求解

The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.

具体安排如下：第一章首先建立复杂地层中自然电位测井的偏微分方程数学模型，证明了该边值问题弱解的存在唯一性，在此基础上研究了自然电位测井电阻率识别问题：然后发展了用于求解椭圆交界面问题的间断捕捉有限差分方法，利用该方法定量分析了目的层电阻率、地层厚度、井径、侵入带和水淹层等因素对自然电位测井响应的影响，取得了满意的结果。

This study uses the soil parameter reduction coefficients to model the seismic pile responses affected by liquefied soils. One dimensional wave equation analyses were conducted for the solutions. Based on the bore-hole data and nearby seismic record, the soil parameter reduction coefficients of liquefied layers can be obtained through a pre-analysis for liquefaction potential of the site. The reduction coefficients were used to reduce the soil modulus for liquefied soils, and the lumped mass analysis is performed to obtain the free-field response of the site. The ground deformations are superimposed onto the pile elements for discrete wave equation analysis, and the non-linear pile responses can be simulated through the modified Bouc-Wen model. Thus the deformations and failure mechanism of the pile are able to investigate.

中文摘要本研究之土质参数折减系数模式，系以一维波动方程模拟地盘液化状态下之桩基础动力反应，依据现场土层钻探资料与邻近测站之地震纪录，由土壤液化潜能评估法配合日本相关规范求得液化土层之土质参数折减系数，以此系数对土壤强度模数进行折减，并使用集中质块法求取自由场之地盘液化反应，再以此为前置解作用於桩基础之波动方程求解，桩身刚度以简化之Bouc-Wen模式模拟其非线性行为，以了解液化地盘内基桩之变形行为与破坏机制。

The effectiveness of this method is verified in the layout problem of bornite craftworks.

以斑铜工艺品布局求解为例，对该算法进行了验证。

Easter′s scheme, which is the modified version of Bott′s forward in time and positive definite numerical advection scheme, is described in this paper.

Easter的方案是把水汽的通量方程和连续方程联立求解，在计算中不会出现水汽负值，而且稳定性好。

Based on the asymptotic homogenization,the periodic boundary conditions for the unit cell are established by using the ANSYS Parametric Design Language,the problem of the unit cell is solved by finite element method and the effective elasto-plastic properties of the composite is obtained,which is compared with other results.

在渐近均匀化方法的基础上，用ANSYS参数设计语言建立周期性边界条件，用ANSYS有限元程序对单胞进行求解，得到材料的有效弹塑性性能。

Based on the asymptotic homogenization , the periodic boundary conditions for the unit cell of composites are established using the ANSYS parametric design.

在渐近均匀化方法的基础上，用ANSYS参数设计语言建立了周期性边界条件，用ANSYS有限元程序对单胞进行求解，得到了复合材料的有效性能。

Based on the asymptotic homogenization theory, the periodic boundary conditions for the unit cell were established by using the ANSYS parametric design language. The problem of the unit cell was solved by finite element method and the effective elasto-plastic properties of dual phase steels were obtained.

在渐近均匀化方法基础上，假设双相钢的结构为周期排列，通过ANSYS参数设计语言建立周期性边界条件，用ANSYS有限元程序对3种平面应变模型的单胞进行求解，得到双相钢的有效弹塑性性能，并与其他计算结果进行比较。

The most-used numerical method for solving direct boundary integral equation is collocation method, which is simple and faster. Seldom have been used the Galerkin scheme in this case.

一般来说，直接边界积分方程可以很方便的用配点法求解，还未见有实际用Galerkin边界元来解的报道。

First, the linear combinations of basic set of solutions to Laplace equation under polar coordinate system are chosen as the approximations for the solution of temperature fields,boundary residual collocation method are applied to calculate the distribution of the temperature fields for single-particle model.

本论文主要完成了两方面的工作，一方面是采用加权残值法和边界元法对不同复合材料模型的2D稳态热传导的温度场进行了求解分析。

The boundary contour formulations of evaluatingstresses from the Somigliana stress identity are derived for 2-D problemswith quadratic boundary elements.The boundary contour method basedon the traction boundary integral equation is further discussed.Elasticproblems are first solved using the traction boundary contour method.Amixed collocation of the displacement boundary contour formulation andtraction boundary contour formulation is given.(4)The dual boundarycontour method is developed for the analysis of crack problems.

3建出了Somigliana应力积分式的二维和三维问题的边界轮廓法理论；给立了二维问题由Somigliana应力积分式计算应力的二次形函数的边界轮廓法方程，进而给出了基于面力边界积分方程的边界轮廓法；提出了一种以位移边界轮廓法方程与面力边界轮廓法方程混合配置的方案，首次实现了用两种积分方程相结合来求解弹性力学问题。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。