GLOBAL ATTRACTOR OF NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES

The initial-boundary value problem of the propagation of nonlinear longitudinal elastic waves in an initially strained rod is considered. The rod is assumed to interact with the surrouding elastic and viscous external medium. The long time behavior of solutions are derived and global attractors in E-1 space is obtained.

NONLINEAR STRAIN COMPONENTS OF GENERAL SHELLS WITH INITIAL GEOMETRIC IMPERFECTIONS

On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation is not confined to a special shell, therefore they possess general properties. These formulations provide the theoretical basis of the strain analysis for geometric nonlinear problems of shells with initial geometric imperfections.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids with Rheology

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVES) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-Kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVES with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVES with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVES with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVES with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented in the paper. Factors or the physics influencing dynamic response and dynamic bifurcation for TVES with rheology are identified and are also demonstrated through model problem studies. A simple model problem consisting of a rod (1D) of TVES material with memory fixed at one end and subjected to harmonic excitation at the other end is considered to study nonlinear dynamics of TVES with rheology, frequency response as well as dynamic bifurcation phenomenon.

Finite Deformation, Finite Strain Nonlinear Dynamics and Dynamic Bifurcation in TVE Solids

This paper presents the mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and the constitutive theories derived using entropy inequality and representation theorem for thermoviscoelastic solids (TVES) matter without memory. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics. This mathematical model is thermodynamically and mathematically consistent and is ideally suited to study nonlinear dynamics of TVES and dynamic bifurcation and is used in the work presented in this paper. The finite element formulations are constructed for obtaining the solution of the initial value problems (IVPs) described by the mathematical models. Both space-time coupled as well as space-time decoupled finite element methods are considered for obtaining solutions of the IVPs. Space-time coupled finite element formulations based on space-time residual functional (STRF) that yield space-time variationally consistent space-time integral forms are considered. This approach ensures unconditional stability of the computations during the entire evolution. In the space-time decoupled finite element method based on Galerkin method with weak form for spatial discretization, the solutions of nonlinear ODEs in time resulting from the decoupling of space and time are obtained using Newmark linear acceleration method. Newton’s linear method is used to obtain converged solution for the nonlinear system of algebraic equations at each time step in the Newmark method. The different aspects of the deformation physics leading to the factors that influence nonlinear dynamic response and dynamic bifurcation are established using the proposed mathematical model, the solution method and their validity is demonstrated through model problem studies presented in this paper. Energy methods and superposition techniques in any form including those used in obtaining solutions are neither advocated nor used in the present work as these are not supported by calculus of variations and mathematical classification of differential operators appearing in nonlinear dynamics. The primary focus of the paper is to address various aspects of the deformation physics in nonlinear dynamics and their influence on dynamic bifurcation phenomenon using mathematical models strictly based on CBL of CCM using reliable unconditionally stable space-time coupled solution methods, which ensure solution accuracy or errors in the calculated solution are always identified. Many model problem studies are presented to further substantiate the concepts presented and discussed in the paper. Investigations presented in this paper are also compared with published works when appropriate.

GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES

In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and the finiteness of the Hausdorff and the fractal dimensions of the attractors.

Variation of hydraulic gradient in nonlinear finite strain consolidation

In the research field of ground water, hydraulic gradient is studied for decades. In the consolidation field, hydraulic gradient is yet to be investigated as an important hydraulic variable. So, the variation of hydraulic gradient in nonlinear finite strain consolidation was focused on in this work. Based on lab tests, the nonlinear compressibility and nonlinear permeability of Ningbo soft clay were obtained. Then, a strongly nonlinear governing equation was derived and it was solved with the finite element method.Afterwards, the numerical analysis was performed and it was verified with the existing experiment for Hong Kong marine clay. It can be found that the variation of hydraulic gradient is closely related to the magnitude of external load and the depth in soils. It is interesting that the absolute value of hydraulic gradient(AVHG) increases rapidly first and then decreases gradually after reaching the maximum at different depths of soils. Furthermore, the changing curves of AVHG can be roughly divided into five phases. This five-phase model can be employed to study the migration of pore water during consolidation.

Strain-threshold- and frequency-dependent seismic simulation of nonlinear soils

A one-dimensional equivalent linear method （EQL） is widely used in estimating seismic ground response. For this method, the shear modulus and damping ratio of inelastic soil are supposed to be frequency independent. However, historical earthquake records and laboratory test results indicate that nonlinear soil behavior is frequency- dependent. Several frequency-dependent equivalent linear methods （FDEQL） related to the Fourier amplitude of shear strain time history have been developed to take into account the frequency-dependent soil behavior. Furthermore, the shear strain threshold plays an important role in soil behavior. For shear strains below the elastic shear strain threshold, soil behaves essentially as a linear elastic mate- rial. To consider the effect of elastic-shear-strain-threshold- and frequency-dependent soil behavior on wave propaga- tion, the shear-strain-threshold- and frequency-dependent equivalent linear method （TFDEQL） is proposed. A series of analyses is implemented for EQL, FDEQL, and TFDEQL methods. Results show that elastic-shear-strain-threshold- and frequency-dependent soil behavior plays a great influence on the computed site response, especially for the high- frequency band. Also, the effect of elastic-strain-threshold- and frequency-dependent soil behavior on the site response is analyzed from relatively weak to strong input motion, and results show that the effect is more pronounced as input motion goes from weak to strong.

One-dimensional large-strain consolidation of soft clay with non-Darcian flow and nonlinear compression and permeability of soil

Geometrical nonlinearity of the soft soil and the deviation of water flow in the soft clay from Darcy's law have been well recognized in practice. However, the theory of consolidation, which can account for both the geometrical nonlinearity and the non-Darcian flow, has not been reported so far. In this contribution, a model for the consolidation of soft clay which can allow for these two factors simultaneously is proposed. Utilizing the finite difference method, the numerical model for this problem is developed. With the numerical model, the effects of the geometrical nonlinearity and the non-Darcian flow on the consolidation of the soft soil are investigated. The results show that when the self-weight stress is calculated by the same method, the rate of the non-Darcian consolidation for the large-strain case is larger than that for the small-strain case, but the difference between them is limited. However, the difference between the consolidation rates caused by the non-Darcian and Darcian flows is significant. Therefore, when the geometrical nonlinearity of the soft clay is considered in calculating the consolidation settlement, due to the complexity of the large-strain assumption, the small-strain assumption can be used to replace it if the self-weight stress for the small-strain assumption is calculated by considering its sedimentation. However, due to the aforementioned large difference between the consolidation rates with consideration of the non-Darcian flow in soft clay or not, it is better to consider the non-Darcian flow law for both the small and large stain assumptions.

GEOMETRICALLY NONLINEAR ANALYSIS OF MINDLIN PLATEUSING THE INCOMPATIBLE BENDING ELEMENTSWITH INTERNAL SHEAR STRAIN

An approach of the incompatible elements with additional internal shear strain is,in the presem paper,suggested and applied to geometrically nonlinear analysis of Mi-ndlin plate bending problem.It provides a quite covenient way to avoid the whear loc-king troubles.An energy consistency condition for this kind of C°elements is offered.The nonlinear element formulations and some numerical results are presented.

A URI 4-NODE QUADRILATERAL ELEMENT BY ASSUMED STRAIN METHOD FOR NONLINEAR PROBLEMS

In this paper one-point quadrature'assumed strain'mixed element formulation based on the Hu-Washizu variational principle is presented.Special care is taken to avoid hourglass modes and volumetric locking as well as shear locking.The assumed strain fields are constructed so that those portions of the fields which lead to volumetric and shear locking phenomena are eliminated by projection,while the implementation of the proposed URI scheme is straightforward to suppress hour- glass modes.In order to treat geometric nonlinearities simply and efficiently,a corotational coordinate system is used.Several numerical examples are given to demonstrate the performance of the suggested formulation,including nonlinear static/dynamic mechanical problems.

PRINCIPAL COMPONENT DECOMPOSITION BASED FINITE ELEMENT MODEL UPDATING FOR STRAIN-RATE-DEPENDENCE NONLINEAR DYNAMIC PROBLEMS

Thin wail component is utilized to absorb impact energy of a structure. However, the dynamic behavior of such thin-walled structure is highly non-linear with material, geometry and boundary non-linearity. A model updating and validation procedure is proposed to build accurate finite element model of a frame structure with a non-linear thin-walled component for dynamic analysis. Design of experiments （DOE） and principal component decomposition （PCD） approach are applied to extract dynamic feature from nonlinear impact response for correlation of impact test result and FE model of the non-linear structure. A strain-rate-dependent non-linear model updating method is then developed to build accurate FE model of the structure. Computer simulation and a real frame structure with a highly non-linear thin-walled component are employed to demonstrate the feasibility and effectiveness of the proposed approach.

Nonlinear parametric interactions in ion-implanted semiconductor plasmas having strain-dependent dielectric constants

We report nonlinear parametric interactions using a hydrodynamic model of ion-implanted semiconductor plasmas having strain-dependent dielectric constants（SDDC）. High-dielectric-constant materials are technologically important because of their nonlinear properties. We find that the third-order susceptibility varies in the range 10^-14--10^-12m^2·V^-2 for ion-implanted semiconductor plasmas, which is in good agreement with previous results. It is found that the presence of SDDC in ion-implanted semiconductor plasma modifies the characteristic properties of the material.

再生粗骨料混凝土应力-应变关系

再生粗骨料混凝土应力-应变关系是实现其材料到结构力学分析的桥梁纽带,成为再生粗骨料混凝土结构基础理论的基石。介绍了作者团队多年来在再生粗骨料混凝土应力-应变关系方面取得的研究进展:采用模型化再生粗骨料方法,研究了复杂界面过渡区对再生粗骨料混凝土破坏行为的影响,揭示了再生粗骨料混凝土细观损伤本质与演化机理;从静力作用到动力作用,系统地开展了不同工况下再生粗骨料混凝土应力-应变行为试验研究,探明了载荷条件对再生粗骨料混凝土应力与变形的影响规律并建立了相适应的力学与数学模型;进一步考虑再生粗骨料性能时空变异性,发现了再生粗骨料混凝土力学响应的概率分布特征,提出了再生粗骨料混凝土随机损伤本构关系;基于获得的本构模型,完成了再生粗骨料混凝土构件时变可靠度分析和结构动力非线性分析,为再生粗骨料混凝土在实际工程中的安全应用提供了理论支撑;提炼了相关研究结论并对未来研究工作进行了展望。

竖井地基大应变非线性固结解析解

已有的研究表明,高压缩性软土的大应变及非线性固结特性对其固结具有显著影响。但目前能同时考虑两者影响的竖井地基大应变非线性固结解析解还鲜见报道。考虑高压缩性软土在固结中的大变形特性,应用双对数压缩渗透非线性模型描述软土在固结中的压缩渗透特性变化,基于Gibson大应变固结理论,建立竖井地基大应变非线性固结模型并获得模型的解析解。将所获得的解析解与竖井地基大应变非线性固结数值解及特定工况下小应变线性固结解析解进行对比,以验证所获解析解的可靠性。在此基础上,通过大量计算对不同工况下竖井地基非线性固结性状开展分析。结果表明:压缩指数I_(c)为定值时竖井地基固结速率随参数α减小而增大。α保持不变时竖井地基固结速率随I_(c)减小而增大。压缩渗透参数保持不变时,竖井地基固结速率随着外荷载的增大而加快,随着井径比增大而减慢。将所获解析解应用于深港西部通道口岸区填海地基处理的工程计算,表明理论计算的沉降曲线与实测曲线较为吻合,说明了所获解析解的工程可应用性。

循环荷载下红黏土的变形演化分析

为了给施工场地沉降量的预测工作及安全性评估提供依据,以南宁某高速公路的红黏土回填为背景,进行双向循环动三轴试验,研究扰动红黏土在循环荷载下的变形行为,分析围压、循环应力比(CSR)和加载频率对土体动弹性模量的影响规律。依据试验数据绘制滞回曲线、永久应变(εp)-循环次数(N)关系曲线,分析土体弹性应变、永久应变的演化发展规律。并对永久应变曲线进行了非线性拟合,建立满足稳定型和临界型的永久应变预测方程,最后通过试验验证该累积变形模型的可行性以及对模型参数进行分析。结果表明:土样经过一定次数循环后,其应力-应变滞回曲线形状基本保持不变。弹性模量衰减速率与围压、CSR大小呈正相关,且弹性模量随循环次数的增加呈先快后慢的非线性衰减趋势。土样永久应变受围压、CSR和加载频率的影响显著,围压、CSR和加载频率越大累积应变越多;但随循环次数的增加,永久应变曲线逐渐收敛,应变量趋于稳定。永久应变预测方程能较好预测重塑红黏土不同变形状态的累积塑性变形。

考虑Hansbo渗流及变井阻的竖井地基非线性大应变固结分析

大量资料表明,软土中孔隙水渗流在低水力坡降时会偏离达西定律,同时高压缩性软土在外载作用下产生的较大应变致使经典的小应变固结理论不再适用,竖井地基中的软土大应变也必然导致排水体发生弯折、出现淤堵等不良排水状态从而影响竖井的通水量。基于此,应用经典的Hansbo渗流定律描述软土中的渗流规律,采用随时间、深度变化的变井阻模型描述竖井在固结过程中通水量的变化,在Gibson大应变几何假定下建立可以考虑外荷载随时间变化的竖井地基大应变非线性固结模型,并给出其数值解答。通过与退化工况下已有的解答和工程实例开展对比分析,验证所建固结模型的可信性。对不同工况下的竖井地基大变形固结性状进行分析时发现:Hansbo渗流参数m和i1在合理取值范围内时其与达西渗流竖井地基固结度间的差异可高达10%,但当井径比小于13时,两者间的差异不到5%,此时可忽略土中存在的非达西渗流现象,一旦井径比超过13,竖井地基固结计算就有必要考虑土中的Hansbo渗流现象;变井阻导致竖井的通水量逐渐降低,在考虑土中Hansbo渗流后,变井阻与常井阻计算的竖井地基平均固结度间的差异最大达10%;竖井长度与竖井影响区半径之比(H/r_(e))达到12.5时,土中竖向渗流已影响甚微,且随着H/r_(e)的增大竖向渗流的影响会更小,此时可忽略不计。

基于桩侧砂土圆锥型修正应变楔模型的p-y曲线

基于桩侧砂土三维圆锥型应变楔的变形特征,提出砂土中水平受荷桩的非线性p-y曲线。构建圆锥型楔形体前表面应力体系并引入土体应力-应变双曲线模型,进而考虑应变楔的水平受力平衡得到桩侧土反力的表达式。在此基础上,结合弹性地基梁有限差分数值分析,建立了水平受荷桩非线性p-y曲线的理论推导方法。将该理论用于钻孔桩和打入桩模型试验的算例分析,结果表明:相对于API规范的p-y曲线、双曲线型p-y曲线以及传统非圆锥型应变楔模型得到的p-y曲线,本文方法得到的非线性p-y曲线与模型试验结果更为接近。通过比较本文圆锥变形模式与传统非圆锥型应变楔模式的差异以及桩-土参数的影响分析,进一步论证了该方法的优点。

考虑变荷载和变边界的软土大应变非线性固结分析

为了准确预测实际土层的固结速率,在Gibson大应变固结理论基础之上,考虑土体的非线性压缩渗透特性和土层表面随时间改变的变排水边界条件,建立考虑变荷载和变边界的软土大应变非线性固结模型。在此基础上,获得单级加载和多级加载条件下大应变非线性固结模型的显式解析解,利用获得的解析解开展计算以分析界面参数、荷载取值对土层固结性状的影响。结果表明:外荷载对土体内部超静孔压消散的影响表现为随着荷载的增大,超静孔压消散得越快,但其不会影响土体最终完成固结的时间;参数I_(c)(α-2)取值对土体固结性状的影响表现为固结速率随着参数I_(c)(α-2)取值的变化而变化。值得注意的是,描述土体非线性特性的参数取值对固结性状的影响在变边界下显现的固结性状会出现延迟现象,不同参数下的变边界更能反映土体边界的真实透水性情况,在实际工程中可以根据超静孔压实际的消散速率反演界面参数,以便能准确预估土层的固结进程。

考虑粉细砂应变软化特性的修正双曲线模型

在基础建设过程中,以粉细砂为填筑材料的地基在上覆荷载作用下可能发生软化现象。为探究饱和粉细砂应变软化规律,基于自动环境三轴试验系统开展合肥粉细砂固结不排水三轴剪切试验,分析不同围压下粉细砂应变软化特征,揭示其软化机理。研究结果表明:合肥粉细砂不排水剪切应力-应变曲线呈明显驼峰型软化特征;围压对于其应力-应变曲线影响显著,其峰值偏差应力及对应的峰值应变与固结围压呈正相关,偏差应力峰值与固结围压关系可用线性函数(σ1-σ3)p=0.637σ3+255.5拟合表述,拟合决定系数R2达到0.983,应变峰值与固结围压关系可用线性函数εp=0.0031σ3+5.45拟合表述,拟合决定系数R2达到0.982;剪切过程粉细砂试样产生剪胀现象,使得土体结构逐渐破坏,进而发生应变软化现象。通过在沈珠江院士提出的驼峰形双曲线型公式上添加新的边界条件以简化模型参数,构建了合肥粉细砂应变软化修正双曲线数学模型。该模型对合肥粉细砂应力-应变软化曲线的拟合效果良好,为安徽地区地下工程设计与施工提供重要依据。

各向同性磁流变弹性体磁相关非线性动态力学行为的本构模型

各向同性磁流变弹性体是一种将磁性颗粒随机掺入到聚合物基体中制备而成的智能材料。在磁场作用下,其模量发生快速、可逆、连续变化,在振动控制领域显示出良好的应用前景。实验结果表明,各向同性磁流变弹性体的动态力学行为具有很强的频率、应变幅值和磁场相关性。尽管上述行为对于其潜在应用具有重要的影响,但目前关于各向同性磁流变弹性体磁相关非线性动态力学行为的理论研究则关注不够。为准确评价各向同性磁流变弹性体的动态力磁耦合行为,并指导其相关产品的设计,本文建立了一个基于连续介质力学理论,反映各向同性磁流变弹性体磁相关非线性动态力学行为的本构模型。随后,开发了和本构模型对应的数值实现算法,并对模型的预测能力进行了验证。该模型有助于深入理解各向同性磁流变弹性体磁相关非线性动态力学行为的潜在力学机制。此外,该模型有助于指导基于各向同性磁流变弹性体产品的设计和应用。