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In this paper, nonlinear bending of a corrugated circular plate with a plane central region under the combined action of uniformly distributed load and a concentrated load at the center has been investigated by using large deflection theories of isotropic and anisotropic circular plates. The quite accurate analytical solutions for rigidly as well as loosely clamped edge conditions have been obtained following the modified iteration method. 本文按照各向同性和正交各向异性圆板的大挠度理论,研究了具有光滑中心的波纹圆板在均布和中心集中荷载联合作用下的非线性弯曲问题.应用修正迭代法,我们得到了夹紧固定和滑动固定两种边界条件下十分精确的解析解. Chebyshev polynomials are used to solve the problem of large deflection for corrugated circular plates with a plane central region under arbitrary loads based on the nonlinear bending theory of anisotropic circular plates. Numerical results are compared with those available in the literature. The present method shows higher accuracies and larger application ranges. 本文以正交异性板理论为基础,提出了一种波纹圆板非线性弯曲的Chebyshev级数解法,推导出具有中心平台的波纹圆板在任意轴对称载荷作用下的弹性特征方程.文中计算了几个典型的特例,数值结果表明,本文的方法对目前常用的方法有一定的改进和推广. The Chebychev polynomials are used to study large deflection problemsof corrugated circular plates with/without a plane central region under uniformload combined with a concentrited load at the center. The analysis is basedon the non-linear theory of orthotropic circuar plate bending. A plate withzero deflection at the center is treated and solved as a special case. Thenumerical results of a thin circular plate are presented for testing the relia-bility of the proposed method. Numerical studies of different... The Chebychev polynomials are used to study large deflection problemsof corrugated circular plates with/without a plane central region under uniformload combined with a concentrited load at the center. The analysis is basedon the non-linear theory of orthotropic circuar plate bending. A plate withzero deflection at the center is treated and solved as a special case. Thenumerical results of a thin circular plate are presented for testing the relia-bility of the proposed method. Numerical studies of different cases are per-formed. 本文以正交各向异性圆板的非线性弯曲理论为基础,用Chebyshev级数研究了在均布压力和中心集中载荷共同作用下,波纹圆板及具有硬中心的波纹环形板的大挠度问题。处理和分析了波纹板中心挠度为零的特殊情况并进行了具体求解,这是一种新的尝试和探索。用圆薄板的计算结果验证了本文方法的可靠性。文中还给出了波纹圆板和带硬中心的波纹环形板的数值结果。
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