不可压饱和多孔弹性梁的大挠度非线性数学模型

在孔隙流体仅存在沿梁轴线方向扩散的假定下,建立了微观不可压饱和多孔弹性梁大挠度问题的非线性数学模型．利用Galerkin截断法,研究了固定端不可渗透、自由端可渗透的饱和多孔弹性悬臂梁在自由端突加集中载荷作用下的非线性弯曲,得到了梁骨架的挠度、弯矩以及孔隙流体压力等效力偶等的时间响应和沿轴线的分布．比较了大挠度非线性和小挠度线性理论的结果,揭示了两者间的差异．研究发现大挠度理论的结果小于相应的小挠度理论结果,并且,大挠度理论的结果趋于其稳态值的时间小于相应的小挠度理论结果趋于其稳态值的时间．     

不可压饱和多孔弹性杆动力响应的多辛方法

研究了不可压饱和多孔弹性杆的一维动力响应问题.基于多孔介质理论,在流相和固相微观不可压、固相骨架小变形的假定下,建立了不可压流体饱和多孔弹性杆一维轴向动力响应的数学模型.利用Hamilton空间体系的多辛理论,构造了不可压饱和多孔弹性杆轴向振动方程的多辛形式及其多种局部守恒律.采用中点Box离散方法得到轴向振动方程的多辛离散格式和局部能量守恒律以及局部动量守恒律的离散格式;数值模拟了不可压饱和多孔弹性杆的轴向振动过程,记录了每一时间步的局部能量数值误差和局部动量数值误差.结果表明,已构造的多辛离散格式具有很高的精确性和较长时间的数值稳定性,这为解决饱和多孔介质的动力响应问题提供了新的途径.     

饱和多孔弹性杆流固耦合动力响应的保结构算法

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.     

饱和粘弹性土层中端承桩纵向振动的轴对称解析解

基于弹性和饱和多孔介质理论,将桩和饱和土层分别视为单相弹性介质和饱和粘弹性介质,利用Helmholtz分解和变量分离法,在频率域研究了饱和粘弹性土层中端承桩纵向振动的动力特性,给出了饱和粘弹性土层中桩纵向振动时动力响应的轴对称解析解及桩头复刚度的解析表达式．通过数值计算,给出了桩头动刚度因子和等效阻尼随激励频率的响应,考察了饱和土物性参数、桩土模量比、桩长径比、桩Poisson比等参数对桩头刚度因子和阻尼的影响．研究表明:由于考虑了桩的径向变形效应以及饱和粘弹性土层对桩的径向力作用,轴对称精确解的桩头动刚度因子和阻尼分别与经典Euler-Bernoulli杆模型桩的桩头动刚度因子和阻尼有较大的区别,特别是在若干激励频率处．因此,经典Euler-Bernoulli杆模型桩的适用性具有一定的局限,更加精确的分析应采用三维精确模型．     

具有分数导数本构关系的粘弹性Timoshenko梁的静动力学行为分析

利用粘弹性材料的三维分数导数型本构关系,建立粘弹性Timoshenko梁的静、动力学行为研究的数学模型;分析Timoshenko梁在阶跃载荷作用下的准静态力学行为,得出了问题的解析解,考察了一些材料参数对梁的挠度的影响。基于模态函数讨论了粘弹性Timoshenko梁在横向简谐激励作用下的动力响应,并考察了剪切和转动惯性对梁振动响应的影响。     

饱和地基上弹性基础的竖向振动特性研究

采用解析的方法研究了饱和地基上受一简谐竖向荷载作用下弹性基础的动力响应．在分析中,首先利用积分变换技术获得了饱和介质基本控制方程的变换解,然后基于基础-半空间完全放松接触、半空间表面完全透水或不透水的假设,建立了该动力混合边值问题的对偶积分方程,并把该对偶积分方程进一步化为易于数值求解的第二类Fredholm积分方程A·D2文末数值算例给出了动力柔度系数、位移和孔隙水压力随振动频域和土-基础体系物理力学参数特性的变化曲线．结果表明:饱和地基上弹性基础的动力响应完全不同于饱和地基上刚性圆板的动力响应．所用方法可用于研究波的传播、土-结构动力相互作用等许多问题．     

横观各向同性饱和弹性多孔介质非轴对称动力响应

应用Fourier展开和Hankel变换求解了简谐激励下横观各向同性饱和弹性多孔介质的非轴对称Biot波动方程,得到了一般解。用一般解给出了多孔介质总应力分量的表达式。最后对求解横观各向同性饱和弹性多孔介质非轴对称动力响应边值问题的方法作了系统说明,并且给出了数值分析特例。     

粘弹性梁的动力响应

本文利用Voigt力学模型对粘弹性简支梁进行动力分析,得到了梁的自由振动与强迫振动的若干解析解的表达式.并与S.Timoshenko给出的弹性简支梁的相应的结论进行了比较,指出了弹性动力分析的局限性.最后给出了二个数值例子.     

饱和多孔介质粘弹性理论

本文讨论了饱和多孔介质的粘弹体本构关系。把Lee的弹性和粘弹性比拟理论,拓展到饱和多孔介质领域内。用比拟理论解出了饱和粘性土的常载和变载的一维固结问题,并利用比拟理论的属性,可以由简单的粘弹性本构关系来推求复杂的本构关系,得到了粘弹性地基上的粘弹性梁板问题的解答。由此初步形成了饱和多孔介质粘弹性比拟法的完整理论。     

各向异性液体-多孔饱和介质在机械荷载作用下的弹性动力分析

将一个各向异性液体-多孔饱和介质的弹性动力分析,归结为一个横观各向同性液体-多孔饱和介质在机械荷载作用下的变形问题.自然界中有些物理问题,仅在一个方向发生变形,例如,与变形结构和变形柱有关的问题.土力学中,通常假设只有竖向沉降,从而归结为一维多孔弹性模型.采用各向异性液体-多孔饱和介质的一维变形模型,研究了在不同时间和距离下扰动的变化.给出了在不同类型荷载作用下,介质的各向异性对位移分布和应力分布的影响.     

Transient wave propagation in a one dimensional partially saturated poroelastic column

Based on the theory of mixtures, a dynamic three phase model for partially saturated poroelasticity is established. This model is applied to a one-dimensional unsaturated poroelastic column and an analytical solution in the Laplace domain is deduced. By using the Convolution Quadrature Method, the solution in the time domain is obtained. Using some widely distributed porous materials as rock, soil and sediment, the wave propagation behavior in terms of displacement and pore pressure is examined. By neglecting the viscosity of the fluid, assuming very large fluid permeabilities, the second and third compressional waves are identified. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration characteristics of a functionally graded beam by finite element method

This paper presents the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law. The present model is more effective for replacing the non-uniform geometrical beam with axially or transversally uniform geometrical graded beam. The system of equations of motion is derived by using the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Numerical results are presented in both tabular and graphical forms to figure out the effects of different material distribution, slenderness ratios, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of the beam.     

横观各向同性饱和地基上刚性圆板的扭转振动

通过解析方法研究了横观各向同性饱和半空间上刚性圆板在简谐扭转荷载作用下的振动问题．运用Hankel变换求解了横观各向同性饱和土的动力控制方程,结合混合边界条件得出了刚性基础的扭转对偶积分方程,并将对偶积分方程转化为第二类Fredholm积分方程求解了基础的扭转振动问题,同时给出了动力柔度系数,基础的角位移幅值和基底接触剪应力的表达式．通过数值算例研究了地基的各向异性程度对基础扭转振动的影响．     

A reduced model to locate low contrast inclusions in poroelastic media

This paper introduces a numerical method to localize inclusions having slightly different elastic coefficients than those of a fully saturated poroelastic matrix, whose detection is often difficult. This method can be used to find weakly stiffer or softer objects in saturated soils or diseased biological tissues at early stages. To this end, we propose a reduced model from the Biot’s equations by splitting the fluid pressure into two parts: one embedded into an elasticity model and the other one used as a corrector term. By applying the small amplitude homogenization method, we can successfully retrieve the position and extension of inclusions in poroelastic media employing this simplified model. Numerical results show a good agreement for the location of inclusions when the contrast is below 30% stiffer or softer than the matrix, and for a noise level up to 5% for frequencies below 50 Hz.     

Vibration analysis of Euler–Bernoulli nanobeams by using finite element method

In the present study, an efficient finite element model for vibration analysis of a nonlocal Euler–Bernoulli beam has been reported. Nonlocal constitutive equation of Eringen is proposed. Equations of motion for a nonlocal Euler–Bernoulli are derived based on varitional statement. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. The model has been verified with the previously published works and found a good agreement with them. Vibration characteristics, such as fundamental frequencies, are illustrated in graphical and tabulated form. Numerical results are presented to figure out the effects of nonlocal parameter, slenderness ratios, rotator inertia, and boundary conditions on the dynamic characteristics of the beam. The above mention effects play very important role on the dynamic behavior of nanobeams.     

A Phase Field Approach for Dynamic Fracture

In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fundamental solutions for a partially saturated poroelastic continuum

The Boundary Element Method is quite suitable for solving dynamic semi-infinite or infinite linear problems. In order to establish the boundary integral equations, one crucial condition is the knowledge of corresponding fundamental solutions. For a partially saturated poroelastic continuum, the governing equations in Laplace domain are formulated based on the theory of mixtures, and the related fundamental solutions are derived by using Hörmanders method. The singular behavior of the fundamental solutions are investigated by a series expansion with respect to the variable r. Finally, some exemplary fundamental solutions are calculated to visualize the principal behavior as well, and comparisons with the related results of saturated poroelasticity are given. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

横观各向同性饱和地基的三维动力响应

首先引入位移函数,将直角坐标系下横观各向同性饱和土Biot波动方程转化为2个解耦的六阶和二阶控制方程;然后基于双重Fourier变换,求解了Biot波动方程,得到以土骨架位移和孔隙水压力为基本未知量的积分形式的一般解,并用一般解给出了饱和土总应力分量的表达式．在此基础上系统研究了横观各向同性饱和半空间体的稳态动力响应问题,考虑表面排水和不排水两种情况,得到了半空间体在任意分布的表面谐振荷载作用下,表面位移的稳态动力响应,文末给出了算例．