力-应变计算的细观力学模型,由材料的细观组分性能计算出单向板的非线性弹性性能,并将单向板的弹性性能作为层合复合材料模型的输入参数,通过有限元法计算层合陶瓷基复合材料的整体应力-应变响应。与试验数据的对比表明:采用该模型可以实现层合陶瓷基复合材料在单调拉伸载荷及拉伸加卸载条件下应力-应变曲线的预测,其中数据的最大偏离为19.61%.      

基于非线性几何场论求解热弹性板大挠度弯曲的BEM法

基于理性力学非线性几何场理论,建立了热弹性薄板等效速率形式的Ｋａｒｍａｎ方程,通过将热弹性薄板大挠度弯曲问题看成平板弯曲问题与平面大变形问题的耦合,在固定坐标系及拖带坐标系上推导出两组边界积分方程,从而建立起新的分析热弹性薄板大挠度弯曲的边界元法。算例表明本文方法理论可靠、精度高。     

非线性壁板颤振分析

利用一种改进的计算流体力学与计算结构动力学(CFD/CSD)耦合方法研究了由气动和结构几何非线性引起的壁板颤振问题。在非定常气动力计算中,考虑了通量分裂格式、隐式时间推进方法和几何守恒律;二维和三维壁板的结构几何非线性建模则采用了有限元的协同旋转理论,并利用一种近似能量守恒算法求解结构的非线性响应。流场和结构求解器采用二阶松耦合方法联立求解,并将其应用于壁板在超声速、跨声速和亚声速的颤振计算中。当考虑结构几何非线性和气动非线性时,出现了典型的极限环振荡现象,并对颤振边界和极限环振荡幅度进行了对比分析。     

夹层板精密成形的数值模拟

为了实现基于“点阵钉模、真空负压、蜂窝夹层”的双曲度面板精密成形过程的有限元数值模拟,分析了成形 2个阶段的变形过程,建立了简化的力学模形,以一种广义协调薄板弯曲四边形位移单元为基础构造了具有公共横向位移自由度的几何非线性四边形四节点分别考虑和不考虑横向剪切的多层板单元,通过牛顿 -拉斐逊法结合载荷、位移约束量的增量法求解几何非线性方程,较好地再现了真实成形过程