| 1. | A force - method equation about unknown nodal forces of the composite beams is proposed based on the governing differential equation
在粘结剪力和滑移微分控制方程的基础上，建立了关于组合梁单元杆端未知力的力法方程。 |
| 2. | In this paper , the governing differential equations of double pendulum is established with the lagrange methods , the stability margin of corresponding linear equations are obtained by the multiple scale method
采用拉格朗日方法建立参数激励双摆的控制微分方程，通过多尺度法对其线性化方程进行分析，获得稳定性边界。 |
| 3. | In the analysis of the elastic local buckling strength of the stiffener ' s web , the elastic critical stress is analytically derived by solving the characteristic value problem involving the governing differential equation under the corresponding loading and boundary conditions
对于加筋板中加强筋腹板的局部屈曲，则用解析法推导出筋的腹板的挠度方程及其边界条件，求解相应的方程，从而计算出腹板的局部屈曲应力。 |
| 4. | Firstly , with uniaxial symmetrical rectangle cross section , the warping displacement function and tangential displacement function under anti - symmetrical load are supposed . then taking shear deformation into account and with potential principle , the governing differential equation for distortion angle subjected to uniformly distributed distortion load is established
首先，以单轴对称矩形截面薄壁杆件为研究对象，假设其在反对称荷载作用下翘曲位移和切向位移的分布函数，考虑剪切变形的影响，利用最小势能原理建立单位均布畸变荷载作用下的畸变角微分方程。 |
| 5. | A plane - wave expansion method based on the effective medium theory is firstly introduced , and the new method has a better convergence than that of the pwm . as a new method for calculating the band structure of a photonic crystal , a finite difference scheme is also introduced to the governing differential equation based on the effective medium theory
首先提出了基于等效介质理论的平面波方法，显著地改善了平面波算法的收敛性质；同时提出一种新的计算光子晶体能带的有限本征差分算法，与已有的平面波展开法相比，新方法保留了本征值算法的独特优点，同时又克服了平面波展开法的慢收敛性。 |
| 6. | The elastic foundation model is considered as two - parameter elastic foundation model and its effect to moderate - thick plates are taken into account by a set of governing differential equations . united with hu hai - chang ’ s function , least squares collocation weighted residual method which uses b - spline function as trial function is put forward for solving the bending problems . compare with the results of finite element method of lines , spline finite strip method , accurate solution of series etc . it is proved that the method in this article has adequate accuracy and practical feasibility
本文采用瑞斯纳中厚板理论求解弹性地基板,建立双参数地基与中厚板相互作用的控制微分方程,结合胡海昌的解耦函数,运用双五次b样条函数作为试函数的离散型最小二乘加权残值法分析了双参数地基上的中厚板的弯曲问题,并将结果与有限元线法、有限条法、级数精确解等进行比较,证明本文方法具有足够的精确性与实际的可行性。 |
| 7. | In the wrscs , the self - consistent model is used to describe the complex configurations of the particulate composite and the temperature field is solved by weighted residual collocation method with some proper simplifications . this method provides a more efficient way of setting up the algebraic equations corresponding to the governing differential equations . the prediction formula for the effective thermal conductivity of the composite is obtained
权残自洽方法可以用于描述不同形状夹杂的复合材料的微观结构，通过对不同几何形状角点做适当的圆弧化处理，采用加权残值数值计算方法的配点法将求解微分控制方程变为求解线性方程组，进而得到任意形状夹杂内部的温度场，建立含不规则形状夹杂的复合材料有效热导率的预测公式。 |
| 8. | In this paper , the present status of development on the deep foundation pit conserved by frozen wall and coupled problems are analyzed thoroughly . the governing differential equations are obtained based on thermodynamics , while the finite element formulae is achieved by the galerkin ' s method
本文在对冻土墙围护深基坑开挖冻结温度场和应力场耦合分析研究现状的基础上，以热力学为基础，推导了冻土墙温度场控制微分方程，并利用伽辽金方法推导了冻土墙冻结温度场和应力场耦合计算的有限元计算格式。 |
| 9. | Using the displacement functions and the technique of double fourier transform , the governing differential equations for transversely isotropic saturated poroelastic media are easily solved and , the fourier transformed stress and displacement solutions coorespondingly are obtained . then , under the boundary conditions , the analytical solutions for half - space are presented
借助位移函数及双重fourier变换，研究了直角坐标系下横观各向同性饱和土的动力响应问题，得到了饱和半空间体在任意分布的表面谐振荷载作用下稳态响应的一般解。 |
| 10. | Based on the review of coupling theory of porous media , a nonlinear mathematics mechanical model and the governing differential equation of the coupled problem of thermal - gas fluid - mechanical are derived from the theory of continuum mechanics and mixture theory . a constitutive equation of the porous media is obtained in the coupling processes
在全面系统的回顾与总结多孔介质多物理场耦合分析与模拟的研究成果的基础上，以混合物理论以及流体、应力、温度相互作用的机理为基础，建立温度场、渗流场、应力场三场耦合分析的非线性数学模型。 |
