Author(s): Litvinov Vladimir Vital'evich | Andreev Vladimir Igorevich | Chepurnenko Anton Sergeevich
Journal: Vestnik MGSU
ISSN 1997-0935
Issue: 10;
Start page: 95;
Date: 2012;
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Keywords: shell | stability | energy | work | buckling | generalized hoary equation | оболочка | устойчивость | энергия | работа | выпучивание | обобщенное вековое уравнение
ABSTRACT
The problem of stability of a freely supported truncated circular conical shell, compressed by the upper base of a uniformly distributed load per unit length , referred to the median shell surface and directed along the generatrix of the cone, was solved by the Ritz-Timoshenko energy method. The orthogonal system of curvilinear coordinates of the points of the middle surface of the shell was adopted to solve the problem. Possible displacements were selected in the form of double series approximation functions. The physical principle of inextensible generatrix of the cone exposed to buckling at the moment of instability was employed. In addition, the fundamental principle of continuum mechanics, or the principle of minimal total potential energy of the system, was taken as the basis. According to the linear elasticity theory, energy methods make it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. As a result, the problem is reduced to the problem of identifying the eigenvalues in the algebraic theory of matrices. The numerical value of the critical load was derived through the employment of the software.Энергетическим методом в форме Тимошенко - Ритца решена задача устойчивости свободно опертой усеченной круговой конической оболочки, сжимаемой по верхнему основанию равномерно распределенной погонной нагрузкой , отнесенной к срединной поверхности оболочки и направленной вдоль образующей конуса. Задача свелась к проблеме определения собственных чисел в алгебраической теории матриц. Численно на ПЭВМ получено значение критической нагрузки кр.
Journal: Vestnik MGSU
ISSN 1997-0935
Issue: 10;
Start page: 95;
Date: 2012;
VIEW PDF
DOWNLOAD PDF Original pageKeywords: shell | stability | energy | work | buckling | generalized hoary equation | оболочка | устойчивость | энергия | работа | выпучивание | обобщенное вековое уравнение
ABSTRACT
The problem of stability of a freely supported truncated circular conical shell, compressed by the upper base of a uniformly distributed load per unit length , referred to the median shell surface and directed along the generatrix of the cone, was solved by the Ritz-Timoshenko energy method. The orthogonal system of curvilinear coordinates of the points of the middle surface of the shell was adopted to solve the problem. Possible displacements were selected in the form of double series approximation functions. The physical principle of inextensible generatrix of the cone exposed to buckling at the moment of instability was employed. In addition, the fundamental principle of continuum mechanics, or the principle of minimal total potential energy of the system, was taken as the basis. According to the linear elasticity theory, energy methods make it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. As a result, the problem is reduced to the problem of identifying the eigenvalues in the algebraic theory of matrices. The numerical value of the critical load was derived through the employment of the software.Энергетическим методом в форме Тимошенко - Ритца решена задача устойчивости свободно опертой усеченной круговой конической оболочки, сжимаемой по верхнему основанию равномерно распределенной погонной нагрузкой , отнесенной к срединной поверхности оболочки и направленной вдоль образующей конуса. Задача свелась к проблеме определения собственных чисел в алгебраической теории матриц. Численно на ПЭВМ получено значение критической нагрузки кр.
