Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

空间杆系与叠层板组合结构的非线性稳定分析

本文用非线性有限元法研究一种空间杆系与复合材料叠层板组合结构的非线性稳定问题。将杆系离散成空间梁柱单元，将复合材料叠层板离散成复合材料叠层板单元，并考虑了几何非线性和板的成层正交各向异性性质。为了获得较高的计算效率并顺利通过稳定临界点，求解非线性平衡方程采用了变增量步长和柱面弧长法迭代策略。在考证了程序的正确性之后，具体分析了几个工程模型，得出了于工程设计有益的结论。     

自然弯扭梁的非线性分析

研究了两端边界均为完全约束的自然弯扭梁在小应变，大位移和大转动情况下的非线性性质，并考虑了横向剪切变形和扭转翘曲变形的影响，分析中还包括了拉伸，弯曲和扭转的各种弹性耦合。由最小势能原理可以导出所给问题的平衡方程。这里欧拉角可以用来表示任意大的转动。该方法还可方便地推广到其他各种不完全约束边界的情况。此外，利用上述结果还可以得到该梁在小位移理论中的基本方程和有关公式。     

Response of Uncertain Nonlinear Vibration Systems with 2D Matrix Functions

This paper extends the response of uncertain nonlinear vibration systems to vector-valued and matrix-valued functions. Random variables and system derivatives are conveniently arranged into 2D matrices. The method is based on a second order expansion of the governing equations and matrix calculus, Kronecker algebra are used in the mathematical development. The results derived are easily amenable to computational procedures.     

Flux calculation at the interface between two rock types for two-phase flow in porous media

When simulating two-phase flow in porous media, one has to consider the case where there is a discontinuity in the medium. There relative permeabilities and capillary pressure functions may change and we address the problem of calculating the convective part of the numerical flux at the interface between the two rock types. Several solutions are compared.     

平面杆系结构非线性稳定的样条有限元分析法

本文根据ＵＴＬ坐标列式，采用混合样条插值函数，基于虚功原理导出了平面杆系结构非线性稳定的样条有限元分析法。本文方法可以考虑杆件中初始挠度和初始应力的影响，可以计入材料的弹塑性加载卸载效应。算例表明，本文计算结果具有较高的精度。     

齿轮－转子－滑动轴承系统时变非线性动力特性研究

本文应用求周期解的数值计算方法─—打靶法和判定周期解稳定性的Ｆｌｏｑｕｅｔ乘子研究了齿轮－转子－滑动轴承系统中齿轮啮合时变刚度，滑动轴承非线性特性对转子系统不平衡响应和失稳的影响，并比较了平衡位置失稳和不平衡响应周期解失稳，以及按双轴计算与单轴计算结果的差别，为工程设计理论计算提供基础。     

岩质边坡设计坡角和锚固方案的确定

本文运用赤平极射投影、块体理论和岩体力学的基本原理, 试探求一种可供边坡工程设计采用的确定人工岩质边坡最大安全设计坡角和锚固方案的简易方法。     

变温场中具损伤粘弹性矩形板的非线性动力响应分析

基于热粘弹性理论、Von Karman板理论和连续损伤力学,导出了二维状态下各向同性材料的变温粘弹性本构方程,建立了含损伤效应的各向同性粘弹性矩形板在变温场中的非线性运动控制方程,且应用有限差分法对问题进行求解.算例中,讨论了损伤演化及温度场等因素对粘弹性矩形板非线性动力学行为的影响,得出一些有意义的结论.