Response of loose bonding on reflection and transmission of elastic waves at interface between elastic solid and micropolar porous cubic crystal

The problem of reflection and transmission of plane periodic waves incident on the interface between the loosely bonded elastic solid and micropolar porous cubic crystal half spaces is investigated. This is done by assuming that the interface behaves like a dislocation, which preserves the continuity of traction while allowing a finite amount of slip. Amplitude ratios of various reflected and transmitted waves have been depicted graphically. Some special cases of interest have been deduced from the present investigation.     

Numerical analysis of effective elastic properties of geomaterials containing voids using 3D random fields and finite elements

The purpose of the study is to investigate the influence of porosity and void size on effective elastic geotechnical engineering properties with a 3D model of random fields and finite element. The random field theory is used to generate models of geomaterials containing spatially random voids with controlled porosity and void size. A “tied freedom” analysis is developed to evaluate the effective Young’s modulus and Poisson’s ratio in an ideal block material of finite elements. To deliver a mean and standard deviation of the elastic parameters, this approach uses Monte-Carlo simulations and finite elements, where each simulation leads to an effective value of the property under investigation. The results are extended to investigate an influence of representative volume element (RVE). A comparison of the effective elastic stiffness of 2D and 3D models is also discussed.     

各向异性弹塑性中厚度板壳的有限元分析

本文在文献［２，３］的基础上，提出了一个解各向异性弹塑性中厚度板壳问题的有限元方法。考虑材料各向异性的特点，采用了Ｈｉｌｌ推广的Ｈｕｂｅｒ－Ｍｉｓｅｓ屈服准则；借用Ｏｗｅｎ的剪切修正系数，正确计及了叠层复合材料壳体的横向剪切效应；为了避免“自锁”现象，文中采用了９节点的Ｈｅｔｅｒｏｓｉｓ二次壳单元；特别是本文利用插值外推的思想，提出了一个带预测的弧长增量控制法，显著提高了确定变形路径的计算效率。几个数值算例表明本文给出的有限元方法对于各向异性中厚度板壳的弹塑性分析有较好的精度，尤其是对具有复杂变形路径的结构计算，收敛速度提高更快。     

Vibration reduction of floating elastic plates in surface waves

Based on dynamical theories of water waves and dynamics of Mindlin thick plates,the investigation of the wave-induced responses and the vibration reduction of an elastic floating plate are presented using the Wiener-Hopf technique.Without regard to the case of elastic connector,the calculated results obtained by the present method are in good agreement with those from the literature and the experiment.It can be shown that the present method is valid.Relations between the spring stiffness to be used to connect the sea bottom and the floating plate and the parameters of wave-induced responses of floating plates are investigated using the present method.Therefore, these results can be used as theoretical bases for the design stage of super floating platform systems.     

A two-order and two-scale computation method for nonselfadjoint elliptic problems with rapidly oscillatory coefficients

The purpose of this paper is to solve nonselfadjoint elliptic problems with rapidly oscillatory coefficients. A two-order and two-scale approximate solution expression for nonselfadjoint elliptic problems is considered, and the error estimation of the twoorder and two-scale approximate solution is derived. The numerical result shows that the presented approximation solution is effective.     

非完善板屈曲路径的有限元增量摄动法

本文以Thompson一般稳定性理论为基础,提出非完善结构(有初始几何缺陷)屈曲平衡路径分析的有限元增量摄动法,它克服了增量迭代法及摄动法各自的缺点,利用增量摄动法,还建立了非完善板屈曲平衡路径的数学分析模型,对非完善矩形板在各种边界条件下的屈曲路径实现了数值程序分析,得到了符合实验的结果。     

作大范围运动矩形板的动力学建模理论研究

研究了初应力法的作大范围运动矩形板的建模理论。根据连续介质理论,考虑应变-位移中的非线性项,用一致质量有限元法对柔性板进行离散,基于Jourdain速度变分原理导出定轴转动下大范围运动为自由的柔性板刚-柔耦合动力学方程。从其刚柔耦合动力学方程出发,考虑在大范围运动已知情况下的结构动力学方程。通过引入准静态概念,把其结构动力学方程转化为准静态方程。对纵向和横向变形节点坐标进行坐标分离,解出与纵向变形相关的准静态方程,得到准静态时的纵向应力表达式,从而获得附加刚度项;并对此非惯性系下作大范围运动柔性板的结构动力学方程进行数值仿真,验证了采用初应力法柔性板的动力学建模方法来计算经历大范围运动的不规则柔性板的动力学响应是可行的,体现了初应力法对柔性板建模的优越性。     

Hybrid determination of equivalent characteristics of perforated plates

In this paper, we have adopted the hybrid method, which combines experimental and numerical methods, to investigate the dynamic behavior of perforated plates. It was found that the modal assurance criterion is a useful criterion to judge the degree of similarity between experimental and numerical models. The difference between the experimental and numerical models can be reduced via sensitivity testing and by checking the correlation coefficient. The equivalent material properties of the perforated plates were also obtained by the hybrid method. In addition, the curve-fitting technique was utilized to find the relationship of the mass remnant ratio with the parameter ratio. The functions obtained from the curve fitting can be used to predict accurately the equivalent material properties and resonant frequencies of perforated plates of the diagonal array.     

用拉压不同模量理论分析弯曲板

材料的拉压不同弹性模量性对结构计算的影响是一个不容忽视的问题，本文对不同模量弯曲板进行了较系统的分析，构造了相应的有限元算法，通过算例分析，得出了一些较有价值的结论。     

Exact solution of sound reflection on infinite laminated plate and transmission through it

An exact solution is proposed in this paper based on the elasticity theory for sound reflection from an infinite laminated plate and transmission through it, and some phenomena of sound propagation in an isotropic media are also discussed. Some examples given here could be used to test approximate models of laminated plates.     

A finite difference method at arbitrary meshes for the bending of plates with variable thickness

A finite difference method at arbitrary meshes for the bending of plates with variable thickness is presented in this paper.The method is completely general with respect to various boundary conditions,load cases and shapes of plates.This difference scheme is simple and the numerical results agree well with those obtained by other methods.     

Influence of imperfect bonding on the reflection and transmission of QP-wave at the interface of two functionally graded piezoelectric materials

This paper studies the reflection and transmission of two dimensional quasi P wave incident at an imperfect interface between two dissimilar Functionally Graded Piezoelectric Materials (FGPM) half-spaces. The imperfect bonding behavior between the two considered half-spaces is described by the interfacial imperfections. The imperfection is characterized by the normal stiffness and tangential stiffness using the linear spring model. These interface parameters (i.e normal stiffness and tangential stiffness) are dependent on the elastic properties of interphase. Secular equations have been derived analytically for both the half-spaces. Different cases of imperfect interfaces namely perfect interface, slip interface, weak bonding interface and unbounded interface have been assumed and discussed. Influence of material gradients on the reflection and transmission coefficients (RTC’s) have been inflicted graphically for all the four considered interface conditions. Further, a comparative study of the RTC’s with respect to the incident angle has been carried out for the different cases of imperfections. The obtained results may be useful for measuring imperfection at the interface and designing of SAW devices.     

An experimental and numerical study of heave added mass and damping of horizontally submerged and perforated rectangular plates

Forced harmonic heave motions of horizontally submerged and perforated rectangular plates are studied experimentally and numerically at both a deep and shallow submergence. The steady-state vertical forces are expressed in terms of added mass and damping coefficients. The numerical results are partly obtained by combining potential flow with linear free-surface conditions and a nonlinear viscous pressure loss condition at the mean oscillatory plate position. A domain decomposition technique is applied with a boundary element method in the inner domain and an analytical representation of the velocity potential in the outer domain. A drag term accounts for the vortex shedding at the outer plate edges. The numerically predicted Keulegan–Carpenter number dependent heave added mass and damping coefficients agree reasonably with experimental values, in particular for the deeper submergence.     

Variational principles of perforated thin plates and finite element method for buckling and post-buckling analysis

On the basis of the general theory of perforated thin plates under large deflections^{[1, 2]}, variational principles with deflectionw and stress functionF as variables are stated in detail. Based on these principles, finite element method is established for analysing the buckling and post-buckling of perforated thin plates. It is found that the property of element is very complicated, owing to the multiple connexity of the region. Project supported by National Natural Science Foundation of China.     

Numerical analysis of delamination growth for stiffened composite laminated plates

A study of postbuckling and delamination propagation behavior in delaminated stiffened composite plates was presented. A methodology was proposed for simulating the multi-failure responses, such as initial and postbuckling, delamination onset and propagation, etc. A finite element analysis was conducted on the basis of the Mindlin first order shear effect theory and the von-K6rm~n nonlinear deformation assumption. The total energy release rate used as the criteria of delamination growth was estimated with virtual crack closure technique (VCCT). A self-adaptive grid moving technology was adopted to model the delamination growth process. Moreover, the contact effect along delamination front was also considered during the numerical simulation process. By some numerical examples, the influence of distribution and location of stiffener, configuration and size of the delamination, boundary condition and contact effect upon the delamination growth behavior of the stiffened composite plates were investigated. The method and numerical conclusion provided should be of great value to engineers dealing with composite structures.     

一种预测层合板层间剪应力的新后处理方法

层合板是航空航天领域典型的承力构件,过大的层间应力是导致其分层失效的主要原因.准确的层间应力预测往往依赖于三维平衡方程后处理方法(TPM).然而,该方法需要计算面内应力的一阶导,使得基于C0型板理论构造的线性单元无法使用TPM计算横向剪应力.本文在三维平衡方程后处理方法的基础上,提出了一种新后处理方法(NPM).新后处理方法通过虚功等效法消除了三维平衡方程后处理方法中产生的位移参数的高阶导.基于提出的新后处理方法和C0型板理论,仅需使用线性单元就可以预测层合板的横向剪应力.为了验证所提方法的有效性,本文基于修正锯齿理论(RZT)和所提方法构造了一种C0连续的三节点三角形线性板单元.数值算例表明,所提方法和三维平衡方程后处理方法具有相同的计算精度,提出的板单元能够准确高效地预测层合板的横向剪应力.此外,所提方法便于结合现有的有限元商用软件使用,基于商用软件中板壳单元获得的节点位移,使用新后处理方法极易获得准确的层间剪应力.     

The influence of the viscosity and the magnetic field on reflection and transmission of waves at interface between magneto-viscoelastic materials

The influence of the viscosity on reflection and refraction of plane shear elastic waves in two magnetized semi-infinite media is investigated. The numerical results for the absolute values of the reflection and refraction coefficients and their relative changes for a particular choice of the media are presented graphically. The relative changes of these coefficients are calculated for two special orientations of the magnetic field. It is found that the absolute values of these coefficients are not only functions of the angle of incidence but they are also functions of both the large primary magnetic field and the viscosity of the media. They also vary with the orientation of the magnetic field. Finally, we show that the results of earlier works could be obtained here as particular cases. Finally, this study is regarded an attempt to accommodate magnetic field in visco-elastic media where reflection and refraction of plane shear waves are considered. Results which are obtained in this investigation useful for practical applications or for understanding some aspects of physical acoustic.     

A refined theory of elastic thick plates for extensional deformation

Based on elasticity theory, various two-dimensional (2D) equations and solutions for extensional deformation have been deduced systematically and directly from the three-dimensional (3D) theory of thick rectangular plates by using the Papkovich–Neuber solution and the Lur’e method without ad hoc assumptions. These equations and solutions can be used to construct a refined theory of thick plates for extensional deformation. It is shown that the displacements and stresses of the plate can be represented by the displacements and transverse normal strain of the midplane. In the case of homogeneous boundary conditions, the exact solutions for the plate are derived, and the exact equations consist of three governing differential equations: the biharmonic equation, the shear equation, and the transcendental equation. With the present theory a solution of these can satisfy all the fundamental equations of 3D elasticity. Moreover, the refined theory of thick plate for bending deformation constructed by Cheng is improved, and some physical or mathematical explanations and proof are provided to support our justification. It is important to note that the refined theory is consistent with the decomposition theorem by Gregory. In the case of nonhomogeneous boundary conditions, the approximate governing differential equations and solutions for the plate are accurate up to the second-order terms with respect to plate thickness. The correctness of the stress assumptions in the classic plane-stress problems is revised. In an example it is shown that the exact or accurate solutions may be obtained by applying the refined theory deduced herein.     

Study on failure process of delaminated stiffened composite plates under compression

Failure behavior of the delaminated stiffened composite plates under compression is studied by the finite element method, based on a Global-Local variational model. A virtual crack closure technique and a self-adaptive grid moving scheme are proposed to predict the delamination growth process. The contact effect along the delamination front is considered. The numerical results show that the influences of the distribution and location of the stiffeners, the configuration and size of the delamination, the boundary condition and the contact upon the failure behavior of the plates are significant. The project supported by the National Natural Science Foundation of China (59975014)     

A semi-analytical approach for the non-linear large deflection analysis of laminated rectangular plates under general out-of-plane loading

A semi-analytical approach for the geometrically non-linear analysis of rectangular laminated plates with general inplane and out-of-plane boundary conditions under a general distribution of out-of-plane loads is developed. The analysis is based on the elastic thin plate theory with geometrically non-linear von Kármán strains. The solution of the non-linear partial differential equations is reduced to an iterative sequential solution of non-linear ordinary differential equations using the multi-term extended Kantorovich method. The efficiency, accuracy, and convergence of the proposed method are examined through a comparison with other semi-analytical methods and with finite element analyses. The capabilities of the approach and its applicability to the non-linear large deflection analysis of plate structures are demonstrated through various numerical examples. Emphasis is placed on combinations of lamination, boundary, and loading conditions that cannot be analyzed using alternative semi-analytical methods.