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Using the complex variable method and conformal mapping, scattering of flexural waves and dynamic stress concentrations in
Mindlin's thick plates with a cutout have been studied. The general solution of the stress problem of the thick plate satisfying
the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique, the dynamic
stress problem can be reduced into the solution of a set of infinite algebraic equations. As examples, numerical results for
the dynamic stress concentration factor in Mindlin's plates with a circular, elliptic cutout are graphically presented in
sequence.
The project supported by the National Natural Science Foundation of China 相似文献
2.
Chuan-ping Zhou Qiao-yi Wang Denghao Chen Chao Hu Ban Wang Fai Ma 《Acta Mechanica Solida Sinica》2018,(3)
Based on the refined dynamic equation of stretching plates, the elastic tensioncompression wave scattering and dynamic stress concentrations in the thick plate with two cutouts are studied. In view of the problem that the shear stress is automatically satisfied under the free boundary condition, the generalized stress of the first-order vanishing moment of shear stress is considered. The numerical results indicate that, as the cutout is thick, the maximum value of the dynamic stress factor obtained using the refined dynamic theory is 19% higher than that from the solution of plane stress problems of elastic dynamics. 相似文献
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摘要:本文基于复变函数与保角映射法,采用平板弯曲振动精确化方程[9],对含任意形开孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。作为算例,计算了自由边界条件下圆孔和椭圆孔的动弯矩集中系数的数值结果,并对板厚与孔径比对动弯矩分布的影响做了分析研究。结果表明:入射波数、平板厚度和椭圆偏心率等参数对动弯矩的分布都有很大的影响。在较低频率和平板较薄的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布上是基本一致的;在较高频率和平板较厚的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布计算结果相差较大。由于文献[9]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此本文的分析计算结果更精确一些。 相似文献
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SH波作用下界面任意形状孔洞附近的动应力集中 总被引:1,自引:0,他引:1
采用Green函数和复变函数法求解了平面SH波在界面任意形状孔洞上的散射问题.首先,取含有任意形状凹陷的弹性半空间,在其水平表面上任意一点承受时间谐和的反平面线源荷载作用时的位移场作为Green函数.然后,按契合方式构造出界面任意形状孔洞对SH波的散射模型,利用所得Green函数按界面位移连续条件建立求解问题的定解积分方程组,求解界面孔附近的动应力集中系数.最后,给出了界面上椭圆孔和方孔边缘动应力集中系数的数值结果,并讨论了不同介质参数和孔洞形状对孔附近动应力集中系数的影响. 相似文献
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R. N. Neskorodev 《Mechanics of Solids》2014,49(4):413-421
A solution of the bending problem for isotropic plates in a refined statement based on the system of six-order differential equations is proposed. A procedure for determining the general solutions of the corresponding biharmonic and metaharmonic equations is suggested. A method for satisfying the boundary conditions is given. The results of numerical studies of the stress state of an infinite plate with an elliptic cavity are given. 相似文献
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求解任意形状厚板自由振动的微分容积法 总被引:2,自引:0,他引:2
用一种新型的数值方法-微分容积法求解具有任意形状的厚板自由振动问题。该方法的基本思想是将任意一个线性微分算子对函数的作用值如一个连续函数或其任意阶偏导数、或其线性组合在某点处的值表示为域内各点函数值的线性加权组合,如此可将问题的控制方程和边界条件离散成为一组线性齐次代数方程。这是一典型的特征值问题,其特征值可用子空间迭代法求解。文中给出了详细的计算公式,用一些数值算例说明了该方法求解中厚板自由振动问题的可行性、有效性和通用性,并通过与有关文献比较验证了该方法的数值精度。 相似文献
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含孔平板弹性波散射问题的复变函数方法 总被引:1,自引:0,他引:1
本文采用平板弯曲波动理论及复变函数方法,对平板开孔弹性波的散射及动应力集中问题进行了分析研究,得到了传播急剧记波时此种平板弯曲波动问题的分析解。若同时采用保角射技术,就为主解平板任意形状开孔弹性波的散射及动应力集中问题提供了一种统一规范的方法。作为算例,本文给出了平板开圆孔和椭圆孔附近的动应力集中系数的数值结果,并对其进行了讨论。 相似文献
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二维半圆孔附近的动态热应力分布 总被引:1,自引:0,他引:1
在稳态温度场中,由于弹性平面内半圆孔或半圆坑等缺陷在介质裂纹扩展和疲劳损伤机理中所起的作用,因此深入了解半圆孔或半圆坑的表面动态热应力分布显得很有必要.分析在半无限弹性平面内一半圆孔附近施加稳态调谐温度场条件下的半圆孔孔边动态热应力分布问题,利用共形映照等复变函数的方法,给出了汉克函数表示的此问题的解析解,并给出了相应动态热应力分布系数的数值结果. 相似文献
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By considering the effect of interfacial damage and using the variation principle, three-dimensional nonlinear dynamic governing equations of the laminated plates with interfacial damage are derived based on the general sixdegrees-of-freedom plate theory towards the accurate stress analysis. The solutions of interlaminar stress and nonlinear dynamic response for a simply supported laminated plate with interfacial damage are obtained by using the finite difference method, and the results are validated by comparison with the solution of nonlinear finite element method. In numerical calculations, the effects of interfacial damage on the stress in the interface and the nonlinear dynamic response of laminated plates are discussed. 相似文献
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In this paper according to the results of a great quantity of tests and numerical calculations, it is pointed out that the
surrounding rock with thickness of 1/3 span has mechanical characteristics of a thick flexural member in underground rock
cave subjected to transverse blast loading. However, it approaches the stress state of free field outside country rock and
the equation of thick plate theory under the loading of free field pressure may be applied to the solution of this problem.
Therefore, the underground structure-country rock dynamic interaction may be described by dynamic equations of flexural members
of thin plate and thick plate, which express linear and country rock respectively. The interaction force between the liner
and country rock is expressed as contacting pressure function q(x, l). By solving system of simultaneous equations, the analytical
solution for the dynamic analysis of arch-straight liner including elastic half space interaction effect is given and the
analytical expression of function q(x, t) is obtained.
This analytic solution will contribute to the study of some substantive problems of underground structure-medium dynamic interaction
theoretically.
(Instutute of Engineering Mechanics, Academia Sinica) 相似文献
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In this article, an analytical solution for buckling of moderately thick functionally graded (FG) sectorial plates is presented.
It is assumed that the material properties of the FG plate vary through the thickness of the plate as a power function. The
stability equations are derived according to the Mindlin plate theory. By introducing four new functions, the stability equations
are decoupled. The decoupled stability equations are solved analytically for both sector and annular sector plates with two
simply supported radial edges. Satisfying the edges conditions along the circular edges of the plate, an eigenvalue problem
for finding the critical buckling load is obtained. Solving the eigenvalue problem, the numerical results for the critical
buckling load and mode shapes are obtained for both sector and annular sector plates. Finally, the effects of boundary conditions,
volume fraction, inner to outer radius ratio (annularity) and plate thickness are studied. The results for critical buckling
load of functionally graded sectorial plates are reported for the first time and can be used as benchmark. 相似文献
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本文研究的是经常在实际工程中遇到的粘弹性双材料界面裂缝的动断裂问题.由于粘弹性自身的复杂性,使得粘弹性双材料界面裂缝缝端应力的奇异性较弹性呈现出更为复杂的形式,从而使动断裂问题的分析变得更为困难.根据此情况,本文采用复阻尼理论反映粘弹性体的运动规律,用复势理论和平面问题复变函数解答的科洛索夫公式推导了粘弹性双材料界面裂缝缝端位移场及动态应力强度因子的求解公式,利用特解边界元进行了粘弹性双域耦合动力响应计算,按求得的公式用位移外推法计算了单边裂纹板在动荷载作用下的动态应力强度因子.分析了粘性,弹模比和缝长对动态应力强度因子的影响,得出了一些有益的结论. 相似文献
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Based on complex variables and conformal mapping, the elastic wave scat- tering and dynamic stress concentrations in the plates with two holes are studied by the refined dynamic equation of plate bending. The problem to be solved is changed to a set of infinite algebraic equations by an orthogonM function expansion method. As examples, under free boundary conditions, the numerical results of the dynamic moment concen- tration factors in the plates with two circular holes are computed. The results indicate that the parameters such as the incident wave number, the thickness of plates, and the spacing between holes have great effects on the dynamic stress distributions. The results are accurate because the refined equation is derived without any engineering hypothese. 相似文献
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D. I. Chernopiskii 《International Applied Mechanics》2006,42(3):350-356
A numerical solution to elastic-equilibrium problems for nonthin plates is proposed. The solution is obtained by using the
curvilinear-mesh method in combination with Vekua’s method. The efficiency (rapid convergence and accuracy) of this approach
is demonstrated by solving test problems for thick plates that can also be solved exactly or approximately by other methods.
A numerical solution is obtained to the bending problem for orthotropic nonthin plates of constant and varying thickness
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 119–126, March 2006. 相似文献
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Based on the motion equations of flexural wave in Ambartsumian's plates including the effects of transverse shear deformations,
by using perturbation method of small parameter, the scattering of flexural waves and dynamic stress concentrations in the
plate with a cutout have been studied. The asymptotic solution of the dynamic stress problem is obtained. Numerical results
for the dynamic stress concentration factor in Ambartsumian's plates with a circular cutour are graphically presented and
discussed.
The project supported by the National Natural Science Foundation of China. 相似文献