Numerical and analytical solutions are presented.
文章中同时提出解析解与数值解。
Of course, the analytical solutions have their own theoretical value...
当然，解析解还会有其相应的理论价值。
Analytical solutions are obtained by the methods of self-similar functions.
采用自相似函数的方法可以获得解析解。
Analytical solutions are attained by the methods of self-similar functions.
采用自相似函数的方法可以获得解析解。
To provide data analytical solutions for PLM can be an interesting opportunity.
提供数据分析解决方案可能是PLM的一个机遇。
The analytical solutions are obtained by the methods of self-similar functions.
采用自相似函数的方法可以获得解析解。
Implicit and explicit forms of the analytical solutions are given out in the paper.
文中分别给出了隐式和显式形式的解。
Considered various rotational situations, different analytical solutions are derived.
考虑各种不同的旋转情况，得到了不同的分析解。
Taking one stay cable as example confirms the correctness of the analytical solutions.
并以某斜拉索为例进行了计算分析，证明了所得解析式的正确性。
The numerical results are well consistent with analytical solutions within a specific range.
与分析解相比较，在一定范围内，数值计算结果与分析解相符。
Analytical solutions for three dimensional elasticity problems are quite difficult to obtain.
三维弹性问题的解析解是很难得到的。
Present analytical solutions can be simplified as earlier results without the degraded stiffness.
若不考虑刚度劣化，理论结果可蜕化为以前的结果。
The analytical solutions of some problems can be obtained with the method of self-similar functions.
通过自相似函数的方法可以获得若干问题的解析解。
The general expressions of analytical solutions are obtained by the methods of self-similar functions.
采用自相似函数的方法可以获得解析解的一般表达式。
Analytical solutions for the impact problems of conical rod structures with supporting spring are provided.
提供了弹簧连接的锥形杆结构撞击问题的解析解。
By using inverse method, the analytical solutions of couple stress fluids were obtained for steady and unsteady cases.
本文采用逆方法研究并获得了应力偶流体的定常和非定常精确解。
Finally, it is verified that the analytical solutions number of this kind of Barranov truss is 46 by a numerical example.
最后通过一个算例，验证了这种巴氏桁架的解析解的数目为46。
The analytical solutions concerning intracellular calcium spiral and target wave in the Xenopus laevis oocyte are obtained.
第四、首次得到了非洲爪蟾卵母细胞内的螺旋钙波和靶波的解析表达式。
Based on the analytical solutions, the transfer matrixes of circular and annular plate elements with uniform thickness were derived.
基于这些解析解，导出了等厚度圆板和环板单元的传递矩阵。
By comparing the numerical solutions with the analytical solutions, it is proved that the isoparametric graded finite elements are useful.
针对功能梯度材料这种新型材料，提出了采用等参梯度元建立有限元模型的方法。
Degenerate results for the special case of an isotropic homogeneous elastic beam are coincided well with the existing analytical solutions.
该解退化到各向同性均匀弹性情况时与已有的理论解相一致。
The analytical solutions of composite modulus in both elastic and plastic conditions are deduced by applying parametric variational principle.
应用参变量变分原理推导了复合模量在弹性及塑性状态下的解析解。
The analytical solutions for the natural frequences and the dynamic responses of the beam under the action of lateral blast loading are obtained.
并求得了钢板混凝土梁的固有频率和在横向爆炸载荷作用下的动力反应的解析解。
For the plane stress problem of fixed end orthotropic beams subjected to uniform load, the analytical solutions of stress and displacement were resolved.
针对均布载荷作用下正交各向异性梁在两端固支条件下的平面应力问题，求解了应力和位移的解析解。
Considering the residual stress, the total stress analytical solutions for square-shaped boron-doped silicon diaphragms with large deflection are presented.
考虑残余应力的情况下，薄膜在大挠度时总应力的解析表达式。
The improved rock mass parameters have been applied to the support action analysis of tensioned and grouted bolts by using the existing analytical solutions.
这些结果可直接应用于围岩—支护相互作用分析的已有解析解中，并通过控制围岩边界位移量进行锚杆支护参数设计。
The analytical solutions of stresses, displacement and pore pressure amplitude are derived in frequency domain by introducing two scalar potential functions.
引入两个势函数，在频域中得到了应力、位移和超孔隙水压力响应解答。
Having adopted the quadratic approximation of potential, we can solve the equation and get the approximately analytical solutions of Gaussian typed breath mode.
对势函数采用二阶近似后，求解此方程得到高斯型呼吸模式的光束宽度的近似解析式。
Two algebraically explicit analytical solutions of the governing equation set for the coupled heat and mass transfer process of rapid drying in porous media are derived.
对多孔介质快速干燥过程的传热与传质耦合方程组导出了两套代数显式解析特解。
By algebraic dynamical method, the exact analytical solutions of the ordinary differential equations are obtained in terms of Taylor series with local convergent radius.
用代数动力学方法求得了用泰勒级数表示的局域收敛的常微分方程的精确解。
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