Karman型F交异性矩形薄板非线性弯曲的统一求解方法

本方对Karman型四边支承正交异性薄板在5种不同边界条件下的几何非线性弯曲进行了统一分析.所设的位移函数均为梁振动函数.它们精确地满足边界条件,利用Galerkin方法和位移函数的正交属性,转换控制方程为非线性代数方程.用"稳定化双共轭梯度法"求解稀疏矩阵线性方程组以及"可调节参数的修正迭代法"求解非线性代数方程组,最后给出了相应的数值结果.     

高阶剪切变形理论下三边夹紧一边铰支复合材料层板的几何非线性分析

首先用虚位移原理推导出以位移形式表达的Reddy型高阶剪变形理论复合材料层板的非线性控制方程及相应的边界条件。选定的五个位移函数均满足三边夹紧一边铰支边界条件，用Galerkin方法把无量纲化之后的控制方程转化为一组非线性代数方程组，用线性化的方法和可调节参数的修正迭代法求解这组方程。最后求出了不同复合材料的挠度和弯矩值。     

含双圆孔平板弹性波散射与动应力分析

利用复变量及局部坐标系方法，对平板中含双圆孔弹性波的衍射与动应力集中问题进行了研究，给出了不同方向入射弯曲波条件下该问题一般解的函数逼近序列和边界条件的表达式用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解给出了双圆孔附近的动应力集中系数的数值结果，分析了孔间距对动应力分布的影响     

压电层合圆杆中的几何非线性波

利用有限变形理论,导出了描述压电层合杆中几何非线性波的传播方程.在端部作用有限振幅位移函数的边界条件下,用逐步近似法对位移函数进行了假设,推导出了一维压电杆中位移函数与电势函数之间的关系式,并应用变动参数法求解了变换得到的非齐次波动方程,得到了位移和电势的响应.数值分析表明:初始频率的改变对位移和电势的非线性特性影响不大;而初始振幅的增加会使非线性波形畸变特性明显增强.     

求解非线性动力系统周期解的改进打靶法

针对有周期解的动力系统边值问题可以转化为初值问题这一特点，改进了周期解的打靶 法数值求解. 在计算边界条件代数方程关于待定初值参数导数的过程中利用前一次 Runge-Kutta方法计算得到的节点函数值并通过再次利用Runge-Kutta方法获得了该导数值. 用此方法求解了Duffing方程及非线性转子---轴承系统的周期解,用Floquet理论判断了 周期解的稳定性,与普通打靶法作了比较,验证了方法的有效性.     

加权残值法分析轴压圆柱薄壳后屈曲问题

本文首次应用了样条配点法分析了受到轴向压力的圆柱形薄壳的后屈问题,壳体的方程是L.H.Donnell的非线性正交异性圆柱形壳体方程,壳体的挠度试函数及应力函数试函数都是于轴向用了五次B样条函数基函数,周向用余弦函数。计算模型是周向为半个波长的壳块,可适应后屈曲实验变形跳跃现象。非线性代数方程组用了Newton—Rophson迭代法求解。由此所得的理论上的后屈曲曲线与国外近代实验相符。     

非线性转子系统周期响应的分析

基于时域的时间有限元法,将描述转子系统动力学特征的非线性微分方程组离散成一组非线性代数方程,然后应用吴消去法的特征列思维对所得到的非线性代数方程组进行降维求解,进而得到待求节点位移响应的解形式,并据此对一具有非线性支撑的柔性Jeffcott转子模型响应的性质进行了分析。     

求解不连续中厚板自由振动的微分容积单元法

基于区域叠加原理和微分容积法，发展了一种新型的数值方法——微分容积单元法，用以分析具有不连续几何特征的中厚板的自由振动。根据板的不连续情况将其划分为若干单元，在每个单元内用微分容积法将控制微分方程离散成为一组线性代数方程．在相邻的单元连接处应用位移连续条件和平衡条件，引入边界约束条件后得到一套关于各配点位移的齐次线性代数方程，由此可导出求解系统固有频率的特征方程。本文用子空间迭代法求解特征方程，并以开孔板、混合边界条件板和突变厚度板为例研究了方法的收敛性和计算精度。     

改进的移动最小二乘法

近年来发展的无网格方法大多采用移动员小二乘法来构造试函数，而应用移动最小二乘法形成的方程组有时会是病态的甚至奇异的，从而限制了它的发展和应用。本文采用带权正交函数作为基函数对移动最小二乘法做了改进，避免出现病态方程组，且在计算过程中不需要进行短阵求逆运算，提高了计算速度。之后，借鉴牛顿法、平衡法和摄动法对由移动最小二乘法得到的非线性代数方程组提出了新的求解方法。     

弯曲波对含多圆孔薄板的散射与动应力集中

采用复变函数法和多极坐标方法,研究了弯曲波对含有多圆孔薄板的散射问题。通过板的弯曲波动方程和内力方程的推导,求出在入射弯曲波条件下该问题的一般解的函数逼近序列和边界条件的表达式。用展开正交函数的方法将待解的问题归结为对一组无穷代数方程组的求解。最后,给出了含3圆孔薄板的孔边动应力集中系数的结果,并分析了孔间距和波数对动应力分布的影响。     

Bending problems of rectangular Reissner plate with free edges laid on tensionless Winkler foundations

In this paper,an analytical method for solving the bending problems of rectangularReissner plate with free edges under arbitrary loads laid on tensionless Winkler foundationsis proposed.By assuming proper form of Fourier series with supplementary terms,whichmeet derivable conditions,for deflection and shear force functions,the basic differentialequations with given boundary conditions can be transformed into a set of simple infinitealgebraic equations.For common Winkler foundations,this set of equations can be solveddirectly and for tensionless Winkler foundations,it is a set of weak nonlinear algebraicequations,the solution of which can be obtained easily by using iterative procedures.     

Finite element,stream function-vorticity solution of secondary flow in the channels of a rod bundle

A finite element method has been applied to predict the overall features of the fully developed turbulent flow in the non-circular channels of a rod bundle. The finite element discretization is based on the conventional Galerkin method using an isoparametric quadrilateral element with mixed interpolation. The primary axial flow and turbulent kinetic energy distributions have been predicted for fully developed turbulent flow conditions right up to the wall. The secondary velocity is represented by the stream function-vorticity formulation and the no-slip boundary conditions are explicitly introduced in the nonlinear equations by a boundary vorticity formula. The Newton-Raphson method is applied to the stream function-vorticity equations and solved simultaneously by the frontal solution technique. A one-equation eddy viscosity model of turbulence and an algebraic stress transport model have been used to predict primary axial velocity, secondary velocities and turbulent kinetic energy. The predictions obtained for a central subchannel of an equilateral-triangular rod array with p/d= 1.3 are in reasonable agreement with experimental data.     

Bending of rectangular thin plates with free edges laid on tensionless Winkler foundation

In this paper, the bending problem of rectangular thin plates with free edges laid on tensionless Winkler foundation has been solved by employing Fourier series with supplementary terms. By assuming proper form of series for deflection, the basic differential equation with given boundary conditions can be transformed into a set of infinite algebraic equations. Because the boundary of contact region cannot be determined in advance, these equations are weak nonlinear ones. They can be solved by using iterative procedures.Doctor candidate in Civil Engineering Department of Qinghua University at present.     

Large deflection of rectangular sandwich plates

The governing differential equations and the boundary conditions for the large deflection of rectangular sandwich plates are derived using the principle of the complementary energy. The governing differential equations are transformed into systems of nonlinear algebraic equations using the finite difference method, and solved by successive iteration. For the purpose of illustration, deflection behavior of simply supported rectangular plates under uniform load is presented. The deflection behavior of plates with various values of shear rigidities and intensity of applied loads is studied. The change in the stress patterns of the face layers of the plate is also discussed.     

基于边界元法的非均质薄板弯曲问题的解

本文用边界元法研究非均质无限域弹性薄板弯曲问题.在数值实施过程中,对于夹杂和基体分别形成边界积分方程.通过离散边界积分方程,得到相应的方程组,然后结合界面条件,最终获得问题的求解方程组.在界面的相关量求得之后,可以根据需要来求解基体和夹杂中的有关位置的弯矩.数值结果与已有的解做了对比.     

Wiener-Hopf analysis of an acoustic plane wave in a trifurcated waveguide

In this paper, we have made Wiener-Hopf analysis of an acoustic plane wave by a semi-infinite hard duct that is placed symmetrically inside an infinite soft/hard duct. The method of solution is integral transform and Wiener-Hopf technique. The imposition of boundary conditions result in a 2 × 2 matrix Wiener-Hopf equation associated with a new canonical scattering problem which is solved by using the pole removal technique. In the solution, two infinite sets of unknown coefficients are involved that satisfy two infinite systems of linear algebraic equations. These systems of linear algebraic equations are solved numerically. The graphs are plotted for sundry parameters of interest. Kernel functions are also factorized.     

Nonlinear flexural–torsional dynamic analysis of beams of variable doubly symmetric cross section—application to wind turbine towers

In this paper, a boundary element solution is developed for the nonlinear flexural–torsional dynamic analysis of beams of arbitrary doubly symmetric variable cross section, undergoing moderate large displacements, and twisting rotations under general boundary conditions, taking into account the effect of rotary and warping inertia. The beam is subjected to the combined action of arbitrarily distributed or concentrated transverse loading in both directions and to twisting and/or axial loading. Four boundary-value problems are formulated with respect to the transverse displacements, to the axial displacement, and to the angle of twist and solved using the Analog Equation Method, a Boundary Element Method (BEM) based technique. Application of the boundary element technique yields a system of nonlinear coupled Differential–Algebraic Equations (DAE) of motion, which is solved iteratively using the Petzold–Gear Backward Differentiation Formula (BDF), a linear multistep method for differential equations coupled with algebraic equations. Numerical examples of great practical interest including wind turbine towers are worked out, while the influence of the nonlinear effects to the response of beams of variable cross section is investigated.     

半圆环截面细环壳的屈曲

本文由Sanders非线性平衡方程和Koiter小应变协调方程推导出细环壳的非线性微分方程和稳定方程。用伽辽金法求解了静水压或边界载荷作用下的半园环截面细环壳的稳定方程。对于不同的边界条件及一系列几何参数,计算得到了临界载荷及屈曲模态。     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

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