METHOD OF GREEN’S FUNCTION OF CORRUGATED SHELLS  

作　　者：袁鸿 张湘伟 

机构地区：[1]Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P.R.China [2]Faculty of Construction, Guangdong University of Technology, Guangzhou 510640, P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2005年第7期830-837,共8页应用数学和力学（英文版）

基　　金：ProjectsupportedbytheNationalNaturalScienceFoundationofChina(No.10272033)andtheNaturalScienceFoundationofGuangdongProvince(No.032488)

摘　　要：By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.By using the fundamental equations of axisymmetric shallow shells of revolution, the nonlinear bending of a shallow corrugated shell with taper under arbitrary load has been investigated. The nonlinear boundary value problem of the corrugated shell was reduced to the nonlinear integral equations by using the method of Green＇s function. To solve the integral equations, expansion method was used to obtain Green＇s function. Then the integral equations were reduced to the form with degenerate core by expanding Green＇s function as series of characteristic function. Therefore, the integral equations become nonlinear algebraic equations. Newton＇ s iterative method was utilized to solve the nonlinear algebraic equations. To guarantee the convergence of the iterative method, deflection at center was taken as control parameter. Corresponding loads were obtained by increasing deflection one by one. As a numerical example,elastic characteristic of shallow corrugated shells with spherical taper was studied.Calculation results show that characteristic of corrugated shells changes remarkably. The snapping instability which is analogous to shallow spherical shells occurs with increasing load if the taper is relatively large. The solution is close to the experimental results.

关 键 词：corrugated shell Green＇s function integral equation nonlinear bending elastic characteristic 

分 类 号：O343.5[理学—固体力学]