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1.
用配点法计算受轴对称分布荷载的球面扁薄圆壳的非线性稳定 总被引:2,自引:0,他引:2
本文以幂函数为试函数,用配点法计算扁球壳的非线性稳定。考虑了固定夹紧、可移夹紧、铰支承及简单支承等四种边界条件。荷载采用了多项式型的分布荷载及均布边缘力矩。本文的部份结果同摄动法的结果作了比较。 相似文献
2.
变厚度扁薄球壳的非线性稳定 总被引:1,自引:0,他引:1
本文以幂函数为试函数,用配点法求解受轴对称横向荷载或均布边缘力矩的厚度按指数函数变化的扁薄球壳的非线性稳定。在简单支承边界条件下。本文得到的边缘临界力矩同摄动法[1]的结果作了比较。 相似文献
3.
环形薄板轴对称非线性屈曲的样条函数解法 总被引:2,自引:0,他引:2
环形薄板的大挠度计算因为边界条件复杂,仅有少数特殊情形的数值解答。均布边缘径向力作用下环形薄板非线性屈曲迄今尚未有研究成果。作者以三次B样条函数为试函数,用配点法计算环形薄板的大挠度。在12种不同的边界条件下,首次计算了环形薄板的压曲临界荷载及超临界荷载作用的变形。在所有的算例中均取得了收敛的数值结果。结果表明样条配点法具有收敛范围大、精度高和计算时间少的优点。 相似文献
4.
本文用配点法计算厚度按指数函数变化的圆薄板的大挠度。荷载为轴对称分布荷载及均布边缘力矩。边界可为弹性支承。受均布荷载,在固定夹紧边条下,向摄动法的结果作了比较。 相似文献
5.
本文研究了柱面扁壳在均布荷载作用下的大变形弯曲问题。首先导出了位移型非线性控制微分方程,然后结合两种边界情况(简支与固定)给出了用正交配点法进行解算的详细公式。 相似文献
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扁球壳轴对称屈曲问题的样条函数解法 总被引:2,自引:0,他引:2
本文用三次B样条函数和迭代法求解圆底扁球壳在逐次加载时挠度增量和内力增量所满足的变系数非线性微分方程,从而得出均布荷载作用下周边固定圆底扁球壳轴对称弯曲问题的解答。文中计算了λ≤46的各种λ值的极值屈曲荷载,所得结果在λ≤20时与Budiansky等所得结果一致。 相似文献
10.
本文以幂函数多项式作位移函数,用配点法计算了受轴对称分布荷载的圆形大挠度板。文中考虑了固定夹紧、可移夹紧、铰链支承、简单支承等四种边界条件。在计算例题中,荷载采用多项式形式、余弦函数形式的分布荷载以及均布边弯矩荷载或者由它们组合而成的荷载。通过上百个例题的计算,表明此法具有精度高、收敛快等优点。本文还将其所得的结果同用摄动法等得到的结果进行了比较。 相似文献
11.
Cublic spline solutions of axisymmetrical nonlinear bending and buckling of circular sandwich plates
IntroductionBruun[1],Huang[2 ]andWang[3]publishedtheirpapersrelatedtolinearlystaticanalysisofcircularsandwichplates .Liuetal.setupnonlinearbendingequationsofacircularsandwichplate[4 ],andsolvedaseriesofnonlinearproblems[5~ 10 ].Sofartheothersneverdiscuss… 相似文献
12.
CUBLIC SPLINE SOLUTIONS OF AXISYMMETRICAL NONLINEAR BENDING AND BRCKLING OF CIRCULAR SANDWICH PLATES
Cubic B-spline taken as trial function, the nonlinear bending of a circular sandwich plate was calculated by the method of point collocation. The support could be elastic. A sandwich plate was assumed to be Reissner model. The formulae were developed for the calculation of a circular sandwich plate subjected to polynomial distributed loads,uniformly distributed moments, radial pressure or radial prestress along the edge and their combination. Buckling load was calculated for the first time by nonlinear theory. Under action of uniformly distributed loads, results were compared with that obtained by the power series method. Excellences of the program written by the spline collocation method are wide convergent range, high precision and universal. 相似文献
13.
Shu-Xian Gu 《Acta Mechanica Solida Sinica》1988,1(4):369-381
In this paper, we treat the nonlinear stability problem of shallow spherical shells with large values ofk(k=12(1–v) · 2f/h,f = shell rise,h = shell thickness) under the action of uniformly distributed line load along a circle concentric with the shell boundary. Load-deflection curves are computed at successive increments of uniformly distributed line loads by using both cubic B-spline approximations and iterative techniques. Our algorithm yields fairly good convergent results for values ofk as large as 400. The limiting case in which shells are loaded along a circle of small radius has been specially investigated and the computed critical loads are compared with those obtained with central point loads by other authors. 相似文献
14.
叶志明 《应用数学和力学(英文版)》1988,9(2):153-158
In this paper, the nonlinear bending and stability of thin spherical shallow shell with variable thickness under uniformly
distributed loads are investigated by a new modified iteration method proposed by Prof. Yeh Kai-yuan and the author[1]. Deflections and critical loads have been calculated and the numerical results obtained have been given in figures and tabular
forms. It is shown that the final equation determining the central deflection and the load obtained coincides with the cusp
catastrophe manifold.
Projects Supported by the Science Fund of the Chinese Academy of Sciences 相似文献
15.
集中载荷作用下变厚度开顶扁球壳的非线性稳定问题 总被引:1,自引:0,他引:1
首先应用逐步加载法将具有硬中心的开顶扁球壳在集中载荷作用下的非线性微分方程组线性化,然后利用样条配点法解线性微分方程组,得到了临界载荷的大小。 相似文献
16.
Nonlinear static and dynamic analysis for laminated,annular, spherical caps of moderate thickness 总被引:1,自引:0,他引:1
Based on Timoshenko-Mindlin kinematic hypothesis, the shallow shell theory is extended to include the transverse shear deformation for the nonlinear axisymmetric dynamic analysis of the symmetric cross-ply shallow spherical shell. Using the orthogonal point collocation method and the Newmark scheme, an iterative solution is formulated. The numerical results for the nonlinear static and dynamic responses and dynamic buckling of these shallow spherical shells with circular holes under uniformly distributed static or dynamic normal impact loads are presented and compared with available data. 相似文献
17.
A.H. Sofiyev 《International Journal of Non》2011,46(5):711-719
In this study, the non-linear buckling behavior of truncated conical shells made of functionally graded materials (FGMs), subject to a uniform axial compressive load, has been investigated using the large deformation theory with von the Karman-Donnell-type of kinematic non-linearity. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The variation of properties followed an arbitrary distribution in terms of the volume fractions of the constituents. The fundamental relations, the modified Donnell type non-linear stability and compatibility equations of functionally graded truncated conical shells are obtained and are solved by superposition and Galerkin methods and the upper and lower critical axial loads have been found analytically. Finally, the influences of the compositional profile variations and the variation of the shell geometry on the upper and lower critical axial loads are investigated. Comparing the results of this study with those in the literature validates the present analysis. 相似文献
18.
S. N. Kukudzhanov 《Mechanics of Solids》2009,44(4):543-551
In contrast to [1–4], where the stability problem was studied for shells of medium length, in the present paper we study the
stability problem for nearly cylindrical long shells under the action of meridian forces uniformly distributed over their
ends and under the action of the normal pressure distributed over the entire lateral surface of the shell. We consider the
shells whose generating midsurface shape is determined by a parabolic function. The study is performed for nonaxisymmetric
buckling modes by using an equation refined as compared with the equation given in [1]. We consider shells of both positive
and negative Gaussian curvature. We assume that the shell ends are freely supported and obtain formulas for the critical load
under both separate and joint action of the meridian forces and the pressure. In the specific case of a cylindrical shell
under the action of longitudinal compression, the formulas thus obtained imply both the Euler formula and the Southwell-Timoshenko
formula [5]. When solving the problem, we use the Bubnov-Galerkin method combined with the optimal approximation method [6]. 相似文献
19.
严圣平 《应用数学和力学(英文版)》1997,18(10):1015-1020
I.Intr0ducti0nTheclampedtruncatedshailowsphericalshellwithanondeformablerigidbodyatthecenterisoftenusedinstructureandelasticcomponentofprecisioninstrument.Inthebuildingengineering,wemustpreventtheshelllosingstability.Butintheelasticcomponent0fprecisionins… 相似文献
20.
Axisymmetric buckling analysis is presented for moderately thick laminated shallow, truncated conical caps under transverse load. Buckling under uniformly distributed loads and ring loads applied statically or as step function loads is considered. Marguerre-type, first-order shear deformation shallow shell theory is formulated in terms of transverse deflection w, the rotation ψ of the normal to the mid-surface and the stress function Φ. The governing equations are solved by the orthogonal point collocation method. Truncated conical caps with a circular opening, which is either free or plugged by a rigid central mass, have been analysed for clamped and simple supports with movable and immovable edge conditions. Typical numerical results are presented illustrating the effect of various parameters. 相似文献