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The Nonlinear Instability Modes of Dished Shallow Shells under Circular Line Loads

机译：圆形荷载作用下浅壳薄板的非线性失稳模式

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摘要

This paper investigated the nonlinear stability problem of dished shallow shells under circular line loads. We derived the dimensionless governing differential equations of dished shallow shell under circular line loads according to the nonlinear theory of plates and shells and solved the governing differential equations by combing the free-parameter perturbation method (FPPM) with spline function method (SFM) to analyze the nonlinear instability modes of dished shallow shell under circular line loads. By analyzing the nonlinear instability modes and combining with concrete computational examples, we obtained the variation rules of the maximum deflection area of initial instability with different geometric parameters and loading action positions and discussed the relationship between the initial instability area and the maximum deflection area of initial instability. The results obtained from this paper provide some theoretical basis for engineering design and instability prediction and control of shallow-shell structures.
机译：本文研究了碟形浅壳在圆形载荷下的非线性稳定性问题。根据板壳非线性理论，推导了圆盘荷载作用下碟形浅壳的无量纲控制微分方程，将自由参数摄动法（FPPM）与样条函数法（SFM）相结合，求解了控制微分方程。圆形载荷作用下碟形浅壳的非线性失稳模式。通过分析非线性失稳模式并结合具体的算例，得到了具有不同几何参数和载荷作用位置的初始失稳最大挠度面积的变化规律，并讨论了初始失稳面积与初始失稳最大挠度面积之间的关系。不稳定。本文的研究结果为浅层结构的工程设计，失稳预测与控制提供了理论依据。

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  • 来源
    《Mathematical Problems in Engineering》 |2011年第speca期|p.793798.1-793798.21|共21页
  • 作者

    Liu Chang-Jiang; Zheng Zhou-Lian; Huang Cong-Bing; He Xiao-Ting; Sun Jun-Yi; Chen Shan-Lin;

  • 作者单位

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China,Chongqing Vocational College of Architectral Engineering, Chongqing 400039, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China,Internal Trade Engineering and Research Institute, Beijing 100069, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China;

    College of Civil Engineering, Chongqing University, Chongqing 400045, China,Key Laboratory of New Technology for Construction of Cities in Mountain Area (Chongqing University), Ministry of Education, Chongqing 400045, China;

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