孔隙率各向异性下饱和多孔弹性地基动力响应

由于不同的沉积条件和应力状态, 天然土体通常表现出一定的各向异性特征. 文章研究地基上表面受温度载荷和机械载荷时, 孔隙率各向异性参数变化对饱和多孔弹性地基热-水-力耦合动力响应问题的影响. 基于Lord-Shulman广义热弹性理论, 结合孔隙率各向异性基本假设, 建立了孔隙率各向异性饱和多孔弹性地基热-水-力耦合动力响应模型, 利用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度分布的解析表达式并加以图示. 正则模态法是一种利用加权残差求得解析解的方法, 相较于其他方法能快速求解偏微分方程. 当孔隙率各向异性参数为1时, 可将该各向异性耦合动力响应模型退化为热-水-力耦合动力响应模型验证该地基模型的合理性. 着重分析了孔隙率各向异性参数变化对不同物理量的影响. 结果表明: 孔隙率各向异性参数变化对物理量均有一定影响. 在地基上表面受温度载荷作用时, 对超孔隙水压力和竖向应力影响最为明显; 在地基上表面受机械载荷作用时, 对超孔隙水压力和温度影响明显. 整体而言, 无论地基上表面受何种载荷, 随着各向异性参数增大, 峰值逐渐减小, 在地基深度增加方向峰值所在位置向靠近地基上表面方向移动.      

DYNAMIC RESPONSE OF SATURATED POROUS ELASTIC FOUNDATION UNDER POROSITY ANISOTROPY$^{\bf 1)}$

由于不同的沉积条件和应力状态, 天然土体通常表现出一定的各向异性特征. 文章研究地基上表面受温度载荷和机械载荷时, 孔隙率各向异性参数变化对饱和多孔弹性地基热-水-力耦合动力响应问题的影响. 基于Lord-Shulman广义热弹性理论, 结合孔隙率各向异性基本假设, 建立了孔隙率各向异性饱和多孔弹性地基热-水-力耦合动力响应模型, 利用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度分布的解析表达式并加以图示. 正则模态法是一种利用加权残差求得解析解的方法, 相较于其他方法能快速求解偏微分方程. 当孔隙率各向异性参数为1时, 可将该各向异性耦合动力响应模型退化为热-水-力耦合动力响应模型验证该地基模型的合理性. 着重分析了孔隙率各向异性参数变化对不同物理量的影响. 结果表明: 孔隙率各向异性参数变化对物理量均有一定影响. 在地基上表面受温度载荷作用时, 对超孔隙水压力和竖向应力影响最为明显; 在地基上表面受机械载荷作用时, 对超孔隙水压力和温度影响明显. 整体而言, 无论地基上表面受何种载荷, 随着各向异性参数增大, 峰值逐渐减小, 在地基深度增加方向峰值所在位置向靠近地基上表面方向移动.     

饱和多孔黏弹地基热-水-力耦合动力响应分析

天然土体由于沉积条件和应力状态不同, 往往会表现出一定的流变性. 本文研究地基上表面受外载荷作用时, 渗透系数和孔隙率变化对饱和多孔黏弹性地基热-水-力耦合动力响应问题的影响. 基于Biot波动方程、达西定律和Lord-Shulman广义热弹性理论, 并引入了考虑黏弹性松弛时间因子的Kelvin-Voigt黏弹性模型研究地基上表面受热/力源作用时, 孔隙率和渗透系数变化对均质各向同性饱和多孔黏弹性地基中所考虑的各无量纲量的影响. 根据不同的边界条件采用正则模态法推导出无量纲竖向位移、超孔隙水压力、竖向应力和温度的解析表达式, 结合算例分析了不同变量对各物理量的影响. 正则模态法是一种加权残差法, 可不经正、反积分变换将方程快速解耦并消除数值反变换的局限性. 结果表明: 无论何种载荷作用时, 载荷频率变化对所有考虑的物理量均有明显的影响; 孔隙率和渗透系数均对无量纲超孔隙水压力有明显的影响, 当仅考虑热载荷作用时, 孔隙率和渗透系数变化对无量纲温度均无影响. 正则模态法可广泛应用于岩土工程领域, 尤其适用于商业建筑、高速铁路和公路能源基础的热、力学特性研究中. 该研究结果可为工程施工奠定一定的理论基础, 具有一定的指导性意义.      

轴对称热-力埋置载荷下半空间饱和孔隙介质的动力响应

基于修正的Biot热弹性本构理论,得到了饱和多孔介质热-力耦合的动力学控制方程.针对半空间孔隙介质在内置简谐热-力轴对称载荷作用下的动力问题,利用Hankel变换获得了响应的解析表达式,并利用Han-kel逆变换进行数值求解,分析了埋置深度、表面热边界条件等对响应的影响规律.结果表明:孔隙水压力在载荷作用处上方有负压出现;环向、径向及竖向应力在载荷作用处发生突变,且在载荷作用处上方均出现拉应力;在载荷作用处下方,孔隙水压力及竖向、径向和环向应力均随着深度的增大而减小.当内置热载荷仅设置温差,而无外热源输入时,温差对孔隙介质中的响应几乎不产生影响.当孔隙介质表面绝热时,孔隙水压力小于表面等温情况下的值.     

分数阶黏弹性Pasternak地基上两端固支Timoshenko梁的动力响应

本文研究了放置在黏弹性Pasternak地基上的Timoshenko梁在移动载荷作用下的动力响应行为．首先,引入分数阶导数,将整数阶标准固体黏弹性地基模型推广为分数阶标准固体黏弹性模型．对于Pasternak地基,考虑压缩层是黏弹性的而剪切层仍是弹性的情况,给出了地基反作用力．然后,求解了Timoshenko梁的自由振动解,获得含黏性耗散信息的复固有频率及振型函数．在此基础上用振型叠加法分析了在移动简谐荷载作用下梁的位移响应．在数值算例中,给出了不同分数阶导数、地基黏性系数以及载荷移动速度下梁的动态响应,讨论了黏弹性地基对梁的动态响应的影响规律．     

孔隙热弹性体有限变形动力学的若干变分原理

首先通过对熵均衡方程积分,将其变换为无一阶时间导数项的等价方程,再将Hamilton变分原理运用和推广于各向异性孔隙热弹性体有限变形动力学中,建立了相应的非线性控制微分方程、力的边界条件和初始条件.同时,引入孔隙百分比变化和温度变化引起的力矩,将Hamilton变分原理推广到孔隙热弹性结构中,提出了以Kirchhoff-Love假设为基础的孔隙热弹性Karman-型薄板的完全的非线性数学模型,该模型考虑了中面力、中面惯性和转动惯性影响.     

简支饱和多孔弹性梁的非线性动力响应

基于饱和多孔弹性梁大挠度变形的数学模型,利用Galerkin截断法,本文研究了两端可渗透的简支饱和多孔弹性梁分别在突加横向均布常载荷和简谐载荷作用下的动力响应,得到了梁弯曲时挠度、弯矩以及孔隙流体压力等效力偶等随时间的响应,考察了不同载荷下多孔弹性梁弯曲的响应特征.结果表明:随着载荷的增加,在常载荷作用下多孔弹性梁非线性大挠度响应与线性小挠度的差别愈加明显,而在简谐载荷作用下,多孔弹性梁的动力响应呈现较丰富的性态,相图由最初的单一椭圆曲线不断变形,形状随载荷幅值的增加而逐渐复杂,同时,时程曲线也由简单正弦曲线变为具有多峰值特征的一个周期曲线.     

超弹性材料中空穴的动态生成

本文在有限变形动力学的框架下研究了一种不可压超弹性材料圆柱体在表面突加均布拉伸载荷作用下空穴的动态生成问题,除一个相应于均匀变形状态的平凡解外,当外加载荷超过其临界值时,柱体内部还有空穴的突然生成,得到了空穴半径和表面载荷之间的一个精确的微分关系,证明了空穴随时间的演化是非线性的周期性振动,给出了空穴振动的相图、最大振幅、临界载荷及近似的周期。     

半空间饱和土内置点载荷作用下的热弹性波动

基于Biot波动理论及热弹性动力理论,利用已建立的饱和多孔弹性介质热流固耦合控制方程,研究半无限地基在内置点热力源作用下的动力响应问题. 求解过程引用Hankel变换技术,得到了热力源作用下土体中温度增量、应力、位移和孔隙水压力的积分形式解答.利用Hankel数值逆变换得到计算结果,分析了热流固耦合条件下激振频率对竖向位移和孔隙水压力响应的影响. 对热流固耦合、热弹性和多孔弹性模型计算结果进行了比较.      

荷载作用下多孔饱和地基的热-水-力耦合动力响应分析

基于广义热弹性理论,结合达西定律,对Biot波动方程进行修正,研究了一个受到荷载作用的多孔饱和地基的热-水-力多场耦合动态响应问题。建立了多孔饱和地基在荷载作用下的热-水-力耦合模型及控制方程,该模型可退化为热弹性耦合模型。采用正则模态法求解,得到了问题的解析解,讨论了热-水-力耦合模型和热弹性耦合模型的区别,分析了荷载频率变化对地基中各物理量的影响。最终给出了无量纲的竖向位移、超孔隙水压力、竖向应力和温度等物理量的分布规律。     

Response of Generalized Thermoelastic Half-space with Voids to Mechanical and Thermal sources

The dynamic response of a homogeneous, isotropic, generalized thermoelastic half-space with voids subjected to normal, tangential force and thermal source is investigated. The displacements, stresses, temperature distribution and change in volume fraction field so obtained in the physical domain are computed numerically and illustrated graphically. The numerical results of these quantities for magnesium crystal-like material are illustrated to depict the response of various sources in the Lord–Shulman (L–S) theory and Green–Lindsay (G–L) theory for an insulated boundary and temperature gradient boundary. Some particular cases have been deduced.     

Stability of fluid-conveying periodic shells on an elastic foundation with external loads

This paper presents the beam-mode stability of a fluid-conveying periodic shell on an elastic foundation subjected to external loading. A transfer matrix (TM) method was developed to investigate the characteristics of steady-state waves in the system and the dynamic response of the periodic shell system. When subjected to external perturbations, including either a moving load or a stationary one, the shell may be subjected to instability for flow velocities exceeding a certain critical velocity. The system can also become unstable when a travelling load exceeds a certain critical value. The coupled effects of the speed of a moving load and the flow velocity of a fluid on the stability of the shell system were also investigated. A periodic structure was designed for such a shell system to enhance its dynamic stability. The periodic shell system produces innumerable velocity band gaps (VBGs), which could raise the critical velocity and extend the stable range for both the moving load and the flowing fluid. Finally, the formation mechanism of the VBGs was studied, as well as the effects of the thickness, length of the shell cells, Young׳s modulus and stiffness of the elastic foundation on modulating the VBGs.     

Free vibration analysis of elastically supported functionally graded annular plates subjected to thermal environment

Free vibration analysis of functionally graded (FG) thin-to-moderately thick annular plates subjected to thermal environment and supported on two-parameter elastic foundation is investigated. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The equations of motion and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the Hamilton’s principle based on the first order shear deformation theory (FSDT). The initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Differential quadrature method (DQM) as an efficient and accurate numerical tool is adopted to solve the thermoelastic equilibrium equations and the equations of motion. The formulations are validated by comparing the results in the limit cases with the available solutions in the literature for isotropic and FG circular and annular plates. The effects of the temperature rise, elastic foundation coefficients, the material graded index and different geometrical parameters on the frequency parameters of the FG annular plates are investigated. The new results can be used as benchmark solutions for future researches.     

Buckling analysis of functionally graded arbitrary straight-sided quadrilateral plates on elastic foundations

As a first endeavor, the buckling analysis of functionally graded (FG) arbitrary straight-sided quadrilateral plates rested on two-parameter elastic foundation under in-plane loads is presented. The formulation is based on the first order shear deformation theory (FSDT). The material properties are assumed to be graded in the thickness direction. The solution procedure is composed of transforming the governing equations from physical domain to computational domain and then discretization of the spatial derivatives by employing the differential quadrature method (DQM) as an efficient and accurate numerical tool. After studying the convergence of the method, its accuracy is demonstrated by comparing the obtained solutions with the existing results in literature for isotropic skew and FG rectangular plates. Then, the effects of thickness-to-length ratio, elastic foundation parameters, volume fraction index, geometrical shape and the boundary conditions on the critical buckling load parameter of the FG plates are studied.     

Semi-analytical solution for three-dimensional vibration of thick continuous grading fiber reinforced (CGFR) annular plates on Pasternak elastic foundations with arbitrary boundary conditions on their circular edges

In this paper free vibration of continuous grading fiber reinforced (CGFR) annular plates on an elastic foundation, based on the three-dimensional theory of elasticity, for different boundary conditions at the circular edges is investigated. The foundation is described by the Pasternak or two-parameter model. The CGFR annular plates have an arbitrary variation of fiber volume fraction in the thickness direction. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. Some new results for the natural frequencies of the plate are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. Besides, results for CGFR plate with arbitrary variation of fiber volume fraction in the thickness direction of the plate are compared with discrete laminated composite plate. The main contribution of this work is to present useful results for continuous grading of fiber reinforcement in the thickness direction of a plate on an elastic foundation and comparison with similar discrete laminated composite plate. The interesting and new results show that non-dimensional natural frequency parameters of a functionally graded fiber volume fraction is larger than that of a discrete laminated and close to that of a 2-layer. The new results can be taken as the benchmark solutions for those from numerical methods and future researches.     

基于相场法的周期性多孔结构断裂行为研究

周期性多孔结构具有质量轻、比密度低、比强度高、隔音等优良特点, 同时也能很好地满足结构-功能一体化的需求, 在许多领域具有广泛的应用前景. 目前, 对周期性多孔结构在复杂载荷下的力学响应和断裂行为的研究较少. 采用细观力学和相场方法相结合, 基于二维代表性体积单元RVE模型, 施加能实现比例加载的周期性边界条件, 研究周期性多孔结构在复杂多轴比例加载状态下的裂纹萌生位置、断裂模式、承载极限及其变化规律. 本文的数值模拟结果表明: 首先, 周期性多孔结构在竖直方向拉伸载荷作用下, 裂纹均从孔边萌生并沿水平方向同步扩展; 其次, 在双轴载荷作用下, 随着水平载荷的增加, 结构在竖直方向的极限拉伸载荷逐渐增大; 当双轴拉伸载荷等值时, 结构的抗拉强度达到最大, 此时断裂模式呈现为十字正交型开裂; 最后, 面内剪切应力的引入会导致结构的拉伸强度极限降低, 孔边裂纹的萌生位置和扩展路径发生偏移, 裂纹模式从单S型转变为双弧线型, 裂纹向水平位置上相邻的孔洞扩展. 随着水平载荷的增加, 裂纹模式最终转变为斜裂纹, 从孔边对角线位置萌生并沿着45°方向扩展.      

Propagation of wave at the boundary surface of transversely isotropic thermoelastic material with voids and isotropic elastic half-space

The purpose of this research is to study the effect of voids on the surface wave propagation in a layer of a transversely isotropic thermoelastic material with voids lying over an isotropic elastic half-space. The frequency equation is derived after developing a mathematical model for welded and smooth contact boundary conditions. The dispersion curves giving the phase velocity and attenuation coefficient via wave number are plotted graphically to depict the effects of voids and anisotropy for welded contact boundary conditions. The specific loss and amplitudes of the volume fraction field, the normal stress, and the temperature change for welded contact are obtained and shown graphically for a particular model to depict the voids and anisotropy effects. Some special cases are also deduced from the present investigation.     

Thermal Stresses in Plane Strain of Porous Elastic Solids

This paper is concerned with the linear theory of thermoelastic materials with voids. We present a method to reduce the thermoelastic problem to an isothermal one with zero body loads and with certain known boundary data. The results are used to study the thermal stresses in a tube and the thermoelastic deformation of a cylinder subjected to a uniform temperature gradient.