软化材料厚壁筒的解析解及其稳定性分析

将弹塑性材料的应力应变全过程曲线简化为三线性模型(弹性-线性软化-残余理想塑性),并假设材料服从Tresca屈服准则和关联流动法则,推导出受内压厚壁筒的解析解.在这个解析解的基础上,讨论了厚壁筒的平衡稳定性问题,内压达到临界载荷时,厚壁筒丧失稳定性,其临界载荷就是软化塑性材料厚壁筒的承载能力.     

he analytical solutions of thick-walled cylinder of softening material and its stability

将弹塑性材料的应力应变全过程曲线简化为三线性模型(弹性-线性软化-残余理想塑性), 并 假设材料服从Tresca屈服准则和关联流动法则,推导出受内压厚壁筒的解析解. 在这个解析解 的基础上,讨论了厚壁筒的平衡稳定性问题,内压达到临界载荷时,厚壁筒丧失稳定性,其 临界载荷就是软化塑性材料厚壁筒的承载能力.     

粘弹性轴对称平面问题的动态响应

1.引言关于粘弹性轴对称平面问题的一些特殊情况已有若干论述,然而多是讨论材料不可压的情形;有关可压缩粘弹体的求解,往往只是分析准静态问题或讨论一些特例.在文[7]中作组合筒应力分析时给出的动态响应一般解,亦限于不可压材料.Huang等讨论了圆筒高速旋转对材料可压性的影响.Valanis和Sachman分析过弹性波问题,讨论了若干情况下的求解方法. 本文讨论可压粘弹材料在轴对称平面应变状态下的动态响应,从基本方程出发,导出位移应满足的方程,用Laplace变换方法求得在象空间中的一般解.具体分析了厚壁     

柱状装药爆炸条件下厚壁圆筒爆室内 流场及结构动力响应分析

借助非线性动力有限元程序ANSYS/LS-DYNA,采用基于罚函数的流固耦合算法,对厚壁圆筒爆 室在柱状装药爆炸作用下的动态响应过程进行了数值模拟研究。分析了厚壁圆筒爆室内柱状装药爆炸非定 常流场的演化过程以及筒体的动力响应特征。给出了爆炸流场的压力云图、筒壁受到的爆炸压力峰值及冲量 的分布规律、筒体的等效应力云图以及等效应力的分布规律等。流场压力及筒体应变的计算结果与实测结果 吻合较好,并将动力响应的有限元计算结果与理论解进行了比较,证明轴对称平面应变假设下的理论解可以 给出问题的保守估算。分析表明,该厚壁圆筒爆室在柱状装药爆炸作用下在弹性范围内工作,爆室的强度设 计是安全的。     

两端固支强厚度叠层闭口柱壳轴对称问题的精确解

抛弃任何有关应力或位移模式的人为假设,在文献【1】、【2】的基础上,引入δ—函数,在轴对称情况下,对两端固支叠层闭口柱壳建立其状态方程。给出薄的、中厚的以及强厚的叠层闭口柱壳的静力和动力问题的统一的精确解。此解满足所有的弹性力学基本方程,并计及了全部弹性常数。任意需要的精确度都能得到。     

利用 Laplace 变换确定双层厚壁长圆筒的轴对称界面碰撞压力

利用Ｌａｐｌａｃｅ变换，考虑轴对称弹性波的影响，采用特征函数展开法求解双层厚壁长圆筒受爆炸载荷作用下的轴对称弹性碰撞冲击问题，着重研究前几次碰撞冲击引起的轴对称界面碰撞压力。并对轴对称界面碰撞压力与间隙量、爆炸载荷幅值、爆炸载荷衰减系数之间的关系以及相关的动力响应作了初步的分析。     

基于Kriging插值无网格法求解轴对称弹性力学问题

基于Kriging插值无网格法,提出了实际应用中复杂轴对称弹性力学问题求解的一条新途径.Kriging插值无网格法是一种新型的无网格法,该方法构造的形函数满足Kronecker delta函数性质,可以直接施加本质边界条件.采用Kriging插值无网格法分析轴对称问题,得到了轴对称问题的无网格离散方程,并编制了相应的计算程序.通过厚壁圆筒的静力学和动力学分析,对所提方法进行了检验.数值算例结果表明,提出的方法对求解轴对称弹性力学问题是行之有效的.     

任意轴对称弹性体吸附接触的广义Maugis模型

通过线性叠加Sneddon方法和Lowengrub-Sneddon方法分别给出的解, 得到了一个弹性半空间 轴对称混合边值问题的一般解，进而研究了两个一般轴对称弹性体的正向无摩擦吸附接触问 题. 考虑任意有效的表面形状(要求中心部分首先进入接触)和任意的表面吸附作用，推广 得到了广义Maugis模型. 该模型是一个半解析的模型，它可以分解成表面形状和表面吸附 作用的分别独立影响的两部分，以及一个关联变形和吸附作用的式子. 利用Dugdale模型近 似表面吸附作用，得到了具有任意有效的表面形状的广义M-D模型. 它在强吸附或软材料条 件下的极限形式是广义JKR模型，而在弱吸附或硬材料下的另一个极限形式是广义DMT模型.     

受外压厚壁圓管压溃过程的有限元分析

用有限元数值方法研究受外压厚壁圆管的非轴对称分支现象,假定圆管变形满足平面应变,稳定变形一直持续到外压达最大值,其后发生压溃过程.随着压力减少,数值计算中可能出现两种平衡路径,即全面弹性卸载和继续非轴对称变形.为避免前者,采用了降阶法.     

轴对称任意梯度圆筒的弹性动力学解

基于轴对称平面应变问题的运动方程及弹性梯度材料的应力和位移关系,通过将圆筒分层使材料性质离散为分段常数函数,同时在时域内应用有限差分格式,求得了材料性质沿径向梯度变化的圆筒弹性动力学解。本文解不仅适合任意梯度的弹性圆筒,而且容易满足多种形式的初始条件和边界条件。通过对材料性质沿径向为连续函数分布和分段函数分布的梯度圆筒数值分析,并与已有文献结果比较,得出本文解与已有文献的解吻合较好,验证了本文解的正确性和有效性。对材料性质为分段函数的三层组合圆筒分析发现,中间功能梯度层的指数分布因子对圆筒的径向位移和应力随时间变化都会产生显著影响。     

统一强度准则下厚壁圆筒的弹脆塑性承载能力分析

应用统一强度准则和弹脆塑性变形模型，研究材料具有软化效应的厚壁圆筒的承载力。分别导出在内压及外压作用下厚壁圆筒弹脆塑性承载力的计算公式。这些公式不仅给出了以往基于Mohr-Coulomb准则和广义双剪准则的结果，而且给出了一系列新的结果，因而本文的结果可适用于多种材料。实例表明材料软化效应以及分析中所选用的强度准则对厚壁圆筒承载力具有重要影响。因此，在确定厚壁圆筒承载力时，应该合理地选用材料的软化参数及强度准则。     

Effects of radially varying moduli on stress distribution of nonhomogeneous anisotropic cylindrical bodies

In this study, the stress distribution in a nonhomogeneous anisotropic cylindrical body is investigated. Using equilibrium equations, Hooke’s law and strain–displacement relations, a system of equations is obtained in cylindrical coordinates in terms of stress potentials where elastic properties change in radial direction. Young’s and shear moduli are expressed as power functions of r and Poisson’s ratios are kept constant. Closed-form solutions for stress potentials and stress distribution are obtained for an axisymmetric, orthotropic cylinder. Results are checked with FE results. A pressurized thick walled cylinder example is studied in details. Stresses in radial, tangential and axial directions and Von Mises stresses are plotted for different powers of r.     

轴对称横观各向同性热弹性圆柱的分解

为了得到精确的应力场、位移场、温度场,将扭转圆轴的精化理论研究方法推广到轴对称横观各向同性热弹性圆柱。利用Bessel函数以及轴对称横观各向同性热弹性圆柱的通解,给出了轴对称横观各向同性热弹性圆柱的分解定理。根据柱面齐次边界条件获得了精确的精化方程,精化方程可以分解为一阶方程、超越方程、温度方程,从而将横观各向同性热弹性圆柱的轴对称问题分解为轴向拉压问题、超越问题、热-应力耦合问题。超越部分对应端部自平衡情况,可以清晰地了解到端部应力分布对内部应力场的影响,热-应力耦合部分对应无外加应力场时圆柱内部因温度变化引起的热应力。     

Transient thermal stresses in an orthotropic hollow cylinder for axisymmetric problems

For the thermoelastic dynamic axisymmetric problem of a finite orthotropic hollow cylinder, one comes closer to reality to involve the effect of axial strain than to consider the plane strain case only. However, additional mathematical difficulties should be encountered and a different solution procedure should be developed. By the separation of variables, the thermoelastic axisymmetric dynamic problem of an orthotropic hollow cylinder taking account of the axial strain is transformed to a Volterra integral equation of the second kind for a function of time, which can be solved efficiently and quickly by the interpolation method. The solutions of displacements and stresses are obtained. It is noted that the present method is suitable for an orthotropic hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical comparison is made to show the effect of the axial strain on the displacements and stresses. The project supported by the National Natural Science Foundation of China (10172075) and China Postdoctoral Science Foundation (20040350712)     

Axisymmetric circumferential internal crack problem of a thick-walled cylinder with inner and outer claddings

The elastostatic axisymmetric problem for a long thick-walled cylinder containing an axisymmetric circumferential internal crack with two claddings is considered. The claddings having different elastic properties than the hollow cylinder are assumed to be bonded to inner and outer wall of the hollow cylinder. The problem is formulated in terms of a singular integral equation of a well known type, the derivative of the crack surface displacement being the density function, using the standard transform technique. By using appropriate quadrature formulas, the integral equation is reduced to a system of linear algebraic equations. This system is solved numerically and the related stress-intensity factors are calculated for the cases of hollow cylinder with two claddings bonded to inner and outer wall of the cylinder, a cladding bonded to inner wall of the cylinder, a cladding bonded to outer wall of the cylinder and no cladding under axial tensile load. The influence of the geometrical configuration, the claddings and internal crack length on the stress-intensity factors is shown graphically.     

轴对称一维六方准晶圆柱的精化理论

将轴对称圆柱的精化分析推广到一维六方准晶中轴对称圆柱的研究当中。利用准调和函数的Bessel算子函数表示以及一维六方准晶中的通解,在不做任何预先假设的情况下,给出了一维六方准晶中轴对称圆柱的精化理论。首先,根据准调和函数的Bessel算子函数表示,利用三个一维待定函数,表示出声子场和相位子场的位移场和应力分量。再根据非齐次边界条件,推导出柱面受径向外载时的精化方程。通过舍弃高阶项,推导出了在径向方向受到柱面载荷的近似解。     

残余应力下厚壁筒表面裂纹的应力强度因子计算

本文首先介绍了边界元法计算裂纹尖端应力强度因子的基本理论,接着利用边界元法计算了在残余应力下不同厚壁筒内表面椭圆裂纹的应力强度因子,研究了其大不随椭圆裂纹不同而变化的规律,为厚壁筒结构的设计,制造以及疲劳寿命分析提供了许多有价值的参考资料。     

The transient responses of piezoelectric hollow cylinders for axisymmetric plane strain problems

By virtue of the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of hollow cylinder is transferred to an integral equation about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solution of the displacements, stresses, electric displacements and electric potentials are finally obtained. The present method is suitable for the hollow cylinder with arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are also presented.     

Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads

This paper presents an analytical solution of a thick walled cylinder com- posed of a functionally graded piezoelectric material (FGPM) and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson's ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.     

WEIGHT FUNCTION FOR STRESS INTENSITY FACTORS IN ROTATING THICK-WALLED CYLINDER

The equation of stress intensity factors(SIF) of internally pressurized thick- walled cylinder was used as the reference case.SIF equation of rotating thick-walled cylinder containing a radial crack along the internal bore was presented in weight function method.The weight fumction formulas were worked out and can be used for all kinds of depth of cracks,rotating speed,material,size of thick-walled cylinder to calculate the stress intensity factors.The results indicated the validity and effectiveness of these formulas.Meanwhile,the rules of the stress intensity factors in rotating thick-walled cylinder with the change of crack depths and the ratio of outer radius to inner radius were studied.The studies are valuable to engineering application.