CALCULATION OF ELASTIC ERROR OF PLANAR MECHANISM—AN EQUIVALENT METHOD

In rigid mechanism dynamic analysis, the equivalence theorem is often used due to its simplicity and perceivability. Based on conjugation and duality between inertia energy storing element and elastic energy storing element, the equivalence theorem is used in elastic error analysis of planar mechanism. A set of calculation formula of elastic error is introduced, and these equations are similar in expression form to the rigid dynamic equation. To demonstrate the method developed, a computation example is given.

3D elastic waveform modeling with an optimized equivalent staggered-grid finite-difference method

Equivalent staggered-grid(ESG) as a new family of schemes has been utilized in seismic modeling,imaging,and inversion.Traditionally,the Taylor series expansion is often applied to calculate finite-difference(FD) coefficients on spatial derivatives,but the simulation results suffer serious numerical dispersion on a large frequency zone.We develop an optimized equivalent staggered-grid(OESG) FD method that can simultaneously suppress temporal and spatial dispersion for solving the second-order system of the 3 D elastic wave equation.On the one hand,we consider the coupling relations between wave speeds and spatial derivatives in the elastic wave equation and give three sets of FD coefficients with respect to the P-wave,S-wave,and converted-wave(C-wave) terms.On the other hand,a novel plane wave solution for the 3 D elastic wave equation is derived from the matrix decomposition method to construct the time-space dispersion relations.FD coefficients of the OESG method can be acquired by solving the new dispersion equations based on the Newton iteration method.Finally,we construct a new objective function to analyze P-wave,S-wave,and C-wave dispersion concerning frequencies.The dispersion analyses show that the presented method produces less modeling errors than the traditional ESG method.The synthetic examples demonstrate the effectiveness and superiority of the presented method.

An analytical solution of equivalent elastic modulus considering confining stress and its variables sensitivity analysis for fractured rock masses

The equivalent elastic modulus is a parameter for controlling the deformation behavior of fractured rock masses in the equivalent continuum approach.The confining stress,whose effect on the equivalent elastic modulus is of great importance,is the fundamental stress environment of natural rock masses.This paper employs an analytical approach to obtain the equivalent elastic modulus of fractured rock masses containing random discrete fractures(RDFs)or regular fracture sets(RFSs)while considering the confining stress.The proposed analytical solution considers not only the elastic properties of the intact rocks and fractures,but also the geometrical structure of the fractures and the confining stress.The performance of the analytical solution is verified by comparing it with the results of numerical tests obtained using the three-dimensional distinct element code(3DEC),leading to a reasonably good agreement.The analytical solution quantitatively demonstrates that the equivalent elastic modulus increases substantially with an increase in confining stress,i.e.it is characterized by stress-dependency.Further,a sensitivity analysis of the variables in the analytical solution is conducted using a global sensitivity analysis approach,i.e.the extended Fourier amplitude sensitivity test(EFAST).The variations in the sensitivity indices for different ranges and distribution types of the variables are investigated.The results provide an in-depth understanding of the influence of the variables on the equivalent elastic modulus from different perspectives.

Effects of fracture distribution and length scale on the equivalent continuum elastic compliance of fractured rock masses

Fracture systems have strong influence on the overall mechanical behavior of fractured rock masses dueto their relatively lower stiffness and shear strength than those of the rock matrix. Understanding theeffects of fracture geometrical distribution, such as length, spacing, persistence and orientation, isimportant for quantifying the mechanical behavior of fractured rock masses. The relation betweenfracture geometry and the mechanical characteristics of the fractured rock mass is complicated due tothe fact that the fracture geometry and mechanical behaviors of fractured rock mass are stronglydependent on the length scale. In this paper, a comprehensive study was conducted to determine theeffects of fracture distribution on the equivalent continuum elastic compliance of fractured rock massesover a wide range of fracture lengths. To account for the stochastic nature of fracture distributions, threedifferent simulation techniques involving Oda＇s elastic compliance tensor, Monte Carlo simulation （MCS）,and suitable probability density functions （PDFs） were employed to represent the elastic compliance offractured rock masses. To yield geologically realistic results, parameters for defining fracture distributionswere obtained from different geological fields. The influence of the key fracture parameters andtheir relations to the overall elastic behavior of the fractured rock mass were studied and discussed. Adetailed study was also carried out to investigate the validity of the use of a representative elementvolume （REV） in the equivalent continuum representation of fractured rock masses. A criterion was alsoproposed to determine the appropriate REV given the fracture distribution of the rock mass.

Equivalent elastic compliance tensor for rock mass with multiple persistent joint sets:Exact derivation via modified crack tensor

Discontinuities constitute an integral part of rock mass and inherently affect its anisotropic deformation behavior.This work focuses on the equivalent elastic deformation of rock mass with multiple persistent joint sets.A new method based on the space geometric and mechanical properties of the modified crack tensor is proposed,providing an analytical solution for the equivalent elastic compliance tensor of rock mass.A series of experiments validate the capability of the compliance tensor to accurately represent the deformation of rock mass with multiple persistent joint sets,based on conditions set by the basic hypothesis.The spatially varying rules of the equivalent elastic parameters of rock mass with a single joint set are analyzed to reveal the universal law of the stratified rock mass.

Influence of random shrinkage porosity on equivalent elastic modulus of casting： A statistical and numerical approach

Shrinkage porosity is a type of random distribution defects and exists in most large castings. Different from the periodic symmetry defects or certain distribution defects, shrinkage porosity presents a random "cloud-like" configuration, which brings difficulties in quantifying the effective performance of defected casting. In this paper, the influences of random shrinkage porosity on the equivalent elastic modulus of QT400-18 casting were studied by a numerical statistics approach. An improved random algorithm was applied into the lattice model to simulate the "cloud-like" morphology of shrinkage porosity. Then, a large number of numerical samples containing random levels of shrinkage were generated by the proposed algorithm. The stress concentration factor and equivalent elastic modulus of these numerical samples were calculated. Based on a statistical approach, the effects of shrinkage porosity's distribution characteristics, such as area fraction, shape, and relative location on the casting's equivalent mechanical properties were discussed respectively. It is shown that the approach with randomly distributed defects has better predictive capabilities than traditional methods. The following conclusions can be drawn from the statistical simulations:(1) the effective modulus decreases remarkably if the shrinkage porosity percent is greater than 1.5%;(2) the average Stress Concentration Factor(SCF) produced by shrinkage porosity is about 2.0;(3) the defect's length across the loading direction plays a more important role in the effective modulus than the length along the loading direction;(4) the surface defect perpendicular to loading direction reduces the mean modulus about 1.5% more than a defect of other position.

STUDY OF THE EQUIVALENT THEOREM OF GENERALIZED VARIATIONAL PRINCIPLES IN ELASTICITY

The relations of all generalized variational principles in elasticity are studied by employing the invariance theorem of field theory. The infinitesimal scale transformation in field theory was employed to investigate the equivalent theorem. Among the results found particularly interesting are those related to that all generalized variational principles in elasticity are equal to each other. Also studied result is that only two variables are independent in the functional and the stress-strain relation is the variational constraint condition for all generalized variational principles in elasticity. This work has proven again the conclusion of Prof. Chien Wei-zang.

THE DETERMINATION OF AN EQUIVALENT ELASTIC MODULUS FOR BODIES WITH CRACKS BY BOUNDARY ELEMENT METHOD

The equivalent elastic modulus of cracked bodies with orderly distributed cracks was computed with the boundary element method. A practical self-consistent scheme has been proposed in consideration of the mutual interaction effects of the cracks. The Influence of friction coefficients and orientation of cracks has been investigated. Some computational examples have been given, and the results show that the proposed method is adequate and the scheme is efficient.

双向密肋楼盖的计算及设计探讨

在双向密肋楼盖的设计中采用弹性板对楼板进行计算分析,但与实际密肋楼盖结构相比,常用软件的计算模型在柱帽区域的计算假定存在重复考虑柱帽厚板与框梁重叠区域、板柱连接区与梁柱连接区重叠区域的问题。针对该问题,对密肋楼盖柱帽区域建立了多种不同计算假定的计算模型,分析了各模型对楼盖构件内力的影响,结果表明:考虑这些计算假定上的差异后,会导致与柱帽区域相连接的构件内力计算结果产生极大的变化。设计中应充分关注这些差异带来的影响,避免出现结构安全问题。此外,对密肋楼盖采用将柱帽格构化为等代梁的分析方法,能够避免过高估计柱帽承载能力,计算结果合理,且能方便对柱帽进行配筋设计。

基于正交试验的蓄能弹簧优化设计

为了提高蓄能弹簧的回弹性能,采用Ansys Workbench有限元软件建立了蓄能弹簧的有限元模型,并通过对比试验验证了模型的可靠性。以弹性能和最大等效应力作为回弹性能的评价指标,探究了薄片宽度、薄片厚度、截面直径、盘绕圈数以及盘绕中径等参数对蓄能弹簧回弹性能的影响。通过正交试验分析了各结构参数对蓄能弹簧的弹性能和等效应力的敏感性。基于弹性能最大和等效应力最小两个目标,对蓄能弹簧的结构参数进行了优化设计。研究结果表明:蓄能弹簧的弹性能随着薄片宽度、薄片厚度、截面直径以及盘绕圈数的增大而增大;最大等效应力随着薄片宽度增大而增大,随着截面直径和盘绕圈数的增大而减小;薄片厚度对弹性能的影响最大,盘绕圈数对最大等效应力的影响最大,而盘绕中径对弹性能与最大等效应力的影响均最小;优化后的蓄能弹簧弹性能提升了190.14%,同时等效应力峰值下降了2.26%。

不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能分析

为研究不同增强方向的带支柱体心立方点阵及其填充结构的压缩力学性能,制备了硅橡胶填充点阵结构试验件。通过试验和仿真方法研究了硅橡胶填充BCC1或BCC2(加载方向分别与带支柱体心立方点阵的支柱杆方向相同或垂直)两种点阵结构的压缩力学性能,并采用铁摩辛柯梁理论和极限载荷法分析了两种点阵结构的等效弹性模量和压缩平台应力。结果表明:提出的理论模型能够很好地预测两种点阵结构的等效弹性模量和压缩平台应力。经过填充后两种点阵结构的压缩强度和吸能性能均会得到增强,BCC2结构的增强效果更加显著。对于BCC1点阵结构,填充提高了其内部杆件的承载力;而对于BCC2点阵结构,填充减小了其“V”形剪切带附近的杆件弯曲变形。随着点阵结构半径的增大,两种结构的吸能耦合因子均先增大后减小,而BCC1型结构的吸能耦合因子变化更明显。

VTI介质流体因子及各向异性参数直接反演方法

储层流体识别是油气勘探领域的重要研究方向。页岩储层具有较强的垂直横向各向同性(Transverse Isotropy with a Vertical Axis of Symmetry,VTI)介质特征,在流体因子估测中带来不容忽视的影响。为此,根据Rüger纵波反射系数方程,提出了一种基于VTI介质弹性阻抗的流体因子、杨氏模量及各向异性参数反演方法。首先,推导以Russell流体因子、杨氏模量和等效各向异性参数表示的反射系数近似公式和弹性阻抗方程;然后,通过弹性阻抗反演估计流体因子、杨氏模量和各向异性参数,并比较了各向异性参数对反演结果的影响。模型测试和实际工区数据应用结果表明,该方法可以合理、准确地预测流体因子、杨氏模量和各向异性参数,为页岩储层流体识别、脆性参数和各向异性发育程度预测提供了一种新的方法。

基于加速度反应谱与地震动持时的地震输入能量谱研究

建立具有设计意义的地震动总输入能量谱是实现结构能量设计的基础。根据中长周期段修正的加速度反应谱及地震动有效持时,提出了一种生成地震动输入能量谱的方法。统计270组人工波的时程分析结果,得到了以等效速度表征的四段式弹性单自由度(single degree of freedom,SDOF)体系总输入能量谱,并给出了不同场地类型、抗震设防烈度等设计条件下归一化等效速度谱的参数取值。在考虑延性系数及刚度折减系数的影响后,提出了弹塑性SDOF体系修正输入能量谱的等效速度谱,估算了引起结构损伤的滞回耗能占总能量的比值。该能量谱可为基于能量的结构设计及研究提供参考。

风力机叶片截面主刚度系数与横向剪应力分析

针对风力机复合材料叶片弯曲与扭转刚度计算,以及当叶片在横向剪力作用下对空心薄壁截面上剪应力的数值计算方法进行研究。现代风力机叶片呈细长扭曲形,翼型截面为薄壁且内部拓扑构型复杂,材料具有各向异性。在应用各类梁模型进行叶片气弹计算和强度校核等力学分析时,叶片截面的刚度系数和截面剪应力分布是必需参数。基于复合材料薄壁结构层合理论和加权平均方法,结合Bredt-Batho剪力理论,考虑了复合材料叶片的剪切腹板效应和翘曲效应,建立了复合材料层合板等效弹性常数与截面刚度系数数值分析算法;根据弹性力学板壳理论,考虑横向剪切和截面翘曲对截面变形的影响,建立了横向剪力引起的剪力流数值计算方法,并开发了相关算法的Matlab程序。分析10 MW风力机叶片主刚度系数和剪力流分布,并对比文献结果,验证了模型的正确性和算法的有效性。

索道用钢丝绳轴向弹性模量有限元仿真研究

轴向弹性模量是索道用钢丝绳重要的力学特性,影响着索道设计中对钢丝绳的选用。应用微分几何理论推导每根钢丝的中心线参数方程,通过Creo建立一个捻距长度的钢丝绳三维模型,将三维模型文件导入Hypermesh中划分网格、设置边界条件,最后利用Abaqus计算得到不同轴向拉力下钢丝绳的变形与等效应力云图,得出钢丝绳拉力与等效弹性模量的关系。结果表明,在拉力较小时,钢丝绳等效弹性模量随拉力增大而增大,当拉力到达一定值后,等效弹性模量稳定在钢丝材料弹性模量的0.64倍。

多点点焊件疲劳寿命分析

根据ST12钢的双点及三点拉剪电阻点焊试件的恒幅疲劳测试结果,分别使用缺口应力法和等效结构应力法进行疲劳寿命预测。在使用缺口应力法时,按试件的实际尺寸和国际焊接学会(International institute of welding, IIW)推荐标准,分别建立了双点和三点拉剪试件的三维实体有限元模型进行弹性应力分析,从有限元分析结果提取von Mises最大应力变化值,结合IIW推荐标准中的S-N曲线对试件进行疲劳寿命分析预测;在使用结构应力法时则采用梁壳混合单元进行有限元应力分析,并且根据主S-N曲线进行疲劳寿命预测。结果表明,在低周疲劳范围内,缺口应力法和等效结构应力法预测的结果相对于试件的实际寿命有较好地相关性,其中等效结构应力法的结果更接近实验寿命结果。

不同弹性模量计算机辅助设计和计算机辅助制造桩核材料的应力分析

背景:桩核修复是牙体缺损修复的一种常规选择,然而不同桩核材料的修复效果存在差异。目的:利用有限元方法评估不同弹性模量桩核修复模型中桩核与牙根黏结剂部位的应力分布情况。方法:在三维建模软件中构建一个三维根管治疗过的上颌中切牙模型,进行全瓷冠修复,修复中的桩核材料分别使用纳米陶瓷树脂(弹性模量12.8 GPa)、复合树脂(弹性模量16 GPa)、混合陶瓷(弹性模量34.7 GPa)、玻璃陶瓷(弹性模量95 GPa)、钛合金(弹性模量112 GPa)和氧化锆(弹性模量209.3 GPa),将模型约束在皮质骨中,在中切牙牙冠舌侧1/3处加载与牙体长轴呈45°的100 N集中力,通过最大主应力分析修复模型中桩核、牙本质及桩与牙根黏结剂的应力分布。结果与结论:(1)当使用弹性模量较高的桩核材料时,修复模型中的桩核应力较集中;当使用弹性模量接近牙本质的桩核材料(纳米陶瓷树脂和复合树脂)时,桩核的应力分布较均匀;无论桩核材料如何,各修复模型中牙本质上的应力分布相似;使用弹性模量更高的桩核时,修复模型中桩与牙根黏结剂处显示出更多的应力集中。(2)纳米陶瓷树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为31.00,33.21,0.51 MPa,复合树脂模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为36.84,33.14,0.59 MPa,混合陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为64.05,32.83,1.00 MPa,玻璃陶瓷模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为112.30,32.69,1.73 MPa,钛合金模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为120.00,32.17,1.86 MPa,氧化锆模型中桩核、牙根及桩与牙根黏结剂处的最大应力值分别为148.80,31.85,2.28 MPa。(3)桩核材料的弹性模量越高,进行桩核修复时桩核处的最大应力值越大,桩核材料弹性模量对修复模型中桩与牙根黏结剂处与牙本质的最大应力值无明显影响。

共固化穿孔纤维增强阻尼薄膜结构面内力学性能研究

共固化穿孔纤维增强阻尼薄膜结构(CCPFRDFE)是一种大阻尼、高层间结合性能的新型阻尼处理模式,在空天技术、尖端武器、快速交通等领域具有广阔的应用前景。但复杂的结构为其力学性能的研究增加了难度,未知的力学性能限制了该新结构的开发与应用。介绍了CCPFRDFE的制作工艺,建立了CCPFRDFE有限元模型,并搭建实验平台对有限元模型进行了验证。利用有限元模型,分别研究了纤维增强阻尼层穿孔孔径、孔距和阻尼材料厚度对CCPFRDFE面内等效弹性参数的影响规律。结果表明,增加穿孔孔径、减小孔距、增加阻尼层厚度有利于提高CCPFRDFE面内等效剪切模量,但不利于提高面内等效弹性模量。所得结果将为非连续阻尼薄复合材料的振动特性研究与大挠度设计奠定基础。

嵌入式共固化缝合阻尼复合材料面内弹性参数

嵌入式共固化缝合阻尼复合材料(embedded co-cured stitched damping composite, ECSDC)相对于传统的复合材料具有高比刚度、高比强度,高层间结合性能及三向力学可设计性等优点。ECSDC在共固化时蒙皮中的树脂处于熔融态后沿缝线贯通整个层合结构形成“复合钉”,复合钉的引入会导致纤维增强阻尼薄膜的面内力学性能分布不均,对ECSDC结构的理论分析造成困难。针对该问题,应用复合钉贯通的面内纤维折线变形模型,将变形区域进行划定,分别建立经、纬纱变形区,富树脂区,缝线等各区域的面内等效弹性参数理论模型,由此过渡到ECSDC结构。采用一个算例,运用ANSYS有限元模拟和Matlab数值计算研究了ECSDC典型结构,并与文献值进行对比,三者所得的结果吻合较好,验证了该理论模型和方法的准确性。在此基础上,用验证的理论模型研究了设计参数对ECSDC面内等效弹性参数的影响。该解析模型建模方法为研究胞元结构复合材料的力学性能提供了参考,为ECSDC结构的动力学与几何非线性研究提供基础。

基于DLP工艺的柔弹性点阵吸能支架研究

面向微小多功能支架结构设计与原型制造需求,开展了基于数字光处理(Digital Light Processing,DLP)快速成形工艺的柔弹性点阵支架设计与制备研究。以胞元结构几何拓扑设计为主线,利用Timoshenko梁理论对胞元结构建立等效力学模型,得到预测能量吸收的数学模型,聚焦分析胞元几何尺寸和承载方向对其影响规律。配置新颖柔弹性光敏树脂为成形材料,选用DLP成形工艺,实现对应点阵结构的高精、高效制备。结合数值模拟和物理实验,着重探究了杆径、胞元边长、点阵层数对点阵结构吸能特性的影响。结果表明,该点阵结构面外压缩较面内压缩具有显著优越的吸能特性,且胞元边长越小,杆径越大,点阵层数越多,吸能特性越佳。理论分析、数值模拟和物理实验所得规律基本一致,可为后续皮肤组织工程支架的研制提供相关理论参考。