共查询到18条相似文献,搜索用时 125 毫秒
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把Rekner型平板裂纹尖端位移场展开式推广到任意切口、任意边界的多材料问题.证明了Reissner型平板断裂问题的特征根等价于相类似的反平面切口问题和平面切口问题两部分的特征根迭加. 相似文献
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多材料反平面断裂问题特征值的超逆幂迭代求解 总被引:3,自引:2,他引:3
从反平面切口问题的特征方程入手,采用换元逆幂迭代法并利用特征函数解析表达式已知及一些有效技巧研究了可以精确有效地求解具有任意张角、多种不同材料及不同边界条件的反平面切口问题的完备特征解的求解方法。 相似文献
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为理解压电材料反平面切口尖端奇异状态,提出了一种切口奇性特征分析法.基于切口根部位移场幂级数渐近展开假设,从应力平衡方程和电荷守恒条件出发,导出了关于压电材料反平面切口奇性指数的特征微分方程组,并将切口的力电学边界条件以及界面协调条件表达为奇性指数和特征角函数的组合.从而,压电材料切口反平面奇性指数的计算被转化为相应边界条件下常微分方程组特征值的求解问题,采用插值矩阵法可以计算出各阶奇性指数和相应的特征角函数.该法既适合裂纹奇性分析,也可用于单、双材料切口的奇性计算,并避免了用迭代法求解超越方程的不足.因而具有适应性强的特点.计算发现,压电材料反平面切口存在两个奇性指数,切口的奇异性程度随着开角的增大而增强. 相似文献
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基于考虑横向剪切变形直角坐标下矩形中厚扁壳的几何方程、本构关系、平衡方程,建立了关于三个中面位移和两个中面转角为独立变量的矩形中厚扁壳小挠度屈曲的基本微分方程。该方程可退化为矩形中厚板屈曲的基本微分方程,从而说明本文推导过程的正确性及一般性。文中矩形中厚扁壳小挠度屈曲的基本微分方程是一组耦合的变系数二阶偏微分方程,对常曲率扁壳使用双重三角级数并将其作为广义坐标对该方程组进行解耦,进一步建立中厚扁壳小挠度屈曲的特征方程,并得到了简支矩形中厚壳屈曲的临界荷载表达式,最后获得了其屈曲的临界荷载曲线及其相应的临界荷载值。该临界荷载曲线及其相应的临界荷载值可以退化为矩形中厚板的临界荷载曲线及临界荷载值。结果表明:本文提出的算法求解过程简便,矩形中厚扁壳临界荷载收敛较快。 相似文献
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本文先推导反平面复合材料切口尖端位移多应力场,然后用分区混合有限元法计算切口应力强度因子。 相似文献
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论文提出了用插值矩阵法计算幂硬化塑性材料反平面V形切口和裂纹尖端区域的应力奇异性.首先在切口和裂纹尖端区域采用自尖端径向度量的渐近位移场假设,将其代入塑性全量理论的基本微分方程后,推导出包含应力奇异性特征指数和特征角函数的非线性常微分方程特征值问题.然后采用插值矩阵法迭代求解导出的控制方程,得到一般的塑性材料反平面V形切口和裂纹的前若干阶应力奇异阶和相应的特征角函数,该法的重要优点是以上求解的特征角函数和它们各阶导函数具有同阶精度,并且一次性地求出前若干阶特征对.同时,插值矩阵法计算量小,易于和其他方法联合使用,这些优点在后续求解尖端区域完全应力场非常优越.论文方法的计算结果与现有结果对照,发现吻合良好,表明了论文方法的有效性. 相似文献
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扁壳的微分方程组可以分解成两个相对独立的方程,平板方程和薄膜方程,其力学意义是视扁壳为在全平面中板与薄膜的组合。将荷载进行分解,使一部分属于平板,另部分属于薄膜,平板与薄膜之间满足形变连缓性条件。方程组经分解后,建立了解决平衡、振动与稳定诸问题的简便计算方法。 相似文献
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提出一种计算广义平面应交状态下复合材料切口应力奇性指数的新方法.在切口尖端的位移幂级数渐近展开式被引入正交各向异性材料的物理方程后,将用位移表示的应力分量代入切口端部柱状邻域的线弹性理论控制方程,切口应力奇性指数的计算被转化为常微分方程组特征值的求解.采用插值矩阵法求解该常微分方程组,可一次性地获取切口尖端多阶应力奇性指数.本法适合平面和反平面应力场耦合或解耦的情形,并可退化计算裂纹或各向同性材料切口的应力奇性指数.算例表明,所提方法对分析复合材料切口应力奇性指数是一种准确有效的手段. 相似文献
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Damaged nonlinear antiplane shear problems with a variety of singularities are studied analytically. A deformation plasticity theory coupled with damage is employed in analysis. The effect of microscopic damage is considered in terms of continuum damage mechanics approach. An exact solution for the general damaged nonlinear singular antiplane shear problem is derived in the stress plane by means of a hodograph transformation, then corresponding higher order asymptotic solutions are obtained by reversing the stress plane solution to the physical plane. As example, traction free sharp notch and crack, rigid sharp wedge and flat inclusion, and mixed boundary sharp notch problems are investigated, respectively. Consequently, higher order fields are obtained, in which analytical expressions of the dominant and second order singularity exponents and angular distribution functions of the near tip fields are derived. Effects of the damage and hardening exponents of materials and the geometric angle of notch/wedge on the near tip quantities are discussed in detail. It is found that damage leads to a weaker dominant singularity of stress, but to little stronger singularities of the dominant and second order terms of strain compared to that for undamaged material. It is also seen that damage has important effect on the angular distribution functions of the near tip stress and strain fields. As special cases, higher order analytical solutions of the crack and rigid flat inclusion tip fields are obtained, respectively, by reducing the notch/wedge tip solutions. Effects of damage and hardening exponents on the dominant and second order terms in the solutions of the crack and inclusion tip fields are discussed. 相似文献
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不同压电介质界面上的反平面运动裂纹 总被引:1,自引:1,他引:0
利用积分变换技术,得到不同压电介质界面上的平面运动裂纹问题的分析解。结果表明应力及电位移强度因子均与界面裂纹扩展速度及材料参数相关,这不同于均匀压电介质中运动裂纹的结论,当两种压电介质完全相同时,本文结果将退化为均匀压电介质中反平面运动裂纹问题的解。 相似文献
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周边切口短圆柱试件的杆杆型冲击拉伸试验系统的弹塑性有限元分析 总被引:6,自引:3,他引:6
基于一维试验原理提出了用带有周边切口的短金属圆柱试件进行平面应变型弹塑性动态断裂韧度的测试方法;对该复杂的动力学系统进行了轴对称的弹塑性有限元分析,并计算了动态围道^J积分;根据对试件功能转换关系的分析和Rice公式的物理意义,提出了用试件两端平功载荷-两端相对位移曲线(P^-△)推广Rice公式计算试件的远场J积分,由此得到的P^-△曲线基本上消除了与裂纹运动无关的质心运动动能的影响。论证了J积分作为裂端的表征参量,且当切口深度比大于70%时,Rice公式有较高的计算精度,为平面应变型弹塑性动态断裂韧度的表征与测试提供了依据。 相似文献
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This paper is concerned with the plane elastostatic problem of a crack emanating from an open notch where it is assumed that the crack is directed parallel to one side of the notch. The problem is reduced to two simultaneous Fredholm integral equations which are then solved numerically for three loading conditions of the crack faces. In particular, it is shown that the crack tip intensity factors are almost independent of crack length if the singular stress field associated with the uncracked notch is used as the loading of the crack faces. 相似文献
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WangBaolin HanJiecai DuShanyi 《Acta Mechanica Solida Sinica》2004,17(4):290-296
The electrical boundary conditions on the crack faces and their applicability in piezoelectric materials are discussed. A slit crack and a notch of ?nite thickness in piezoelectric materials subjected to combined mechanical and electrical loads is consi… 相似文献
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A. I. Anpilogov 《International Applied Mechanics》2011,46(8):929-941
The possibility for diagnostics of a breathing crack type damage in a long cylindrical shell is examined. The damage is modeled
by a notch that alters the cross-sectional geometry. The method of conformal mappings is used to solve the first main boundary-value
problem of elasticity for domains in the form of an annular sector with and without a notch. The solutions are analyzed and
compared to estimate the relative decrease in the stiffness of the shell because of the opening of the crack 相似文献