一种提高四边形四节点平面壳单元计算精度的新方法

平面壳单元是由平面应力单元和平板弯曲单元叠加组合而成,具有简单的理论表达,但是它在计算曲面壳体结构时误差较大。为了进一步提高平面壳单元的计算精度,本文提出了一种计算平面壳单元刚度矩阵的新方法。通过该方法在高斯积分点建立多个单元局部坐标系,并保证每个局部坐标系都位于单元在高斯点处的切平面上,从而可以有效适应曲面壳体形状,达到进一步提高平面壳单元计算精度的目的。为了在这种新坐标系下计算单元刚度矩阵,给出了求解形函数对局部坐标的导数、局部到自然坐标系积分转换的雅可比、以及局部到整体坐标系的转换矩阵的新型计算方法。通过将这些新坐标系以及新计算方法运用到平面壳单元DKQ24中,可以有效提高平面壳单元尤其是在计算曲面壳体时的精度。计算结果表明,本文方法和平面壳单元相结合,不仅具有平面壳单元简单的理论表达式,还能得到满意的精度。另外,本文方法还可以应用到其他类型的平面壳单元,为提高其他类型平面壳单元的计算精度提供了一种新的途径和思路,具有广阔的应用前景。     

曲面成像法—散斑测量中的一种新方法

本文首次提出,在散斑技术中,采用曲像面代替平像面,以记录物体曲表面运动。作者推导了曲面的曲像面方程及曲面上点的位移与其像点位移之间的关系;证明了任何可展曲面的像面都是可展曲面,可用平底片贴合成形;并给出了平面、圆柱面、圆锥面等特殊可展曲面的像面几何形式。     

辛解析奇异元在动荷载作用下V型切口问题中的应用

利用辛解析奇异单元,结合时域精细算法,研究了动荷载作用下的含平面V型切口问题。时域上,采用时域精细算法,并结合自适应算法控制展开项数,保证了计算精度。空间域上,切口尖端附近采用辛解析奇异单元,其余区域采用常规有限单元,避免了局部网格加密。本文使用的辛解析奇异单元不需要过渡单元和局部网格加密,且能够通过奇异单元内部的参数关系直接给出切口尖端的应力强度因子,不需要复杂的后处理过程。数值结果表明,本文方法具有良好的精度和稳定性,可以准确地计算动态应力强度因子。     

用可退化有限单元进行平面连续体拓扑优化

提出一种基于准则法的平面连续体结构拓扑优化方法。该方法根据单元在结点处的厚度或应力值决定删除单元或将矩形单元退化为三角单元 ,使迭代过程更加平稳。在一定的计算量下 ,提高了计算精度 ,减少了迭代次数 ,使优化结构的边界更加光顺。该方法可同时应用于等厚度和变厚度平面连续体的拓扑优化问题。本文推导了变厚度矩形有限单元的刚度矩阵 ,并给出了相应的拓扑优化迭代方法     

汽车覆盖件工具曲面有限元网格自适应转换方法

提出一种适用于汽车覆盖件曲面有限元网格转化和在单元水平上提高模拟精度的方法,将平面下通过合并三角形单元成四边形单元的有限元网格转换方法的应用范围扩展到曲面,并且降低了对初始网格形状的要求。算法的关键在于增加了对曲面相邻单元不同夹角情况下的处理和优化规则,以使其能够更好地拟合原始CAD曲面。     

基于参数曲面三维势问题的边界面法

提出了边界元法(BEM)的一种新的实现方法——边界面法(BFM)。在传统的边界元法中,单元不仅用来进行边界积分和函数插值,而且用来近似几何体。当离散网格较稀疏时,会引起较大几何误差,因而影响计算精度。本文基于参数曲面,将几何实体的边界曲面离散为参数空间里的曲面单元,边界积分和场变量的插值都是在曲面参数空间里进行。积分点...     

巨型型钢混凝土柱双向偏心受压校核分析方法

利用ETABS截面设计器对某超高层建筑巨型型钢混凝土柱截面进行了双向偏心受压校核分析.首先由ETABS截面设计器得到构件截面相关曲线数据,通过编制的拟合及绘图程序采用空间相关曲面法对构件进行校核分析,针对空间相关曲面法的不足进一步提出了等效平面相关曲线法加以改进.等效平面相关曲线法基于映射原理将空间相关曲面转换成等效平面相关曲线,同时将空间内力点转换成等效内力点,方法直观简便,可在一个图形中给出各工况的校核结果,并且能定量地给出构件受力的安全程度.最后,以一个巨型型钢混凝土柱截面为例给出了等效平面相关曲线法的校核结果,对比了考虑型钢作用及不考虑型钢作用两种情况对巨型柱受力性能的影响.文中提出的方法可为类似工程和建筑结构设计软件的开发提供借鉴.     

基于六面体网格的向量式有限元分析及应用

基于向量式有限元基本原理,给出了八节点六面体等参实体单元的基本公式,通过投影方式将空间曲面六面体转换为投影六面体,采用参考面的逆向运动求解节点纯变形,通过单元形函的虚功方程计算节点内力;针对坐标模式和内力积分模式等关键问题提出了有效的处理方案。编制了六面体实体单元的数值计算程序,并进行工程结构算例分析。结果表明,所编制程序可有效模拟实体结构的静力、动力及大变形大位移行为分析,验证了本文理论和程序的正确性和实用性。     

基于六面体网格的向量式有限元分析及应用

基于向量式有限元基本原理,给出了八节点六面体等参实体单元的基本公式,通过投影方式将空间曲面六面体转换为投影六面体,采用参考面的逆向运动求解节点纯变形,通过单元形函的虚功方程计算节点内力;针对坐标模式和内力积分模式等关键问题提出了有效的处理方案。编制了六面体实体单元的数值计算程序,并进行工程结构算例分析。结果表明,所编制程序可有效模拟实体结构的静力、动力及大变形大位移行为分析,验证了本文理论和程序的正确性和实用性。     

空间杆系结构实用几何非线性分析

从简单实用的角度论述了空间杆系结构的几何非线性分析方法。文中分析了非线性有限元方法的求解过程,特别强调决定几何非线性收敛结果的关键问题,即由节点位移增量计算单元的内力增量。通过引入转随转坐标系,论述了平面和空间梁单元小应变时单元内力增量的计算问题。针对杆系结构的大应变问题,从有限应变理论出发进行分析,提出了对该问题的有效处理方法,并且用实例进行了验证。计算结果表明,该实用几何非线性分析方法是可靠和有效的。     

Photography without lenses

Good photographic records fo brittle coating, photoelasticity and moiré patterns can be obtained in certain cases by direct contact of the specimen and the photographic film. No lenses are required. Several examples of application of the technique are given. The method is particularly useful when brittle coating or moiré are applied to transparent curved developable surfaces.     

贴片散斑法及其应用

贴片散斑法将一种可剥离铝箔贴附在试件表面,经随机划痕制栅后,以其精细的光学结构和高度的反射本领,在白光或激光照射下,表面辐射率随机分布函数作为散斑场,采取直接记录手段,用全息底片对此作物体变形前后的两次曝光,所得到的散斑底片将包含宽广的空间频谱范围,且全场分析条纹清晰、灵敏度高、量程调节范围大。此方法不仅适用于各种材料的直接散斑法测量,具有经济、可靠、操作简便的特点,还能应用于平面及可展曲面构件的现场量测。     

曲面曲率对Rayleigh波传播特性的影响

对任意形状的均匀各向同性线弹性曲面物体,用 WKB～（1）方法求解了沿曲面传播的Rayleigh表面波的运动微分方程,同时考虑了波传播方向及其垂直方向曲面曲率对波的穿透性的影, 所获波动方程的势函数解答表明,在一般情况下垂直波传播方向的曲面曲率对波的穿透深度的影响是不容忽视的.进而以同种介质平面表面情况下的Rayleigh面波的传播特性为基准,给出了曲面曲率引起波数或波速变化的解析表达式.通过理论分析和数值算例,描述了曲面上Rayleigh面波传播行为的一些基本特征.     

Infinitesimal Isometries on Developable Surfaces and Asymptotic Theories for Thin Developable Shells

We perform a detailed analysis of first order Sobolev-regular infinitesimal isometries on developable surfaces without affine regions. We prove that given enough regularity of the surface, any first order infinitesimal isometry can be matched to an infinitesimal isometry of an arbitrarily high order. We discuss the implications of this result for the elasticity of thin developable shells.     

Shape gradient and classical gradient of curvatures: driving forces on micro/nano curved surfaces

Recent experiments and molecule dynamics simulations have shown that adhesion droplets on conical surfaces may move spontaneously and directionally. Besides, this spontaneous and directional motion is independent of the hydrophilicity and hydrophobicity of the conical surfaces. Aimed at this important phenomenon, a general theoretical explanation is provided from the viewpoint of the geometrization of micro/nano mechanics on curved surfaces. In the extrinsic mechanics on micro/nano soft curved surfaces, we disclose that the curvatures and their extrinsic gradients form the driving forces on the curved spaces. This paper focuses on the intrinsic mechanics on micro/nano hard curved surfaces and the experiment on the spontaneous and directional motion. Based on the pair potentials of particles, the interactions between an isolated particle and a micro/nano hard curved surface are studied, and the geometric foundation for the interactions between the particle and the hard curved surface is analyzed. The following results are derived: (a) Whatever the exponents in the pair potentials may be, the potential of the particle/hard curved surface is always of the unified curvature form, i.e., the potential is always a unified function of the mean curvature and the Gaussian curvature of the curved surface. (b) On the basis of the curvature-based potential, the geometrization of the micro/nano mechanics on hard curved surfaces may be realized. (c) Similar to the extrinsic mechanics on micro/nano soft curved surfaces, in the intrinsic mechanics on micro/nano hard curved surfaces, the curvatures and their intrinsic gradients form the driving forces on the curved spaces. In other words, either on soft curved surfaces or hard curved surfaces and either in the extrinsic mechanics or the intrinsic mechanics, the curvatures and their gradients are all essential factors for the driving forces on the curved spaces. (d) The direction of the driving force induced by the hard curved surface is independent of the hydrophilicity and hydrophobicity of the curved surface, explaining the experimental phenomenon of the spontaneous and directional motion.     

Beam generating and sound field modeling of flexible phased arrays for inspecting complex geometric components

The flexible phased array ultrasonic technology has been developed to tackle the long-term challenge of damage inspection in complex-profiled components. However, due to the influences of curved interfaces, it is sometimes difficult to control the transmission signal of the sound field, thereby creating unreliable transducer performances. This paper proposes the time delay laws for generating steering or focusing beams on curved surfaces (concave, convex, concave/convex) based on the ray acoustics theory. Then, we derive the analytic expression of the entire flexible array ultrasonic field based on the multiple line source model and the time delay laws. Finally, the acoustic pressure distribution of curved structures is simulated to verify the feasibility of the derived principles. The numerical results show that the beams can realize dynamic steering and focusing without distortions or disorientations even when the steering angle reaches 45 degrees. Furthermore, the influences of the specimen surface profile, steering angle and focusing distance on the acoustic field are also analyzed by the axial sound pressure plots. These preliminary results represent an essential step in the development of a nondestructive testing (NDT) system for inspecting components with complex surfaces.     

Curved laser-sheet for conformal surface flow diagnostics

Three-dimensional surface illumination using curved laser-sheet techniques is introduced for optical flow measurements in conformal curved surfaces. The illumination method is applicable to many different optical-based flow measurement techniques, with this paper focusing on application to flow visualization and particle image velocimetry. A brief discussion and example of curved laser-sheet generation is given followed by an example of the technique applied to PIV of low Reynolds number transitional flow around a low-pressure turbine blade.     

含刚性体可展开结构的展开过程动力学分析方法

在可展结构中设置刚性体可以有效提高展开效率,保证形状精度,因此含刚性体可展结构具有较高的实用价值。刚性体按需要可为刚性曲板等,一般形状复杂且形式多样,含任意形状刚性体可展结构的展开过程动力学分析比较困难。本文以笛卡尔坐标系下节点坐标及位移为变量,利用广义逆矩阵建立了一种通用的刚性体动力学方程,给出了利用Newmark—...     

薄壁曲梁的稳定性研究进展

 曲梁是桥梁、建筑、船舶、航空和航天工程中常见的薄壁构件，根据外载荷与主曲率平面的关系，又被称为拱或水平曲梁．随着工程材料的日益发展，如复合材料、功能梯度材料的引入，曲梁的应用范围更加广泛，进一步推进了薄壁曲梁稳定性问题的研究．本文首先对薄壁梁结构的稳定性行为进行了分类．接着简述了薄壁构件的基本假设，对比了近几十年来薄壁曲梁的基本理论，针对复合材料薄壁曲梁，总结了相应的本构关系，并对各理论间存在的分歧进行了归纳．结合最新的薄壁曲梁研究，根据平衡法、能量法和虚位移（虚功）原理推导出控制微分方程，阐述了相应的求解方法，如解析法、半解析法和数值解法．为验证薄壁曲梁理论的准确性，曲梁承载能力试验验证尤为重要，但目前国内外相关研究还很少，亟待发展．最后讨论了现阶段薄壁曲梁研究的局限性和未来发展的方向．     

Numerical modeling of three-dimensional vortex structures in hypersonic transverse flow past a cylinder

A new mechanism of the formation of spatially periodic structures on the nose surfaces of cylindrically blunted bodies in a hypersonic transverse flow is investigated. According to this mechanism, a curved shock wave produces a vortex flow, while the vortex, which is conserved in the presence of weak dissipation, acts on the shock and maintains its curved shape. The realizability of this vortex formation mechanism is verified by direct numerical simulation using the FLUENT software package. It is confirmed that in the case of uniform hypersonic freestream both plane and three-dimensional modes of the steady flow past the cylinder nose can exist. The three-dimensional mode is characterized by periodic-in-span vortex structures and considerable heat flux peaks on the nose surface. The calculated results are compared with the experimental data.