正交各向异性材料的弹塑性损伤本构关系

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,在此基础上,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程,并以具局部损伤的正交各向异性矩形薄板为例,采用Galerkin法和迭代法,对其弹塑性屈曲问题进行了分析,讨论了局部损伤对正交各向异性矩形薄板弹塑性屈曲临界应力的影响.      

具确定弱区域正交各向异性薄板的弹塑性屈曲分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的具损伤正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,在此基础上,建立了正交各向异性材料的增量型和全量型弹塑性损伤本构方程,并以具确定弱区域正交各向异性矩形薄板为例,根据屈曲时的能量准则和全量理论,以等效塑性应变为内变量,对其弹塑性屈曲问题进行了分析,讨论了几何参数和弱区域对正交各向异性薄板弹塑性屈曲临界应力的影响.     

正交各向异性地基平面问题动力响应研究

以位移分量为基本未知量,在直角坐标系下建立正交各向异性地基的平面应变问题动力偏微分方程．采用Laplace-Fourier变换和逆变换方法,引入初始条件和边界条件,推导了任意形式表面动荷载作用下正交各向异性地基平面问题在时域内动力反应的积分形式解．基于理论解,编制了相应的计算程序,并对正交各向异性土
体表面作用线性移动谐振荷载进行了算例分析,研究了土体参数、荷载移动速度、荷载频率不同而导致的土体表面各点竖向位移幅值的变化规律,以及荷载速度对竖向应力分量的影响规律．数值分析结果表明：土体的各向异性、荷载频率和移动速度对表面位移幅值有较大影响,土体阻尼比对于荷载中心点附近的位移幅值影响较小;荷载移动速度对于竖向应力分量有较大影响,这对工程实践具有重要指导意义．     

考虑损伤效应的正交各向异性板的弹塑性静动力分析

基于弹塑性力学和损伤理论,建立了一个与应力球张量有关的正交各向异性材料的混合硬化屈服准则,该准则无量纲化后与各向同性材料的Mises准则同构,进而建立了混合硬化正交各向异性材料的增量型弹塑性损伤本构方程和损伤演化方程.基于经典Kirchhoff板理论,获得了正交各向异性薄板的增量型运动控制方程,且采用有限差分法和迭代法进行求解.数值算例中,讨论了损伤演化、外载荷参数等因素对正交各向异性薄板弹塑性静动力性质的影响,数值结果表明,考虑结构的损伤和损伤演化时,结构的力学性质将发生显著的变化.     

正交各向异性韧性材料应力-应变关系

采用大变形弹塑性有限元方法分析了各向同性和正交各向异性韧性材料光滑圆棒拉伸试件的颈缩问题．首先给出了采用计算机模拟确定各向同性韧性材料真实应力-应变曲线的具体方法；对正交各向异性韧性材料的分析表明，颈缩截面呈椭圆形，其长短轴方向的等效塑性应变基本上均匀分布，与Bridgman假设一致；轴向拉伸载荷-位移曲线与其它两方向的各向异性参数关系不大．在此基础上，建议了一种确定正交各向异性韧性材料真实应力-应变曲线的方法．     

理想正交各向异性弹塑性材料平面应变条件下静止裂纹尖端场

以Hill唯象理论为基础,建立正交各向异性弹塑性材料的本构关系,给出理想正交各向异性弹塑性材料在平面应变条件下混合型静止裂纹尖端的弹塑性场.与J.Pan的解不同,采用自相似假定,可以用解析方法求得不存在应力间断的应力场.对满塑性区条件和应变的奇异性加以讨论,这些为建立断裂准则提供了理论的依据.     

本构模型对复合材料中X射线热击波数值模拟结果的影响

以碳酚醛靶中的一维应变热击波为例,讨论本构模型对热击波数值模拟结果的影响.数值模拟采用3种本构模型,即各向同性理想弹塑性本构模型、各向异性理想弹塑性本构模型及各向异性动态弹塑性本构模型.结果表明:与各向同性理想弹塑性、各向异性理想弹塑性本构模型相比,利用各向异性动态弹塑性本构模型获得的热击波应力峰值较小、应力峰值衰减较...     

理想正交各向异性弹塑性材料平面应力条件下Ⅰ型静止裂纹尖端场

在本文中,以 Hill 的塑性理论为基础,详细地讨论了理想正交各向异性弹塑性材料,平面应力条件下Ⅰ型静止裂纹尖端场解。裂纹尖端应力场不包含应力间断线,但包含弹性区。分析的结果表明(i)对于平面应力静止裂纹问题,应力场解不是唯一的,场解中的自由参数必须由远场条件来确定。(ii)裂纹尖端的应力、应变的奇异性,无论是各向异性材料还是各向同性材料,都是相同的。但在各向异性材料中,各向异性参数影响着应力、应变的幅度和分布。     

理想正交各向异性弹塑性材料平面应力条件下Ⅰ型静止裂纹尖端场

在本文中,以 Hill 的塑性理论为基础,详细地讨论了理想正交各向异性弹塑性材料,平面应力条件下Ⅰ型静止裂纹尖端场解。裂纹尖端应力场不包含应力间断线,但包含弹性区。分析的结果表明(i)对于平面应力静止裂纹问题,应力场解不是唯一的,场解中的自由参数必须由远场条件来确定。(ii)裂纹尖端的应力、应变的奇异性,无论是各向异性材料还是各向同性材料,都是相同的。但在各向异性材料中,各向异性参数影响着应力、应变的幅度和分布。     

平面应变各向异性本构关系及在应力波传播模拟中的应用

为了研究平面应变条件下各向异性材料中应力波传播的特点,利用各向异性弹性Hooke定律、 Tsai-Hill屈服准则、经典塑性流动理论,引入修正的物态方程计及高压下的体积压缩非线性,建立了平面应 变条件下正交各向异性复合材料的弹塑性本构关系,并且分析了二维问题中材料变形引起的主轴旋转及客 观应力率修正问题。最后采用动态显式有限元方法自行编写程序模拟某种纤维增强复合材料碰撞过程中平 面应力波的传播,模拟结果显示,在平面应变条件下应力波在该材料的传播过程中表现出明显的二维效应、各 向异性特点及弹塑性特点。     

Residual Stress Analysis of Orthotropic Materials by the Through-hole Drilling Method

The present study deals with the development and the application of the through-hole drilling method for the residual stress analysis in orthotropic materials. Through a systematic theoretical study of the stress field present on orthotropic plates with a circular hole, the relationships between the relaxed strains measured by a rectangular strain gauge rosette and the Cartesian components of the unknown residual stresses are obtained. The theoretical formulas of each influence coefficient allow the user an easy application of the method to the analysis of uniform-residual stresses on a generic homogeneous orthotropic material. Furthermore, to extend the method to the analysis of the residual stresses on orthotropic laminates, caused by initial in-plane loadings, an alternative formulation is implemented. The accuracy of the proposed method has been assessed through 3D numerical simulations and experimental tests carried out on unidirectional, cross-ply and angle-ply laminates.     

四边转角约束正交异性板的临界载荷

考虑横向剪切变形的影响和四边弹性转角约束的边界条件,给出了一种求解正交异性板临界应力的方法。弹性转角约束的极限情况就是简支和固支。应用本给出的方法,在几种退化的情况下,对若干矩形板进行计算,并与现有献进行了比较,结果吻合较好,从而验证了中给出的方法。     

Exact solutions for variable-thickness inhomogeneous elastic plates under various boundary conditions

In this paper, an exact solution to the governing equations of the bending of a variable-thickness inhomogeneous rectangular plate is presented. The procedure is applicable to variable-thickness inhomogeneous rectangular plates with two opposite edges simply supported. The remaining ones subjected to a combination of clamped, simply supported, and free boundary conditions and between these two edges the plate may have varying thickness. The procedure is valuable in view of the fact that tables of deflections and stresses cannot be presented for variable-thickness inhomogeneous orthotropic plates as for uniform-thickness homogeneous isotropic plates even for commonly encountered loads because the results depend on the inhomogeneity coefficient and the orthotropic material properties instead of a single flexural rigidity. Numerical results, useful for the validation or otherwise of approximate solutions, are tabulated. The influences of the degree of the inhomogeneity, aspect ratio, thickness parameter and degree of non-uniformity on the deflections and stresses are investigated. This paper is partially supported by the Deanship of Scientific Research at King AbdulAziz University (Grant no. 172/427).     

Modified equations of finite-size layered plates made of orthotropic material. Comparison of the results of numerical calculations with analytical solutions

This paper describes the modified bending equations of layered orthotropic plates in the first approximation. The approximation of the solution of the equation of the three-dimensional theory of elasticity by the Legendre polynomial segments is used to obtain differential equations of the elastic layer. For the approximation of equilibrium equations and boundary conditions of three-dimensional theory of elasticity, several approximations of each desired function (stresses and displacements) are used. The stresses at the internal points of the plate are determined from the defining equations for the orthotropic material, averaged with respect to the plate thickness. The construction of the bending equations of layered plates for each layer is carried out with the help of the elastic layer equations and the conjugation conditions on the boundaries between layers, which are conditions for the continuity of normal stresses and displacements. The numerical solution of the problem of bending of the rectangular layered plate obtained with the help of modified equations is compared with an analytical solution. It is determined that the maximum error in determining the stresses does not exceed 3 %.     

Analysis of adhesive lap joint

This paper is to solve the interlaminar stresses of adhesive lap joint by the energy method without considering the adhesive layer. The joint is made of two identical narrow plates. Two cases are discussed: one is for the isotropic material and the other is for orthotropic material. Because of the different materials forming the joint, the length of distribution and the magnitude of the interlaminar, stresses for the two cases will be very different.Projects supported by the Science Fund of Chines Academy of Sciences (1986–1988).     

Stresses due to an adhesion crack in T-shaped junction of two orthotropic plates

The general solution of stresses is derived for a T-shaped junction of two thin plates with an adhesion crack.The plates are orthotropic.A shear force is applied on the crack surface.The analysis is based on the supposition that the stresses in each plate can be approximated by a plane stress condition.The results obtained are verified by numerical calculation of FEM.     

Stress analysis in adhesive-bonded joints for orthotropic plates

In the current paper we present the tensile force, the edge moment and edge transverse force acting on the single-lap joint and get the moment reduction factork for orthotropic plates. We use the variational method based on the principle of complementary energy. Considering Hooke's law for orthotropic materials, carrying out the variationV=0 and using the Euler-Poisson's equation we establish all the expressions of stresses in the joint for orthotropic plates. All numerical calculations can be made on a computer.     

Non-linear least-squares solution to the moiré hole method problem in orthotropic materials. Part II: Material elastic constants

This is the second of two papers dealing with inverse problems arising from the hole method problem in orthotropic materials. Two inverse problems are of interest in this second paper: one relates to the use of the hole method as a means of separation of stresses; the other deals with using it for orthotropic material elastic constant identification. The problem of separation of stresses is posed and briefly discussed, but the orthotropic material identification problem is addressed, fully showing how to obtain the five orthotropic elastic constants, four of which are independent, when knowing the applied stresses and examining the isothetics or moiré fringes around a through hole in a biaxially loaded thin wood plate.     

复合板旋转约束刚度推导及箱型结构屈曲分析

基于结构稳定性理论,推导出正交各向异性纤维树脂增强复合材料箱型结构各板连接处旋转约束刚度的近似表达式．与以往的经验公式相比,考虑了材料的正交各向异性和截面尺寸的影响．通过对箱型结构的正交各向异性比、截面属性以及纵横比对旋转约束刚度的影响进行参数研究,验证了旋转约束刚度新公式的精确性和适用范围．通过比较采用不同近似表达式得到的结果与有限元计算结果的对比,表明本文的旋转约束刚度新公式可以更精确地用来计算箱型结构的临界屈曲载荷．     

基于近场动力学微分算子的含裂纹正交各向异性板热传导分析方法

采用近场动力学微分算子(Peridynamic Differential Operator, PDDO)理论建立正交各向异性板热传导的非局部模型。通过构造近场动力学函数,将边界条件和热传导方程由局部微分形式转化为非局部积分形式,引入Lagrange乘子,采用变分分析对含裂纹正交各向异性板温度及裂纹尖端的热通量分布进行求解。通过对比算例,验证了该模型具有较好的收敛性和有效性。分析了正交各向因子、材料铺设角、裂纹倾角及间距对裂纹尖端热通量的影响。结果表明,基于PDDO建立的含裂纹正交各向异性板热传导模型,考虑了热传导问题中的非局部性,能有效提高计算精度,预测含裂纹板中裂纹尖端出现的奇异性。