Numerical analysis for random temperature fields of embankment in cold regions

The stochastic finite element equations for random temperature are obtained using the first-order per-turbation technique taking into account the random thermal properties and boundary condition, based on heat transfer variational principle. The local average method for 2-D is used to discretize random fields. Then, the random temperature fields of embankment in cold regions are investigated on condi-tion that the thermal properties and boundary condition are taken as random fields, respectively, by using the program, which is written by the methods. The expected value of temperature field and the standard deviation of the temperature field of embankment in cold regions are obtained and analyzed.     

比例边界有限元子结构法研究

比例边界有限元法最初应用于土-结构的相互作用分析，经过近几年的完善和发展，如今已经能够应用到其他很多领域。但是因为比例边界有限元理论是基于相似性要求的，使得其在处理几何形状复杂的结构时，会有很大的局限性，从而在某些领域的应用仍旧受到限制。同时由于其全时空耦合，导致大量计算量和工作量，也是其应用受限的一个原因。采用子结构法，打破这些局限性，并且分别针对有限域、无限域的问题，对比例边界有限元子结构法进行了研究，得出了有利于比例边界有限元法在工程实践中应用的结论，为其在实际工程应用中提供了可靠的依据和规律。     

双平面T型方管加强节点的承载力性能研究

通过有限元软件ANSYS对双平面T型方管相贯焊接加强节点轴力和弯矩作用下的极限承载力进行了数值模拟研究，采用的加强方式在主管内部设置纵向加劲肋。研究结果表明这种加强方式对于双平面T型节点的单项承载力都有不同程度的提高作用，且提高幅度与几何参数有关。     

典型振动信号时-频分析方法研究

首先对比较简单的单分量信号和多分量信号进行时-频分析,对比了不同时-频分析方法(STFT、WD、Hilbert时-频谱分析、连续小波分析)的分析精度。结果表明对单分量信号和可以分解为若干单分量信号叠加的多分量信号,Hilbert时-频谱分析精度最好,WD和STFT次之,连续小波变换的精度最差;由于Hilbert时-频谱分析和WD方法要求信号为单分量信号或可以分解为若干单分量的信号,故其不适用于复杂信号的时-频分析;对多分量信号,STFT时-频谱较连续小波时-频谱精度高些。需要指出的是,当使用STFT方法时,取不同的窗参数,STFT的时-频分析精度相差很大,必须使用合适的窗参数,以取得较好的分析效果。此外还对El Centro波的两水平分量和人工合成的地震动进行了时-频分析,虽然STFT的时间分辨率和频率分辨率存在矛盾,但它对信号的适应性最强,对复杂信号的时-频分析精度一般可以满足需要,而连续小波变换进行信号的时-频分析时,时-频分辨精度最差,且对于大于30Hz的频率分量,随频率的增加,时-频分析的效果和精度迅速变差,说明小波变换并不适合于做时-频分析,尤其对于高频信号,用连续小波变换得到的时-频谱图看起来很粗糙,而且很难准确解释。进一步对比了真实地震动和人工地震动的时-频分布,认为用胡聿贤教授合成人工地震动的方法合成的地震动在时-频域上的分布和真实地震动相似。     

油浸式高压变压器地震易损性分析

油浸式变压器是由多种材料组成的复杂结构。本文对油浸式高压变压器建立了较为精确的有限元模型，考虑了各组件之间相互作用的影响。对该设备进行了动力性能和地震响应分析以及易损性分析。分析结果表明，大型高压变压器在地震中的首要破坏模式为瓷套破坏，其地震响应的离散度较高。易损性分析得到设备的地震易损性曲线，可直接应用于电力系统的抗震分析。     

A computational method for approximating a Darcy–Stokes system governing a vuggy porous medium

We develop and analyze a mixed finite element method for the solution of an elliptic system modeling a porous medium with large cavities, called vugs. It consists of a second-order elliptic (i.e., Darcy) equation on part of the domain coupled to a Stokes equation on the rest of the domain, and a slip boundary condition (due to Beavers–Joseph–Saffman) on the interface between them. The tangential velocity is not continuous on the interface. We consider a 2-D vuggy porous medium with many small cavities throughout its extent, so the interface is not isolated. We use a certain conforming Stokes element on rectangles, slightly modified near the interface to account for the tangential discontinuity. This gives a mixed finite element method for the entire Darcy–Stokes system with a regular sparsity pattern that is easy to implement, independent of the vug geometry, as long as it aligns with the grid. We prove optimal global first-order L ² convergence of the velocity and pressure, as well as the velocity gradient in the Stokes domain. Numerical results verify these rates of convergence and even suggest somewhat better convergence in certain situations. Finally, we present a lower dimensional space that uses Raviart–Thomas elements in the Darcy domain and uses our new modified elements near the interface in transition to the Stokes elements.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity II: the discrete-in-time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a discrete-in-time setting. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.     

起伏地表条件下地震波场数值模拟有限积分变换有限差分方法

针对起伏地表条件下的地震波数值模拟问题,提出将起伏的地表映射到一个规则的长方形网格坐标系中,并在此基础上推导出变换域中的波动方程。根据导出来的波动方程应用有限余弦变换有限差分方法进行地震波场的数值模拟,以解决起伏地表条件下的数值模拟。     

地震波多次散射波场的高阶谱统计分析

设计了一个特殊且相对规则的散射界面模型,并利用声波动方程高阶有限差分的方法对其进行正演。通过不断改变模型中散射体的横向尺度来控制多次散射波场的强度和特征,然后结合高阶谱统计分析的方法对所得的多次散射波进行分析,进而可以得到多次散射波频率随散射体横向尺度而变化的一些规律。