计算中近似法

The relationship between transient response and shape design variables is highly non-linear, and the behavior of feasible domains is often not good, which may cause convergence difficulties. In order to improve convergence speed of iteration process, some algorithms the feasible domains adjusting, the adaptive move limit, the approximate line search and the approximate reanalysis, are adopted.

采用基于Newmark积分的直接求导法计算瞬态响应灵敏度，在序列二次规划算法中采用了可行域调整、近似—维搜索、自适应运动极限等改进技术，提高求解效率和收敛稳定性，以解决结构动态响应与设计变量的关系复杂、高度非线性，优化可行区域的性态不良等问题。

The Cholesky decomposition of cross spectral density matrix was approximated and reduced, and then the modified spectral representation method is efficient and requires less computer memory, which is suitable for simulating spatial wind fields of long span bridges.

针对现有Deodatis方法模拟大跨度桥梁空间脉动风场中存在的计算量问题，通过对谱分解矩阵引入插值近似，减少谱分解的次数，从而提高该谐波合成法的计算效率，并节省内存花费，实现了对三维空间脉动风场的有效模拟。

In the dissertation, meshless element free Galerkin method which utilizes moving least square is used for solving heat transfer problems. Lagrange multiplier method is used to deal with the essential boundary condition. Some parameters in element free Galerkin method, which influence the precision, are also discussed in the numerical simulation. The adaptive method of meshless method is also stated.

本文采用了基于移动最小二乘近似的无网格伽辽金法计算了热传导问题，采用拉格朗日乘子处理本征边界条件；讨论了无网格伽辽金法各个计算参数在数值模拟中对计算精度的影响；并对无网格的自适应方法进行了研究。

In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

主要内容有：为了合理地描述金属塑性成形中摩擦约束弹性、弹塑性基本问题，提出和研究了有限变形下以Kirchhoff第一应力表示的Coulomb摩擦定律形式和弹塑性流动理论下以增量形式表示的Coulomb摩擦定律表示形式；系统建立了摩擦约束弹塑性问题的Hilbert函数空间，使本文规范在一个具有合理的代数拓扑结构内进行一切操作和运算；利用Lagrange乘子，从泛函极值的角度系统地阐述和论证了一系列摩擦约束弹性、弹塑性广义变分不等原理与相应的实际问题之间的等价性，它为处理摩擦约束的弹塑性力学数值方法提供了合理的理论基础；从变分不等式的角度出发，阐述了对应于摩擦约束弹性、弹塑性问题的广义变分不等式理论，首次提出了在应力相容性条件下，它的有限元解具有存在唯一性，进而讨论了其有限元近似及离散解法；基于摩擦约束弹塑性广义变分不等式原理，首次提出了直接广义变分不等式方法，这一方法是直接变分法的合理推广和发展；利用直接广义变分不等式方法对金属压力加工中的平面变形问题、镦粗、挤压等塑性成形问题进行了分析计算，验证了该理论和数值算法的正确性、实用性、精确性和优越性。

To study numerical solution of the linear equations,the article presents direct method ,Jacobi iterate method and Gauss-seidel iterate method to approximately calculate,and has given its process in MATLAB.

为研究线性方程组的数值解，文章用直接解法、雅可比迭代法、高斯-赛德尔迭代法进行了近似计算，并给出在MATLAB中计算的程序。

The major implementations of the developed model include: Pseudo-spectral and finite-difference schemes are employed to approximate the spatial-differential operators in the horizontal and vertical directions, respectively. A second-order Runge-Kutta method is adopted to integrate in time for the velocity field and the free-surface elevation. The solenoidal condition of the velocity field is satisfied by solving the transformed pressure Poisson equation. A modified secant method is used to accelerate the iterative solution of the non-separable Poisson equation.

模式的主要数值方法包括：分别以拟频谱法以及二阶有限差分法近似控制方程与边界条件中的水平与垂直导数；以二阶Runge-Kutta法进行非稳态的自由液面位移与流场速度的时间积分；利用改良式割线叠代法求解计算区间中不可分离的压力Poisson方程式，以满足不可压缩流条件。

In consideration of large computational efforts of Deodatis simulation,a modified spectral representation method was proposed for simulating the fluctuating wind field of long span bridges.

针对现有Deodatis方法模拟大跨度桥梁空间脉动风场中存在的计算量问题，通过对谱分解矩阵引入插值近似，减少谱分解的次数，从而提高该谐波合成法的计算效率，并节省内存花费，实现了对三维空间脉动风场的有效模拟。

By time-varying filtering, we realize the signal selectivity and interference suppression, especially for the signals with time-varying power spectrum. It is shown herein that conventional eigenstructure based methods are lower dimensional special case of the time-frequency subspace fitting method. The closed-form array response estimation algorithms for blind source separation in wireless communication is also developed in the dissertation by exploiting the data structure of second-order statistics of the array output in the presence of multipath. The proposed method achieves array response estimation with little constraint on signal property and propagation environment such as scatters or angular spread. Moreover, the array utilized here can be of arbitrary geometry and even uncalibrated. Since the closed-form solution is obtained, no misconvergency may occur and large amount of computation can be saved. The equivalent feed model and corresponding optimization designation are proposed to realize the downlink multi-user selective transmission. By coherent and non-coherent superposition of the electromagnetical field, multiple beams can be formed using a single array, so that each co-channel user signal is transmitted in each beam and will not interfered with each other. The proposed system scheme implements the digital beamforming and the channel allocation in the base band, therefore is suitable for the utilization of the radio software technology. The feasibility and effectiveness of the proposed model are proved by the RF experiment.

在窄带条件下，GSC－SSF方法还可以提高阵列的虚拟孔径，从而提高估计的性能；可以证明，Cyclic DOA 和SC-SSF方法可看作该方法的特例或近似； 3、提出了二维GSC－SSF方法和宽带谱相关DOA矩阵方法，利用信号的循环平稳特性解决了宽带条件下二维 DOA 估计问题，并具有阵元数少、计算量较小的特点； 4、提出了时频子空间拟合和宽带时频DOA估计算法，将联合时频分析的理论和方法引入到阵列信号的空间谱估计研究中，利用时变滤波实现信号选择性测向和干扰抑制，特别适合于谱时变信号；可以证明传统特征结构法可看作是时频子空间拟合方法的特例； 5、提出了多用户环境下阵列响应的估计方法——CARE方法，该方法对信号结构和传播参数（主要是散射源分布与角度散布）的约束较少，适用于各种几何结构的阵列甚至未校准的阵列，能够直接得到阵列响应的闭式解，因此计算量小、稳健性好，不存在收敛问题； 6、提出了针对多用户下行选择性发送的阵列等效激励模型、优化设计方法及其系统实现方案，通过空间场的相干叠加与非相干叠加使得单一阵列能够形成多个波束，并保证各波束内的用户信号各不相同且相互干扰最小；其系统方案具有在基带实现数字波束成形、信道分配并便于软件无线电实现的特点，其有效性已得到外场实测数据的证实。

In this paper, the following progress has been discussed:(1) the improved conjugate gradient algorithm which combines the inversion equation;(2) the formulation for velvet gene at all directions and the approximation method of Jacobian matrics based on disturbance method;(3) the model is adjusted by analyzing the influence of damp coefficient and correction factor to inversion result ;(4) the influence of damp coefficient to the resolution of inversion is studied. to some degree, we improved the problem of "barycenter ascending shift" to electric anomalous body in 3-D resistivity inversion.

本文主要讨论了以下几个方面的内容：（1）结合反演方程式改进的共轭梯度算法；（2）基于扰动法的线源Jacobi矩阵的近似计算方法及光滑系数矩阵在各个方向上的光滑因子的计算公式；（3）通过分析阻尼系数与修改量校正量对反演结果的影响，提出了利用校正系数对模型修正量进行校正；（4）较为系统的讨论了阻尼系数λ对反演分辨能力的影响，较好的改善了三维电阻率反演中的电性异常体重心的&上漂&现象。

According to the post-tensioning method in prestressed concrete members,the calculation method of prestress losses caused by the deformation anchorage device,slip of tendon and joint compression was big in the error and narrow in the scope of application.

针对后张法预应力混凝土构件中由锚具变形、预应力钢束回缩和接缝压缩等引起的预应力损失计算方法适用范围较窄和误差较大的缺点，基于变形协调条件，通过分段近似计算方法，建立了锚具变形、预应力钢束回缩和接缝压缩等引起的预应力损失计算公式，并与实际预应力混凝土T形截面简支梁的计算结果进行了比较。

Further more, the simplified analysis method on stressed-skin effect of corrugated steel sheet is also discussed in detail.

此外还比较详细地探讨了蒙皮效应的简化分析方法。

If I had known her telephone number,I would have called her.

要是我知道她的电话号码，我就打电话给她了。