共查询到17条相似文献,搜索用时 62 毫秒
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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。 相似文献
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研究了孔隙水压力作用下横观各向同性热弹性多孔介质板的精化理论。在不做任何预先假设的情况下,利用Lur’e方法和横观各向同性热弹性多孔介质的通解,得到了横观各向同性热弹性多孔介质板的精化理论。首先,根据调和函数的sin算子函数表达式,得到了用5个二维待定函数表示的位移场和应力场;其次,在非齐次边界条件下,利用基本的数学算法,得到了在孔隙水压力载荷作用下热弹性多孔介质板的精化方程;最后,通过舍弃高阶项,得到了位移场和应力场的近似解。 相似文献
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将精化理论的研究方法推广到轴对称横观各向同性压电热弹性圆柱的研究中,利用压电热弹性问题的轴对称通解以及准调和函数的Bessel算子函数表示方法,获得了该圆柱在柱面受温度载荷作用下的精确耦合场;当柱面受到随轴向Z增大而逐渐减小的轴对称量纲为一的温度载荷时,绘制出圆柱在半径r分别为0.2、0.4、0.6、0.8、1.0时的位移分量、电势、温度增量沿轴向z的分布。结果表明:圆柱在同一高度的情况下,径向位移和轴向位移随半径增大而增大,电势的绝对值也随半径的增大而增大,而温度增量随半径的变化则不明显。此外,本文还通过算例验证了该精化理论应用的正确性。 相似文献
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本文从横观各向同性梁的二维问题出发,研究了横观各向同性热弹性梁的精化理论。首先,在不作任何预先假设的条件下,利用横观各向同性热弹性理论和Lur’e算子函数,获得了由梁中线上的物理量表示的位移场和应力场。对热弹性梁上下表面承受非齐次边界条件的情况,推导出梁的近似控制微分方程。再舍去温度项,则横观各向同性热弹性梁的精化理论退化为横观各向同性梁的精化理论。 相似文献
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横观各向同性介质中弹性波的吸收边界条件 总被引:2,自引:0,他引:2
在数值求解固体中的弹性波动问题时,常需引入吸收边界条件来限制大范围或无边界的求解区域,使数值计算得以顺利进行。本文通过合成简单的一阶偏微分算子,给出了横观各向同性介质中弹性波的吸收边界条件,其中每个单一的算子均可完全吸收沿某一角度出射的平面波。文中还基于弹性波的势函数理论,导出了准P波和准S波在吸收边界处的反射系数公式,用以检验其吸收能力。本文所给出的吸收条件,形式简单,且算例表明吸收效果良好,因 相似文献
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从位移的通解出发,用分离变量法得到横观各向同性圆柱体的位移和应力的特征函数展开式,并把位移势函数的解用付里叶积分的形式表示。利用留数运算,该积分解可以转换成类似于特征函数的展开式。通过混合端部边界问题,得到与特征函数解成双正交关系的另一组函数。利用这种双正交关系,可以处理不同的端部边界问题。 相似文献
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论证了只要合适选择中间界面层的弹性常数,各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场。讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件。所给出的数值算例显示出该结论的正确性。该方法为纤维增强复合材料的设计提供了一条新途径。 相似文献
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论证了只要合适选择中间界面层的弹性常数, 各向异性线弹性固体在远场均匀反平面剪切应力作用下三相椭圆夹杂内椭圆上仍存在均匀应力场. 讨论了内外两椭圆除过其中心相同外无其它任何几何限制条件. 所给出的数值算例显示出该结论的正确性. 该方法为纤维增强复合材料的设计提供了一条新途径. 相似文献
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本文采用横观各向同性层状弹性模型,模拟半空间上的层状场地,用阻尼器模拟透射边界代替半空间以吸收能量。利用薄层元素法和于结构法,并利用在这种边界下受水平简谐荷载作用下的格林函数,推导了这种场地中竖直单桩在水平—摇摆简谐荷载作用下的横向动力阻抗函数,并用实例计算了不同横观各向同性性质场地下的动力阻抗函数,并由此分析了场地的横观各向同性性质的强弱对单桩的横向动力阻抗函数所将产生的影响。计算表明:弱横观各向同性场地对阻抗函数的影响很小,以至可以忽略这种影响;而强横观各向同性场地对阻抗函数的影响较大,必须考虑其影响。另外,桩头约束的存在与否,对单桩的横向阻抗函数值也有较大的影响,桩头有约束的阻抗函数值要明显大于无约束的阻抗函数值。 相似文献
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The purpose of this research is to further investigate the effects of material inhomogeneity on the decay of Saint-Venant
end effects in linear isotropic elasticity. This is carried out within the context of anti-plane shear deformations of an
inhomogeneous isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates
of solutions to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation
with variable coefficients on a semi-infinite strip. In previous work [1], the elastic coefficients were assumed to be smooth
functions of the transverse coordinate so that the material was inhomogeneous in the lateral direction only. Here we develop
a new technique, based on a change of variable, to study generally inhomogeneous isotropic materials. The governing partial
differential equation is transformed to a Helmholtz equation with a variable coefficient, which facilitates analysis of the
influence of material inhomogeneity on the diffusion of end effects. For certain classes of inhomogeneous materials, an explicit
optimal decay estimate is established. The results of this paper are applicable to continuously inhomogeneous materials and,
in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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The purpose of this research is to investigate the effects of material inhomogeneity on the decay of Saint-Venant end effects
in linear isotropic elasticity. This question is addressed within the context of anti-plane shear deformations of an inhomogeneous
isotropic elastic solid. The mathematical issues involve the effects of spatial inhomogeneity on the decay rates of solutions
to Dirichlet or Neumann boundary-value problems for a second-order linear elliptic partial differential equation with variable
coefficients on a semi-infinite strip. The elastic coefficients are assumed to be smooth functions of the transverse coordinate.
The estimated rate of exponential decay with distance from the loaded end (a lower bound for the exact rate of decay) is characterized
in terms of the smallest positive eigenvalue of a Sturm–Liouville problem with variable coefficients. Analytic lower bounds
for this eigenvalue are used to obtain the desired estimated decay rates. Numerical techniques are also employed to assess
the accuracy of the analytic results. A related eigenvalue optimization question is discussed and its implications for the
issue of material tailoring is addressed. The results of this paper are applicable to continuously inhomogeneous materials
and, in particular, to functionally graded materials.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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The stress-concentration problem for an elastic transversely isotropic medium containing an arbitrarily oriented spheroidal inclusion (inhomogeneity) is solved. The stress state in the elastic space is represented as the superposition of the principal state and the perturbed state due to the inhomogeneity. The problem is solved using the equivalent-inclusion method, the triple Fourier transform in space variables, and the Fourier-transformed Green function for an infinite anisotropic medium. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. In special cases, the results are compared with those obtained by other authors. The influence of the geometry and orientation of the inclusion and the elastic properties of the medium and inclusion on the stress concentration is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 2, pp. 33–40, February 2005. 相似文献
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The magnetoelastic stress-strain problem for a transversely isotropic ferromagnetic body with an elliptical crack in the isotropy plane is solved explicitly. The body is in an external magnetic field perpendicular to the isotropy plane. The magnetic field induces elastic strains and an internal magnetic field in the body. The main characteristics of stress-strain state and induced magnetic field are determined and their features in the neighborhood of the crack are analyzed. Formulas for the stress intensity factors of the mechanical and magnetic fields near the crack tip are presented__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 48–59, January 2005. 相似文献
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V. S. Kirilyuk 《International Applied Mechanics》2005,41(4):358-366
The static-equilibrium problem for an elastic orthotropic space with an elliptical crack is solved. The stress state of the space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’s approach is used. It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material, and Cauchy’s residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 20–29, April 2005. 相似文献
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对材料力学中梁的弯曲应力公式增加一修正项,以反映短梁弯剪翘曲变形对应力分布的影响。提出一种根据短梁横截面边界形状及艾瑞应力函数求解应力修正项的方法,应用弹性力学空间问题的一般理论,通过应力平衡方程、应变相容方程及应力边界条件,建立了关于任意截面短梁的应力修正项及剪应力的基本方程。在所建立的基本方程基础上,导出了矩形截面和圆形截面短梁修正应力的具体计算公式,该修正应力与均布荷载大小及弹性模量与剪切模量之比均成正比,但与截面惯性矩成反比。数值算例表明,本文方法计算的应力与通用有限元软件ANSYS计算的结果吻合良好,从而验证了本文方法及其基本公式的正确性。 相似文献