Abstract
The complete system of equations of a linear theory of thin shells in curvilinear non-orthogonal coordinates proposed in the paper was taken as the basis of the investigation. Earlier, this system was used for static analysis of a long developable helicoid. In the article, this system is applied for the determination of stress-strain state of annular and circular plates under action of the external axisymmetric uniform load acting both in the plane of the plate and out-of-their plane. Presented results for annular plate given in the non-orthogonal coordinates ex-pand a number of problems that can be solved analytically. They can be used as the first terms of series of expansion of displacements of degrees of the small parameter if a small parameter method is applied for examining a long tangential developable helicoid.
Highlights
It is known, that the simplest equations of theory of thin shells are turned out for middle shell surfaces given in principle curvatures
They can be used as the first terms of series of expansion of displacements of degrees of the small parameter if a small parameter method is applied for examining a long tangential developable helicoid
This approach is illustrated by an example of reducing of general equations of a theory of thin shells in curvilinear arbitrary coordinates to the equations for analysis of tangential developable helicoid, and after for analysis of annular plates under action of axisymmetric uniform load of two types
Summary
That the simplest equations of theory of thin shells are turned out for middle shell surfaces given in principle curvatures. It is very difficult to set a surface in principle curvatures and one must use governing equations of a theory of thin shells in curvilinear non-orthogonal coordinates. The complete system of equations in curvilinear non-orthogonal coordinates was proposed by A.L. Goldenveizer [1]. This system contains internal “pseudoforces”, “pseudomoments”, and Christoffel’s symbols. The system of equations, presented by Ya.M. Grigorenko and A.M. Timonin [2], is written in tensor form. The system, proposed by the author, contains internal forces and moments usual for engineers and is free from Christoffel’s symbols [3]. Hereinafter, the equations presented in a paper [3] will be used
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
