样条函数线法分析壳体非线性问题

采用样条函数线法计算圆柱壳有具有封闭截面的一类壳体的几何线性问题，用样条函数插值交二维非线性偏微分问题化为一组用径向结线位移增量表示的非线性常微分方程，然后用常微分方程求解器迭代求解，文中导出了用于非线性分析的样条函数线增量方程，最后给出了算例。     

基于修正样条函数分析滑移边界矩形板的自由振动

提出了一种分析滑移边界各向同性和正交各向异性矩形板振动特性的数值方法一双向样条离散法。该方法适用于各种可能组合边界矩形板的自由振动分析；边界包括自由、简支、固定和滑移边界。在x和y方向，板被离散成N和M个等分区间。为适应任意边界，修改N＋3和M＋3维硝样条函数向量的最前和最后三个函数，得到x方向N＋1个点、y方向M＋1个点和x-y方向两个附加点的修正的邱样条函数向量，并以此作为板的位移试函数。在给定边界下，修正的B3样条函数向量对位移、位移的一阶导数和二阶导数都仅保留一个未知系数。基于矩形板的势能泛函导出其特征方程。与有限元法和样条有限条法相比，本文方法具有自由度少、计算效率高和输入数据少等优点。数值计算结果表明，本方法具有高的计算精度。     

拱结构双重非线性稳定分析的样条有限点法

本文提出利用样条有限点法来分析拱结构非线性稳定问题。用3次B样条函数来构造结构的位移模式,基于最小势能原理导出了拱式结构的单元刚度矩阵。分析中考虑了材料及几何非线性特征,计算公式简便,易于编程。依本文方法编制了程序,对一典型算例进行了分析。     

用样条有限点法分析中厚矩形板的自由振动和稳定问题

样条有限点法的特点是位移函数在一个方向解析,另一个方向用B样条函数插值。本文用来分析中厚板的自由振动和稳定问题,推导了刚度矩阵,质量矩阵和几何刚度矩阵的显式表达式,并通过典型算例与有限元及级     

样条配点法在拱桥大挠度内力分析中的应用

运用拱的挠度理论,推导出考虑结构几何非线性影响的控制微分方程;应用样条配点法,三条次B样条函数为位移试函数,导出了拱结构非线性内力分析的新方法。文末针对某特大跨度钢管混凝土拱桥进行了数值对比分析,计算结果表明,该方法的计算精度与效率令人满意。     

广义函数论在厚板动力分析中的应用

本文运用广义函数论处理δ函数的导数,对集中力作用下的厚板进行动力分析。基本方程采用由本文作者推演得到的改进的Donnell厚板振动方程。用样条配点法求解广义坐标,对集中力作用下的厚板弹性动力响应给出解的一般表达式。文中以能形板为例给出了数值结果,对按改进理论和经典理论所预示的结果进行了比较。本文方法可以用于厚板物理非线性和几何非线性动力分析和厚板与连续介质共同作用的场合,文中给出了有关表达式。     

样条函数配点法分析薄板的压曲及自由振动与薄壳的稳定问题

本文采用单五次B一样条函数配点分析了薄板的压曲以及自由振动,用九次样条函数配点分析了几种薄壳的稳定问题。计算了不同的例题并与解析解进行比较,证明样条函数配点法是分析板、壳稳定问题的简便、有较的方法。     

粘弹性非均质地基动力柔度的样条半解析解法

应用样条半解析法求解粘弹性非均质平面地基上条形基础的动力柔度系数。将地基划分为有限个水平条单元,位移函数表示为一次样条函数与Fourier级数的乘积形式,根据复阻尼理论的拉格朗日方程,使问题归结为求解若干次低阶复代数方程。数值分析结果表明这一方法具有良好的精度,从而为结构与地基的相互作用分析提供了一种有效的分析方法。     

薄壁曲梁的横向弯曲稳定分析

根据势能驻值原理,从曲梁的变形几何方程出发,采用转换B3样条函数模拟薄壁杆件横截面的纵向位移场,得到含非线性应变的薄壁曲梁的能量方程,采用样条有限杆元法求解薄壁曲梁的横向弯曲稳定问题。方法很好地描述了薄壁曲梁的翘曲位移和剪滞效应,为分析薄壁曲梁弯扭问题提供了一种有效的方法。数值算例表明本方法的前处理简单、收敛速度快,精度高。     

各向异性层合板壳的弹塑性分析

用最小二乘配点法对各向异性层合扁薄壳体的弹塑性弯曲问题进行分析。文中以双五次样条函数为位移试函数，采用弹塑性增量理论和由Hill推广的Huber-Mises屈服准则，把材料塑性变形的影响作为等效荷载处理，从而使推出的基本迭代公式为一常系数线性代数方程组，然后用变步长增量加载和初应力法求解。算例证明该法收敛快、精度高，是一种简便、经济的分析方法。     

A robust methodology for the simulation of postbuckling response of composite plates

The application of a robust numerical method, namely the differential quadrature method (DQM) for the analysis of buckling and postbuckling of laminated composite plates is introduced. The method is combined with an arc-length strategy to solve the resulting system of nonlinear equations. The treatment accounts for the effect of large deformation by including the von Karman strains. Imperfections in the form of global deflection, conforming to the preferred buckling modes are introduced throughout the plate. Case studies are used to evaluate the geometrically nonlinear response of composite plates under the set conditions, and the results are compared with those obtained by finite element solution and the results obtained from a published literature.     

梁杆结构几何非线性有限元的数值实现方法

梁杆结构几何非线性有限元方法主要包括两个部分, 建立虚功方程和实现数值求解. 该文运用对比方法, 分析了采用UL型增量理论的梁杆结构几何非线性有限元法求解过程与连续体求解过程的主要不同点, 特别是论述了确定加载步末的内力状态的重要性和方法.     

双轴受压反对称角铺设复合材料层合板在固支边界下的后屈曲和模态跃迁

为有效分析双轴受压反对称角铺设复合材料层压板在固支边界下的后屈曲性能, 由渐近修正几何非线性理论推导其双耦合四阶偏微分方程(即应变协调方程和稳定性控制方程), 通过双Fourier级数将耦合非线性控制偏微分方程转换为系列非线性常微分方程, 从而获得相对简单的求解方法。使用广义Galerkin方法求解与角交铺设复合层合板相关的边界值问题, 研究了模态跃迁前后不同复杂程度的后屈曲模式。对四层固支边界复合层合板的数值模拟结果表明: 该解析法与有限元方法在主后屈曲区域的线性屈曲荷载计算结果吻合良好; 有限元方法在解靠近二次分岔点时失去收敛性, 而解析方法可深入后屈曲区域, 准确捕捉模态跃迁现象; 对于反对称角铺设层合板, 可仅用纯对称模态来定性预测主后屈曲分支、二次分岔荷载及远程跃迁路径。      

Nonlinear zigzag theory for electrothermomechanical buckling of piezoelectric composite and sandwich plates

Summary A coupled geometrically nonlinear efficient zigzag theory is presented for electrothermomechanical analysis of hybrid piezoelectric plates. The geometric nonlinearity is included in Von Karman sense. The thermal and potential fields are approximated as piecewise linear across sublayers. The deflection accounts for the transverse normal strain due to thermal and electric fields. The inplane displacements are considered to have layerwise variations, but are expressed in terms of only five primary displacement variables, independent of the number of layers. The coupled nonlinear equations of equilibrium and the boundary conditions are derived from a variational principle. The nonlinear theory is used to obtain the initial buckling response of symmetrically laminated hybrid plates under inplane electrothermomechanical loading. Analytical solutions for buckling of simply-supported plates under thermoelectric load are obtained for comparing the results with the available exact three-dimensional (3D) piezothermoelasticity solution. The comparison establishes that the present results are in excellent agreement with the 3D solution, when the pre-buckling transverse normal strain is neglected in the latter solution. The present results are also compared with the third order theory with the same number of displacement variables to highlight the positive effects of the layerwise terms in the displacement field approximations of the zigzag theory.     

解析型几何非线性圆拱单元

为研究圆拱结构几何非线性内力和位移计算以及平面内稳定分析问题,基于圆拱几何非线性静力分析模型,构造了解析位移形函数,进而利用能量法和势能变分原理,构造了解析型几何非线性圆拱单元,给出了单元列式;同时将该文模型通过理论退化,得到了不考虑轴向变形的无压缩圆拱模型,进一步得到了解析型无压缩几何非线性圆拱单元,并将此单元应用于圆拱的平面内稳定分析。研究结果表明:采用本单元模型进行平面内分岔失稳分析得到的失稳临界荷载系数与经典Timoshenko模型、Dinnik模型及静力法模型计算结果一致,相对误差为0%;平面内分岔失稳的临界荷载与平面内极值点失稳的临界荷载一致。该文单元具有解析型、高精确性以及良好的适用性,可用于任意工况下圆拱结构几何非线性位移、内力和平面内稳定分析。     

A geometrically exact formulation for thin multi-layered laminated composite plates: Theory and experiment

A geometrically exact approach is employed to formulate the equations of motion of thin multi-layered isotropic and laminated composite plates subject to excitations that cause large strains, displacements, and rotations. The linearization of the obtained semi-intrinsic theory leads to the Mindlin–Reissner theory while an ad hoc truncated kinematic approximation delivers, as a by-product, the Föppl–von Kármán theory of plates. An experimental validation is sought for fully clamped plates which are either of the isotropic single-layered type or of the multi-layered laminated composite type. To this end, nonlinear equilibrium paths are constructed both theoretically and experimentally when the plates are subject to a quasi-statically increasing central point load. The comparisons between the experimentally obtained results and those furnished by the geometrically exact theory as well as by the Föppl–von Kármán (FVK) theory show the high accuracy of the proposed nonlinear theory while the FVK theory becomes increasingly inaccurate at deflection amplitudes of the order of the plates thickness.     

A finite element–equivalent energy linearization technique for the analysis of nonlinear plate vibration

A simplified technique for the dynamic analysis of geometrically nonlinear plate structures is developed. The essence of this technique is the construction of a linear substitute of the nonlinear problem. The linear substitute problem is derived from an equivalence criterion which involves balancing the energies of the linear substitute model and the nonlinear model over one period of oscillation. The linearized equations are discretized by a finite element method, and solutions at different amplitudes are obtained numerically by an incremental-iterative scheme. To verify the equivalent energy linearization approach, example problems consisting of the free and forced vibration of nonlinear circular plates with various boundary conditions are studied. All results are compared to theoretical and numerical solutions in the literature. In addition, the forced vibration results are compared to available experimental results. These comparisons tend to validate the assumptions made in the equivalent energy linearization procedure. The proposed method is found to be computationally more efficient than other available procedures.     

柔性飞机大变形曲面气动力计算及配平分析

柔性飞机在载荷作用下产生较大的弹性变形并呈现出几何非线性特性,机翼升力面呈现出大变形空间曲面的特征,传统平面气动力的工程分析方法无法给出空间变形下的真实载荷状态进而影响柔性飞机气动弹性分析的准确性。该文基于柔性飞机几何非线性气动弹性分析的需求,建立了曲面三维升力线和曲面涡格两种不同的曲面定常气动力方法,并结合曲面样条插值完成了大变形下结构运动信息与气动载荷信息之间的相互作用和交换,实现气动面随结构变形的自适应更新。进行了柔性飞机的全机非线性配平分析,并对两种不同的气动力方法的分析结果进行对比,归纳出柔性飞机几何非线性气动弹性配平分析的特点。升力线方法分析快速简单,涡格法可以考虑机翼弯度影响,便于复杂模型的多轮次反复计算。两种方法的分析结果具有较好的一致性,当飞机变形较小时都与传统的线性分析方法吻合较好;当结构变形较大时,非线性配平结果随风速和结构质量呈非线性变化,与传统线性分析结果产生明显差别需在设计初期引起重视。     

Nonlinear dynamic analysis of tapered sandwich plates with multi-layered faces subjected to air blast loading

The nonlinear dynamic behavior of simply supported tapered sandwich plates subjected to air blast loading is investigated theoretically and numerically. The plate is supposed to have both tapered core and tapered laminated face sheets and be subjected to uniform air blast load. The theory is based on a sandwich plate theory, which includes von Kármán large deformation effects, in-plane stiffnesses, inertias and shear deformations. The sandwich plate theory for plates with constant thickness which have one-layered face sheets found in the literature is developed to analyze the tapered sandwich plates with multi-layered face sheets. The equations of motion are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations. The Galerkin method is used to obtain the nonlinear differential equations in the time domain. The finite difference method is applied to solve the system of coupled nonlinear equations. The tapered sandwich plate subjected to air blast load is also modelled by using the finite element method. The displacement–time and strain–time histories are obtained. The theoretical results are compared with finite element results and are found to be in an agreement.