中空轴对称域多孔介质力学问题的解析解

给出在有界中空轴对称域多孔介质中渗流－力学耦合问题解析解。根据Ｂｉｏｔ理论推导了在弹性多孔介质中渗流－力学耦合问题的方程，并指出在轴对称问题中渗流方程可以化为解耦形式。在无界域中，解耦的渗流方程是齐次的，只有扩散系数的改变。在有界域中，解耦的渗流方程是非齐次的。这时，它是一个线性微分－积分方程，在时间域用分离变量法求解。     

一类广义Hirota-Satsuma Coupled KdV系统的新精确行波解

利用新近提出的(G'/G)-展开法,借助齐次平衡方法的思想原则和吴文俊消元法,对一类Hirota-Satsuma Coupled KdV方程进行研究,获得了该系统的含有多参数的双曲函数、三角函数和有理函数表示的三种形式的精确通解.从求方程组精确行波解的过程看,此方法不仅是求解非线性发展方程行波解的一种简捷和有效的方法,...     

色散系数可调的球KdV方程精确衰减孤波解

根据简化齐次平衡原则,导出了一个由齐次方程的解到一个可变色散系数的球KdV方程解的非线性变换。该齐次方程容许有指数函数形式的解,通过非线性变换,获得了可变色散系数的球KdV方程的精确衰减单孤波解和双孤波解。     

一维齐次波动方程Cauchy问题达朗贝尔公式的另一种推导

主要针对齐次波动方程Cauchy问题的通解求解,也就是达朗贝尔公式的推导。大部分文献通过求出特征方程,进而得到达朗贝尔公式,利用方程的算子形式将齐次波动方程方程转化为常微分方程组,通过对两个常微分方程利用特征线法求解,同样能够得到达朗贝尔公式。     

混凝土结构非稳态温度场的增维精细积分法

根据有限元原理推导出非稳态温度场空间上的有限元方程,并转换为以状态方程表示的非齐次方程,其次采用增维的方法将非齐次方程再化为齐次方程,最后用精细积分法导出了每一时间步内的解。结果表明,这是一种可行的、可靠的、稳定性好的数值方法。     

二维双相介质多参数反演的同伦法

从材料响应的理论合成应与实际测量数据相拟合这一出发点，双相介质波动方程参数的反演，可以转化为非线性算子方程的零点求解问题，然后用同伦方法求出非线性算子等于零的根作为反问题的解。本文将同伦方法应用于具有边界元数值解的二维双相介质波动方程的多参数反演，并将反演结果同非线性全局优化方法进化策略法进行了比较，数值计算结果表明了同伦方法的可行性和有效性。     

考虑剪切效应的悬梁大挠度问题摄动解

本文导出了在考虑了剪切附加作用时的悬梁大挠度问题的基本方程,并取最大挠度为摄动参数,用摄动法得出了二次渐近解.中文给出了有关图表,并对各种情况时的横向力效应进行了讨论.     

基底隔震框-剪结构的动力模型

在结构连续化假定的基础上，提出了基底隔震结构的剪-弯梁隔震模型，导出了问题的控制微分方程，求出了相应矩阵形式的初参数解，给出了该模型下的频率方程及振型函数的解析表达式。     

Toda链方程的孤子解和周期解

分析了Ｔｏｄａ链方程的单孤子解和周期解及其相互关系，并应用数值控制算法求出了孤子解和周期解图。     

应用阶梯折算法计算塔机变截面臂架的内力和挠度

应用含有Heaviside函数的阶梯折算法,列出臂架挠度通用公式。引用弹性支承条件,并借助力矩平衡方程,由计算机解线性方程组求出拉索力,从而确定变截面臂架任意截面上的内力和挠度。     

Free vibration of partially supported piles with the effects of bending moment, axial and shear force

The pile parts above the soil and embedded in the soil are called the first region and the second region, respectively. The fourth order partial differential equations of both regions for free vibration of partially supported pile subjected to bending moment, axial force and shear force are obtained using the small-displacement theory and the Winkler model. It is assumed that the behavior of the material is linear-elastic, and that axial force along the pile length and modulus of subgrade reaction for the second region to be constant. Shear effect is included in the partial differential equations by the second derivative of the elastic curve function with respect to shear deformation. Natural circular frequencies and relative stiffness of the pile are calculated for non-trivial solution of linear homogeneous system of equations obtained due to the values of axial forces acting on the pile, the shape factors, and the boundary conditions of the pile with both ends free and both ends simply supported; the results are presented in graphs.     

平坦二维薄膜结构的失稳临界风速

给出了一种利用稳定性理论确定薄膜结构颤振失稳临界风速的方法。首先 ,利用扁壳的无矩理论得到了平坦薄膜结构的基本力学方程。假设来流为均匀的理想势流 ,利用流体力学中的势流理论确定了薄膜结构上的气动力 ,从而得到风与薄膜结构的气动耦合作用方程。然后 ,采用Bubnov Galerkin法将复杂的耦合作用方程转换为一组具有常系数的二阶微分方程 ,最后采用Routh Hurwitz稳定性准则确定了薄膜结构的临界风速。     

Asymptotic solutions of axisymmetric laminated conical shells

The three-dimensional (3D) solution of laminated conical shells subjected to axisymmetric loads is presented using the method of perturbation. The formulation begins with the basic 3D elasticity equations without making any static or kinematic assumptions in advance. After introducing a set of proper dimensionless variables, asymptotically expanding the field variables and then successively integrating the resulting equations through the thickness direction, we obtain the recursive sets of governing equations for various orders. The edge boundary conditions at each order level are derived as the resultant forms by following the variational approach. The method of differential quadrature (DQ) is used to determine the present asymptotic solution for various orders. For illustration purposes, the simply supported laminated conical shells under uniformly and sinusoidally distributed lateral pressure and the clamped laminated conical shells under edge torsion, are studied. It is shown that the present asymptotic DQ solution can be obtained order-by-order in a hierarchic and consistent manner and asymptotically approaches to the 3D elasticity solution.     

Coupled axial–torsional vibration of thin-walled Z-section beam induced by boundary conditions

The coupled axial–torsional vibration of thin-walled Z-section beam induced by the boundary conditions is investigated. The value of the warping function is not zero at centroid for Z-section beam. If the axial displacement of the pin end is restrained at the centroid of the Z-section for thin-walled Z-section beam, the axial vibration and torsional vibration may be coupled. The governing equations for linear axial and torsional vibration of a thin-walled Z-section beam are derived by the d’Alembert principle and the virtual work principle. The bending vibration is uncoupled from axial and torsional vibrations and is not dealt with in this paper. For harmonic vibration, the general solution of these equations with undetermined constant coefficients may be obtained. Substituting the general solution into the displacement and force boundary conditions, a set of homogeneous equations can be obtained. The natural frequencies and the coefficients of the general solution may be obtained by solving the homogeneous equations using the bisection method.Numerical examples are studied to verify the accuracy of the proposed method and to investigate the effect of boundary conditions and the value of warping function at centroid on the coupled axial and torsional natural frequency of Z-section beam.     

Buckling and postbuckling of shear-deformable rectangular plates of composite construction

Buckling and postbuckling behaviours of rectangular plates of composite construction are studied by means of the generalised von Karman equations counting for arbitrary lamination and material properties. In conjunction with four edges simply supported, higher order asymptotic solutions to the large deflection equations with incorporation of initial geometrical imperfection are constructed by the deflection type perturbation technique. Effects of initial imperfection, transverse shear deformation, shear-bending material interaction, and in-plane edge condition on buckling and post-buckling of the plates are examined through typical examples, and comparison of the present solution are made with other theoretical and numerical results. It is shown that the present predications are of fairly good accuracy.     

Distortional eigenmodes and homogeneous solutions for semi-discretized thin-walled beams

The classical Vlasov theory for torsional analysis of thin-walled beams with open and closed cross-sections can be generalized by including distortional displacement fields. We show that the determination of adequate distortional displacement fields for generalized beam theory (GBT) can be found as part of a semi-discretization process. In this process the cross-section is discretized into finite cross-section elements and the axial variation of the displacement functions are solutions to the established coupled fourth order differential equations of GBT. We use a novel finite-element-based displacement approach in combination with a weak formulation of the shear constraints and constrained wall widths. The weak formulation of the shear constraints enables analysis of both open and closed cell cross-sections by allowing constant shear flow. We use variational analysis to establish and clearly identify the homogeneous differential equations, the eigenmodes, and the related homogeneous solutions. The distortional equations are solved by reduction of order and solution of the related eigenvalue problem of double size as in non-proportionally damped structural dynamic analysis. The full homogeneous solution is given as well as transformations between different degree of freedom spaces. This new approach is a considerable theoretical improvement, since the obtained GBT equations found by discretization of the cross-section are now solved analytically and the formulation is valid without special attention also for closed single or multi-cell cross-sections. Further more the found eigenvalues have clear mechanical meaning, since they represent the attenuation of the distortional eigenmodes and may be used in the automatic meshing of approximate distortional beam elements. The magnitude of the eigenvalues thus also gives the natural ordering of the modes.     

Viscoplastic axisymmetrical buckling of spherical shell impulse subjected to radial pressure

The solution of viscoplastic axisymmetrical buckling of a complete thin spherical shell subjected to radial pressure impulse is presented. Analytically, the problem is formulated as a superposition of small perturbations on the basic unperturbed motion. The amplitudes of perturbed motion are restricted to be so small that the homogeneous compressive deformation predominates over the local bending. This condition allows the constitutive equations to be linearized by the expansion into Taylor's series in the vicinity of unperturbed motion. As a result, a set of two linear partial differential equations of the fifth order is obtained for describing the perturbed motion of the shell. The functional coefficients of these equations are determined by the solution for the unperturbed motion. The governing set of equations is solved using the series of Legendre's functions. As a result, for the time-dependent amplitudes in the series, the set of two ordinary equations with variable coefficients is arrived at. It turns out that certain harmonics grow very rapidly and cause the shell to exhibit a characteristic wrinkled shape which is characterized by a critical mode number. This property of the amplitudes is used to determine the threshold impulse that a shell can tolerate without excessive deformation.The influence of the meridional displacement on the magnitude of radial displacement, buckling mode and critical impulse is investigated. Also, the influence of the viscosity and the initial imperfections of the geometry and loading is shown. The numerical results for a steel shell are presented diagrammatically.     

关于某些Fuchs型方程平坦解的唯一性

本文研究某些类型的Fuchs型方程平坦解的唯一性。首先证明了一个一阶Fuchs型拟微分算子的Carleman估计,然后用经典的方法,证明了一类一阶,二阶Fuchs型方程解的唯一性,并且对t-对合的高阶方程得到了类似的唯一性结果。     

饱和土体圆柱形热源热固结问题的一个近似解

在考虑土骨架和孔隙水热膨胀特性差异的基础上,根据力平衡条件、有效应力原理、能量守衡定理及线弹性应力–应变关系,建立了考虑耦合效应的饱和土体热固结问题控制方程。利用 Fourier 变换、Laplace 变换及其逆变换,给出了热固结问题的求解方法。对一无限长圆柱形热源向外传导和扩散问题进行研究,给出了非等温条件下周围饱和土体的温度、孔隙水压力和位移的解析解,并对其变化规律进行研究,分析了热固结系数等参数的影响。     

齐次函数的一些性质及其应用

本文证明了齐次函数的一些性质。主要是证明了仿齐次函数为亚齐次函数的一个充分条件。由此而得到了关于齐次函数与其各变元偏导数间的关系。最后应用这些性质于多元函数的全微分求积以及一阶全微分方程的求解,得到了十分简捷的解法。