REFINED HYBRID MINDLIN PLATE ELEMENT FOR GEOMETRICALLY NON LINEAR ANALYSIS

Based upon a generalized variational principle, which relaxed the inter element continuity requirements, a novel refined hybrid Mindlin plate element is developed, its non linear element stiffness matrices are decomposed into a series of matrices with respect to the assumed strain modes. The formulation presented in this paper is different from any other non linear mixed/hybrid element formulation all successful experience of linear hybrid formulation is absorbed into the formulation(adding non conforming modes and realizing orthogonalization) Numerical results show that the present approach is more effective than any other non linear hybrid element formulation over the accuracy and computational efficiency. In addition, non conforming modes can also overcome the shear locking effect.

Geometrically Nonlinear Random Responses of Stiffened Plates Under Acoustic Pressure

An algorithm integrating reduced order model(ROM),equivalent linearization(EL),and finite element method(FEM)is proposed to carry out geometrically nonlinear random vibration analysis of stiffened plates under acoustic pressure loading.Based on large deflection finite element formulation,the nonlinear equations of motion of stiffened plates are obtained.To reduce the computation,a reduced order model of the structures is established.Then the EL technique is incorporated into FE software NASTRAN by the direct matrix abstraction program(DMAP).For the stiffened plates,a finite element model of beam and plate assembly is established,in which the nodes of beam elements are shared with shell elements,and the offset and section properties of the beam are set.The presented method can capture the root-mean-square(RMS) of the stress responses of shell and beam elements of stiffened plates,and analyze the stress distribution of the stiffened surface and the unstiffened surface,respectively.Finally,the statistical dynamic response results obtained by linear and EL methods are compared.It is shown that the proposed method can be used to analyze the geometrically nonlinear random responses of stiffened plates.The geometric nonlinearity plays an important role in the vibration response of stiffened plates,particularly at high acoustic pressure loading.

带线性红利和干扰的复合Poisson-Geometric风险模型的破产问题

考虑了常利力环境下,包含线性红利、随机干扰和随机保费的复合P-G风险模型。通过应用全期望公式,推导出该模型的Gerber-Shiu函数及破产概率的更新方程。在不考虑分红且保费额和索赔额均服从指数分布时,进一步得到了破产概率所满足的具体微分方程,并求解得到了其解析表达式。通过数值实验,系统分析了多个关键因素对破产概率的具体影响,所得结论与保险公司的实际经营情况相吻合。

Geometric interpretation of several classical iterative methods for linear system of equations and diverse relaxation parameter of the SOR method

Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective.

Non-Linear Effects in Optical Systems by Lie Algebra and Symplectic Mapping

The use of signals of different frequencies determines the geometrical deviation with respect to the optical axes of a given beam. This angle can be determined by Sympletic Map (SM), a powerful and simple mathematical tool for the characterization and construction of images in Geometrical Optics. The Sympletic Map constitutes a Lie Group, with an algebra associated: the Lie Algebra. In general, the SM can be expressed as an infinite series, where each term corresponds to different contributions produced by the optical devices that constitute the optical system (lenses, apertures, bandwidth cutoff, etc.). The level of correction to be performed on the image to recover the original object is clear and controllable by SM. This formalism can be extended easily to physical optics to describe diffraction and interference phenomena.

线性红利下带干扰的复合Poisson-Geometric风险模型

研究了常利力下存在红利界限和随机干扰的风险模型,其中保费收入为复合Poisson过程、索赔为复合Poisson-Geometric过程。利用全期望公式和Ito公式,得到了该模型下保险公司的生存概率和红利付款的期望现值分别满足的积分微分方程。

Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM

The existing concepts of picture fuzzy sets(PFS),spherical fuzzy sets(SFSs),T-spherical fuzzy sets(T-SFSs)and neutrosophic sets(NSs)have numerous applications in decision-making problems,but they have various strict limitations for their satisfaction,dissatisfaction,abstain or refusal grades.To relax these strict constraints,we introduce the concept of spherical linearDiophantine fuzzy sets(SLDFSs)with the inclusion of reference or control parameters.A SLDFSwith parameterizations process is very helpful formodeling uncertainties in themulti-criteria decisionmaking(MCDM)process.SLDFSs can classify a physical systemwith the help of reference parameters.We discuss various real-life applications of SLDFSs towards digital image processing,network systems,vote casting,electrical engineering,medication,and selection of optimal choice.We show some drawbacks of operations of picture fuzzy sets and their corresponding aggregation operators.Some new operations on picture fuzzy sets are also introduced.Some fundamental operations on SLDFSs and different types of score functions of spherical linear Diophantine fuzzy numbers(SLDFNs)are proposed.New aggregation operators named spherical linear Diophantine fuzzy weighted geometric aggregation(SLDFWGA)and spherical linear Diophantine fuzzy weighted average aggregation(SLDFWAA)operators are developed for a robust MCDM approach.An application of the proposed methodology with SLDF information is illustrated.The comparison analysis of the final ranking is also given to demonstrate the validity,feasibility,and efficiency of the proposed MCDM approach.

AN IMPROVEMENT ON UNCONSTRAINED CONVEX PROGRAMMING APPROACH TO LINEAR PROGRAMMING

For satate form linear gram as Fang and sao deined and approach which would find an optimal solution by solving an anconstrained convex dual programming.Thedual was construcied by applying an emropic peturbation and a simple Inequality Inz【z-1 for z】0n,In this paper,we suggest than a paperbation functiontake the place of Inx such that the new approdt has good numerical stability andhas all properties of the original

高精度地形星载激光测高仪在轨几何标定方法

激光测高仪数字化标定方法由于标定频次高、人力物力消耗少等突出性优点越来越受到关注。本文提出了一种两步法的激光测高仪数字化标定方法,针对线性体制激光测高仪的几何定位模型,构建了关于翻滚角、俯仰角和测距系统误差的几何标定模型,并使用公开参考地形数据SRTM与高精度机载LiDAR点云进行了标定试验。与GF-14实际外场面探测器试验标定的数据比较分析。结果显示,本文提出的几何标定方法与地面探测器标定参数测角差异在0.5角秒以内,测距差异在0.2 m以内。通过独立数据验证标定结果的高程精度,本文提出的数字化标定方法和探测器标定方法的足印高程偏差表现出良好的一致性,两种方法标定所获取的足印高程与高精度机载点云高程的RMSE均优于0.3 m。本文方法在保证精度的同时,减少了人力物力的消耗,为星载激光测高仪在轨常态化标定提供了新的思路和方法。

基于共旋坐标法的几何非线性裂纹梁单元

现有有限元软件模拟裂纹结构主要采用指派裂纹的实体和壳单元,但缺少梁单元。因此,在弹性梁单元的曲率函数中引入Dirac-δ函数表征局部损伤的曲率变化,得到位移分布函数;推导出应变矩阵和单元刚度矩阵,提出了裂纹梁单元。基于共旋坐标法理论进一步发展了考虑裂纹损伤的几何非线性裂纹梁单元,给出了单元的具体算法及流程。利用课题组开发的有限元求解框架,在程序中实现了裂纹梁单元及共旋列式裂纹梁单元。经过典型算例,对比分析了裂纹位置、裂纹深度及外荷载对裂纹梁弯曲性能的影响。结果表明:该单元能够准确描述裂纹结构的挠度变化,同时与现有模拟裂纹结构弯曲变形的单元相比,提出的裂纹梁和共旋列式裂纹梁在精度分别提高了约1%和4%,并且能够退化成无损伤的梁单元和几何非线性梁单元。

织构几何参数对超疏水钛合金表面润湿性的影响

目的研究表面织构几何参数对超疏水钛合金表面润湿性的影响规律。方法利用纳秒激光在钛合金表面构筑不同织构间距、边长和形状的微织构,通过氟硅烷改善钛合金表面的润湿性;借助电子扫描显微镜(SEM)观察钛合金表面织构,利用接触角测量仪表征织构表面接触角;通过多元线性回归方法研究织构参数对钛合金表面润湿性的影响规律。结果氟硅烷改性试样表面静态接触角达到150°,满足超疏水要求,各织构表面滚动角基本稳定在4°~11°,满足疏水要求。当钛合金表面织构间距在0~0.6 mm变化时,织构相对试样表面的占比从80%至20%发生不等变化,随织构占比的减小,织构表面静态接触角明显下降,滚动角呈上升趋势。当织构边长在0~0.6 mm变化时,液滴在不同织构图案上的接触角变化并不一致,正方形钛合金表面接触角从164.6°增加到170°,而圆形、三角形钛合金表面接触角减小,分别从166.9°降低到162.1°、从169.6°降低到160.2°,滚动角呈先增后减的趋势。结论织构几何参数变化对试样表面润湿性有显著影响。织构间距不同会改变织构占比,织构图案几何特征的不同会影响表面润湿性,并且表面润湿性随织构面积的改变而显著变化。通过研究典型织构几何参数对表面润湿性的影响有利于进一步深入理解织构特征对表面润湿性的影响,为未来设计具有多元功能化的表面结构具有重要意义。

几何特征重要度算法支持下的大规模线状要素地图综合方法

面向地理信息单个矢量瓦片数据在地图缩放级别较低时出现的大规模线状要素地图渲染效率低的问题,本文提出了一种几何特征重要度算法支持下的大规模线状要素地图综合方法。该方法提出了线要素几何特征重要度指数,作为线要素删除时的排序依据,从而实现顾及数据全局特征的线要素自动综合,既保留了单个矢量瓦片上的主要几何信息,又有效提高了地图渲染的效率。以“天地图·甘肃”矢量数据为例的试验结果表明,通过应用本文方法,线要素渲染速度比原来提升了3倍。

线性代数教学中若干“可视化”教学案例

本文从几何角度出发,介绍了低维情况下的线性空间、线性变换、矩阵、行列式这些线性代数基本概念的几何含义,旨在帮助初学线性代数的同学并为后续掌握高维空间的内容打基础.

基于Li-Strahler几何光学模型的区域人工林郁闭度反演

森林郁闭度是描述森林结构的一个重要因子,传统的森林郁闭度遥感反演经验模型对地面样地数据要求较高,且反演难以推广至区域尺度。针对上述问题,文章提出了一种结合Li-Strahler几何光学模型与线性光谱分解技术的区域人工林郁闭度反演方法,以小班为基本单元利用不同优势树种的平均树高与平均冠幅半径等几何光学模型输入参数,基于混合像元线性光谱分解提取的光照地表分量丰度,实现郁闭度参数的反演。基于该方法分别在北方赤峰以及南方南宁研究区开展区域人工林郁闭度反演,并通过野外样地实测数据对估测结果进行精度验证,精度评价结果表明:北方赤峰研究区平原区域反演的均方根误差为0.08、平均绝对百分比误差为9.45%,山地区域反演的均方根误差为0.12、平均绝对百分比误差为14.04%;而南方南宁研究区平原区域反演的均方根误差为0.11、平均绝对百分比误差为8.68%,山地区域反演的均方根误差为0.13、平均绝对百分比误差为13.27%。上述结果表明文章提出的郁闭度遥感反演方法能够有效提升区域人工林郁闭度的估测精度,具有重要的应用价值。

地铁营业线几何线形病害整治全过程测量技术应用研究

地铁线路经过长时间运营,其轨道几何姿态均出现了不同程度的病害,为有效保障城市轨道安全平稳运营,急需开展几何线形病害专项整治。在独立空间两级控制的基础上,利用高精度测量手段采集现场数据,研发三维几何线形拟合系统,对地铁营业线几何线形病害整治进行测量及施工指导。结果表明,该套测量技术贴合现场施工需求,实现了全过程控制,推进了维保施工数字化建设,相对现有技术减少30%工作量。

空间六边形提篮拱安装线形算法研究

异形拱肋安装过程中,易出现控制点不能通视或棱镜无法保持垂直等情况,需重新计算新建控制点安装坐标。而拱肋处于空间倾角姿态,坐标计算极为复杂、计算量大,且对加工偏差的节段修正难度大,安装线形控制极为困难。针对实际问题,同时考虑有限元计算得到的预拱度值,将空间拱肋结构转化为几何模型,提出了一种空间六边形提篮拱安装控制点坐标参数化算法。通过合龙后线形测量结果发现,本方法具有较高的计算精度,且有效地解决了拱肋安装过程中新建控制点坐标计算的时效性和准确性。

基于蚁群算法的无人机协同任务规划研究

无人机搜寻具有机动性强、定位精度高的优势。本文结合实际情况,模拟红蓝两方的无人机协同海域规划问题。一是协同搜索问题,利用BFS算法先将热力图可视化,根据蚁群算法将红方无人机最优搜索路线规划出来,再利用K-means聚类算法将多架无人机分配到多个区域,实现无人机协同搜索。二是全区域覆盖问题,通过计算区域圆度是否大于0.86判断是用螺旋法还是割草法搜寻方式,实现全区域覆盖。根据不同的搜寻模式对热点区域进行分割处理,建立蓝方搜寻船的机动模型。

大跨悬索桥非线性随机静力分析

大跨度悬索桥结构具有显著的几何非线性行为,且存在材料特性、几何尺寸的随机性.先对缆索采用较小抗弯刚度参数的梁单元,对悬索桥进行确定性的几何非线性分析;然后采用响应面法进行非线性随机静力分析;最后针对1座大跨悬索桥,计算了在竖向活载作用下材料、几何尺寸的随机性对主梁跨中位移的影响.结果表明,结构随机性的影响十分明显.

INS/DGPS支持的机载线阵推扫影像几何校正

论述了利用INS/DGPS系统的导航输出计算外方位元素的原理,介绍了行方位数据支持下机载线阵CCD影像直接和间接法几何校正的基本方法,重点分析并解决了直接法纠正中的目标定位、灰度重采样及间接法校正中最佳扫描行的确定问题。PH I高光谱影像的实验结果表明,文中的校正算法可达到优于1.5m的绝对定位精度及0.7m的相对精度。

基于平行光管的CCD相机标定新方法

阐述了一种由二维精密转台、平行光管和CCD相机构成的光学实验室相机标定的方法.首先通过Hough变换和最小二乘模板匹配方法得到平行光管十字丝钣孔在CCD相机焦平面上的成像交叉点的位置,然后根据相机畸变模型,由最小二乘回归解算出内方位元素和畸变参数,实验证明该方法标定结果满足空三处理和测图精度的要求.