A Nonlinear Theory of Elastic Plates without Using Kirchhoff-Love Assumptions and Its Application

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Mathematical framework of nonlinear elastic waves propagating in pre-stressed media

Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.

Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

The dynamic behavior of a rectangular crack in a three-dimensional （3D） orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional （2D） Fourier transform is applied, and the mixed- boundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Monitoring the change in horizontal stress with multi-wave time-lapse seismic response based on nonlinear elasticity theory

Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.

Factors influencing pore-pressure prediction in complex carbonates based on effective medium theory

A calculation model based on effective medium theory has been developed for predicting elastic properties of dry carbonates with complex pore structures by integrating the Kuster-Toksǒz model with a differential method.All types of pores are simultaneously introduced to the composite during the differential iteration process according to the ratio of their volume fractions.Based on this model,the effects of pore structures on predicted pore-pressure in carbonates were analyzed.Calculation results indicate that cracks with low pore aspect ratios lead to pore-pressure overestimation which results in lost circulation and reservoir damage.However,moldic pores and vugs with high pore aspect ratios lead to pore-pressure underestimation which results in well kick and even blowout.The pore-pressure deviation due to cracks and moldic pores increases with an increase in porosity.For carbonates with complex pore structures,adopting conventional pore-pressure prediction methods and casing program designs will expose the well drilling engineering to high uncertainties.Velocity prediction models considering the influence of pore structure need to be built to improve the reliability and accuracy of pore-pressure prediction in carbonates.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Nonlinear free vibration of piezoelectric cylindrical nanoshells

The nonlinear vibration characteristics of the piezoelectric circular cylindrical nanoshells resting on an elastic foundation are analyzed. The small scale effect and thermo-electro-mechanical loading are taken into account. Based on the nonlocal elasticity theory and Donnell's nonlinear shell theory, the nonlinear governing equations and the corresponding boundary conditions are derived by employing Hamilton's principle. Then,the Galerkin method is used to transform the governing equations into a set of ordinary differential equations, and subsequently, the multiple-scale method is used to obtain an approximate analytical solution. Finally, an extensive parametric study is conducted to examine the effects of the nonlocal parameter, the external electric potential, the temperature rise, and the Winkler-Pasternak foundation parameters on the nonlinear vibration characteristics of circular cylindrical piezoelectric nanoshells.

Against Phase Veloсities of Elastic Waves in Thin Transversely Isotropic Cylindrical Shell

This paper receives the characteristic equation for the determine of wave numbers of phase velocities of elastic waves, in the thin cylindrical shell with the help of the dynamic theory of the elasticity for the transversely isotropic medium and of the hypothesis of thin shells.

Winkler弹性介质中多孔功能梯度材料截锥壳的弯曲

弹性介质中板壳结构的力学特性研究,大都假设结构体在变形过程中始终与介质紧密接触。为研究可脱离的Winkler弹性介质中含孔隙功能梯度材料截锥壳在环向荷载作用下的弯曲问题,以陶瓷材料质量分数、体积指数和孔隙率为控制参数,根据混合律计算含均匀孔隙功能梯度材料的物性参数。基于Donnell经典薄壳理论和Hamilton原理,建立Winkler弹性介质和环向荷载共同作用下截锥壳的平衡方程和变形协调方程。考虑锥壳两端简支边界条件,采用Galerkin积分法求解得到截锥壳弯曲挠度的解析解。研究在弹性介质与壳体接触和脱离两种情况下,孔隙率、功能梯度材料组成和截锥壳尺寸等因素对壳体挠度值的影响。结果表明,截锥壳挠度值随着孔隙率、体积指数、壳体长径比、径厚比和半锥角的增大而增大,随着陶瓷质量分数的增大而减小。截锥壳与Winkler弹性介质接触时的挠度值比脱离时小,这是因弹性介质对壳体有一定的反作用力。在截锥壳母线方向上,其中部的挠度值较大,而由中部到两端的挠度值逐渐减小;在截锥壳环向方向上,其挠度值呈现周期变化。分析多孔FGM截锥壳在弹性介质和环向荷载作用下的弯曲问题,为FGM截锥壳在工程领域中的应用提供了理论基础。

地震构造类比法的应用——以川东地区华蓥山断裂带为例

本文通过野外地震地质考察和系统的年代学样品的采集与测试，对华蓥山断裂带的第四纪活动性进行了讨论，并分析了该断裂带可能存在的分段特征。在对川东地区为数不多的中强地震震例分析的基础上，探讨了川东地区中强地震（Ｍｓ＝４７－５７）的发震构造条件。以此为依据，确定了华蓥山断裂带中段的最大可能潜在地震能力。

多因素组合影响阶段矿柱上采顶板临界厚度研究

采用散体充填法的矿山,由于充填体无法直接暴露,阶段矿柱回采临界厚度的保留成为残矿回收的突出难题。基于传统弹性梁理论,结合实际情况,将阶段矿柱简化为均布载荷下两端固定的弹性梁力学模型,推导了其弹性应力解,揭示了x?是阶段矿柱上采过程的第1破坏应力。理论分析表明:影响矿柱上采顶板临界厚度的主要因素为:散体载荷、回采跨度和岩体抗拉强度。利用FLAC3D完成了多因素组合影响阶段矿柱上采过程数值模拟正交试验,分析了单一影响因素与顶板临界厚度的关系,利用多元非线性回归的数学方法,建立了上采过程三因素组合影响下阶段矿柱临界厚度数学预测公式。最终,实现了散体介质下阶段矿柱上采临界厚度的预测。结合凤凰山铜矿-240 m阶段矿柱回采实际,表明了该预测公式的适用性。

节理岩体双重非线性弹性介质中的纵波传播特性

基于应力-应变关系中包含三阶非线性项的岩石介质和非线性法向变形节理模型,结合波动方程特征线法,得到在非线性岩石介质中纵波法向入射单节理时透射波的半数值解,并编写计算程序。对波源参数、节理参数和岩石非线性、节理位置等进行一系列参数研究,探讨节理岩石双重非线性弹性介质对透射波波形、透射系数和频谱分布的影响。研究结果表明,岩石的非线性系数会对节理的高频滤波作用以及节理面质点位移的恢复路径产生影响。双重非线性作用下的透射波除了和线性岩石中一样受节理参数、波源参数的影响外,还与节理位置和岩石的非线性系数有关。在纵波受岩石非线性作用较大的情况下,频率相同振幅较小的纵波的透射系数较大。大振幅波在双重非线性的影响下,透射波中会产生一系列高谐波,该高谐波是应力波受岩石和节理综合作用的结果。

双相介质分界面上弹性波的反射与透射

本文基于Biot理论,推导出Zoeppritz形式的双相介质分界面上弹性波的反射与透射公式,对单相Zoeppritz公式与双相反射系数公式进行了比较,对双相介质含油、水、气不同流体时的反射规律以及孔隙度、渗透率、饱和度等储层参数对纵波反射的影响进行了研究.数值模拟分析表明,双相与单相反射公式的主要差异在于双相介质反射公式中考虑了液相、固液耦合相弹性模量的影响;油砂、水砂、气砂岩的慢P波反射差异明显;快P波反射对孔隙度的变化敏感,饱和度次之,对渗透率和频率的变化不敏感.

地球各向异性介质中地震波动理论、检测与应用研究

地下岩石的各向异性主要表现在地震波速度随传播方向发生变化，不同类型体波间相互耦合，横波发生分裂，波速度频散依赖于传播方向等。薄互层与裂隙定向分布等产生视各向异性，它在石油地震勘探、地震预测和岩石圈物理与动力学研究中有极大潜力和应用前景，并受到广泛重视。为此，文中讨论了地震各向异性研究在解决地球科学问题中的重要性与必要性；系统地介绍了中国在地震各向异性研究领域的各个方面，如波动传播、波场激发、数值模拟、偏移与反演成像，以及应用于油气资源探测、深部地球物理研究和地质灾害监测等方面所取得的新进展。结合笔者参加的第八届地震各向异性国际学术讨论会，及ＳＥＧ，ＩＡＳＰＥＩ，ＩＵＧＧ等有关学术会议情况，综述了国际上在该领域内的主要成果与发展动向，分析了国际上各国地震各向异性研究现状及存在问题，并对我国在该领域研究的进一步开展提供了主攻问题与相应建议。

低渗透油藏的非线性渗流理论探讨

针对拖市低渗透油田储集层天然裂缝发育、开发过程中油层渗透率非常数、地下流体渗流不服从达西定律的性质,从变形介质渗流理论研究入手,建立了变形介质带启动压力梯度的非线性渗流的数学模型,推导出了变形介质非线性稳定渗流条件下,油井的产油量和压力计算公式,并对弹性介质达西渗流、变形介质达西渗流、弹性介质非达西渗流和变形介质非线性渗流条件下,油井产油量进行了对比分析,研究表明在相同生产压差下,变形介质非线性渗流条件下油井产油量最低。

对基于渗透注浆理论公式的探讨

把土体当作理想塑性体，根据材料服从Ｔｒｅｓｃａ 屈服准则，并结合Ｍａｇｇ 公式，按球体扩张理论推导出点状注浆时，劈裂地层中浆液的扩散半径、注浆压力和注浆时间，经与实测对比较为吻合。

深基坑降水引起的地面沉降预测

由于上海地区有较高的承压水位,深基坑施工时,为了基坑的稳定,有时需要大深度的降水来保证。由于基坑内外地下承压水连续相通,降水影响范围大,引起坑外地面产生沉降,对周围建筑物和管线造成不利影响。针对浅层承压含水层基坑降水,以粘弹性理论和随机介质理论为基础,推导了一种新的基坑降水引起地面沉降的计算方法。该方法通过Merchant流变模型模拟抽水条件下土的应力-应变关系来反映抽水引起含水层变形的时间效应,以随机介质理论反映地面沉降的空间分布规律,能够较好地预测基坑降水引起的地面沉降。最后通过计算实例对该方法进行了验证。

西安地铁盾构施工地表沉降随机介质预测研究

研究目的:针对应用随机介质理论预测盾构施工过程中诱发的地表沉降量时盾尾隧道断面收敛量的确定问题,文中在考虑盾构施工工艺的基础上,结合工程地质条件,并运用弹性力学的相关理论知识计算出随机介质理论预测地表沉降所需的参数。本文意在利用随机介质理论预测地表沉降量时,将预测计算所需参数可以进行量化计算,并能对影响其大小的各个因素针对施工环境进行优化。研究结论:通过对西安地铁隧道盾构施工诱发的地表沉降分析表明:(1)在盾尾断面收敛量的影响因素中,偏心超挖的影响最为敏感,而且最不容易控制;(2)盾尾应力释放引起的收敛变形是控制地表沉降的关键因素,而在弹性变形范围内,适当的增大注浆压力可以控制盾尾应力释放引起的隧道断面收敛量,有效地减小地表沉降;(3)使用本文提出的计算断面收敛量的方法并结合随机介质理论预测得到的地表沉降数据和沉降曲线趋势与实际结果符合;可对土体结构致密、强度较高的黄土地层中盾构施工中地表沉降控制措施的采取提供一定的理论依据。

含单组节理的双重非线性弹性岩石介质中的P波传播规律

为研究含单组节理的双重非线性弹性岩石介质中的P波传播规律,在空间域内设置许多间距极小、刚度极大的假节理。对特定节理位置赋予节理非线性变形BB模型,结合非线性波传播的特征线方程,得到一维P波传过含单组不同条数节理的双重非线性弹性岩石介质时透射波的时域半数值解。编写有限差分程序,利用已有计算实例对程序进行验证,并通过计算模拟作进一步参数研究。详细讨论P波参数、节理力学参数、节理条数、节理间距和岩石非线性系数对透射波首波与后续波波形、首波透射系数、首波与后续波能量的影响。研究结果表明,随着传播距离的增大,大振幅且低频的P波波形发生畸变;小振幅且低频的P波对岩石的非线性作用不敏感。节理间距和岩石非线性系数对首波透射系数、首波能量和后续波能量产生不同程度的影响。振幅较小、频率较高的P波传过条数较多的单组节理时,节理表现出明显的滤波和分解能量的作用。

大变形耦合热弹性动力学的变分原理

应用半反推法及动态差分变换和初终值条件的新处理法 ,建立了各向异性线性材料大变形耦合热弹性动力学的经典型 (即不含卷积的非 Gurtin型 )统一变分原理族 ,从而为应用有限元法求解奠定了理论基础 .