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In analysing the geometrically nonlinear problem of an axisymmetrical thin-walled shell, the paper combines the perturbation method with the finite element method by introducing the former into the variational equation to obtain a series of linear equations of different orders and then solving the equations with the latter. It is well-known that the finite element method can be used to deal with difficult problems as in the case of structures with complicated shapes or boundary conditions, and the perturbation method can change the nonlinear problems into linear ones. Evidently the combination of the two methods will give an efficient solution to many difficult nonlinear problems and clear away some obstacles resulted from using any of the two methods solely. The paper derives all the formulas concerning an axisym-metric shell of large deformation by means of the perturbation finite element method and gives two numerical examples,the results of which show good convergence characteristics. 相似文献
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本文用对两个小参数的摄动法,对于轴对称圆薄板大挠度问题,在板厚按指数规律变化、载荷为均布的情况下,求出了三级摄动解。所得摄动解在特殊情况下与精确解的比较表明结果是较为理想的。 相似文献
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<正> 大专院校的材料力学实验课中引进了矩形梁的弯曲应力及变形实验,多年教学实践证明,这类实验对于学生的理论学习有一定的作用,但不能启发学生去思考问题,不能调动同学学习的积极性和培养学生解决问题的能力.在生产实践中,梁往往不是简单的矩形梁,如工厂用桥式吊车就大都是组合结构;吊车轨道梁则是钢筋混凝土梁上辅有钢轨,共同支撑起吊的重量;汽车板簧是由多层弯曲的钢板重叠组合而成的等等. 相似文献
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用子域边界元法研究各向异性材料中的界面裂纹,在边界元公式中,采用了带特征根的基本解,以增量形式的边界积分方程为基础,通过二次等参元及国分之一面力奇异远离散化处理,可以得到各子域的代数方程组,依据凝集技术,可得到仅含有子域公共边界及裂纹边界未知量的求解方程组,通过迭代法,可以寻求到每种载荷作用下的裂纹所处的真实状态,然后,由文献「2」中的方法求解界面裂纹的应力强度因子。结果表明,子域边界方法是正确的 相似文献
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The perturbation method is one of the effective methods for so-lving problems in nonlinear continuum mechanics.It has been de-veloped on the basis of the linear analytical solutions for the o-riginal problems.If a simple analytical solution cannot be ob-tained.we would encounter difficulties in applying this method tosolving certain complicated nonlinear problems.The finite ele-ment method appears to be in its turn a very useful means for sol-ving nonlinear problems,but generally it takes too much time incomputation.In the present paper a mixed approach,namely,theperturbation finite element method,is introduced,which incorpo-rates the advantages of the two above-mentioned methods and enablesus to solve more complicated nonlinear problems with great savingin computing time.Problems in the elastoplastic region have been discussed anda numerical solution for a plate with a central hole under tensionis given in this paper. 相似文献
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边界积分方程中超奇异积分的解法 总被引:4,自引:0,他引:4
本文对边界积分方程中所存在的超奇异积分的数值解法作了综述,并介绍了它的一些应用。 相似文献
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PERTURBATION METHOD IN THE PROBLEM OF LARGE DEFLECTIONS OP CIRCULAR PLATES WITH NONUNIFORM THICKNESS
In this paper the perturbation method about two parameters is applied to the problem of large deflection of a cricular plate with exponentially varying thickness under uniform pressure.An asymptotic solution up to the third-order is derived. In comparison with the exact solutions in special cases, the asymptotic solution shows a precise accuracy. 相似文献
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It has been noted in the present paper that the finite element method using linear elements for solving axisymmetrical shells cannot be applied to the analysis of axisymmetrical shells with abrupt curvature change,owing to the fact that the influence of the curvature upon the angular displace-ments has been neglected.The present paper provides a finite element method using linear elements in which the influence of curvature is considered and the angular displacements are treated as continuous parameters.This method has been applied to the calculation of corrugated shells of the type C,and compared with the experimental results obtained by Turner-Ford as well as with the analytical solution given by Prof.Chien Wei-zang.The compari-sons have been proved that this theory is correct. 相似文献