A semi-analytical solution for stress analysis of moderately thick laminated cylindrical panels with various boundary conditions

2009 ◽  
Vol 89 (4) ◽  
pp. 543-550 ◽  
Author(s):  
F. Alijani ◽  
M.M. Aghdam
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Stress Analysis ◽  
Various Boundary Conditions ◽  
Cylindrical Panels

scholarly journals Three-dimensional semi-analytical solutions for the transient response of functionally graded material cylindrical panels with various boundary conditions

2019 ◽  
Vol 39 (4) ◽  
pp. 1002-1023
Author(s):  
Xu Liang ◽  
Yu Deng ◽  
Xue Jiang ◽  
Zeng Cao ◽  
Yongdu Ruan ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Transient Response ◽  
Functionally Graded Material ◽  
Analytical Method ◽  
Composite Structures ◽  
Outer Radius ◽  
Functionally Graded ◽  
Cylindrical Panels ◽  
Graded Material

In this paper, a 3D semi-analytical method is proposed by introducing the Durbin’s Laplace transform, as well as its numerical inversion method, state space approach and differential quadrature method to analyse the transient behaviour of functionally graded material cylindrical panels. Moreover, to investigate the effectiveness of the proposed semi-analytical solution, four boundary conditions are used to undertake the analyses. Comparing the proposed approach with other theoretical methods from the literatures, we see better agreements in the natural frequencies. Besides, the semi-analytical solution acquires nearly the same transient response as those obtained by ANSYS. Convergence studies indicate that the proposed method has a quick convergence rate with growing sample point numbers along the length direction, so do layer numbers increase along the radial direction. The effects of thickness/outer radius ratio, length/outer radius ratio and functionally graded indexes are also studied. When carbon nanotube is added to functionally graded material cylindrical panel, the composite structures have been reinforced greatly. The proposed 3D semi-analytical method has high accuracy for the analysis of composite structures. This study can serve as a foundation for solving more complicated environments such as fluid–structure interaction of flexible pipe or thermal effect analysis of functionally graded material in aerospace field.

scholarly journals ANALYTICAL SOLUTION OF THE EQUATION OF CONDUCTIVITY FOR VARIOUS BOUNDARY CONDITIONS

2019 ◽  
Vol 2019 (4) ◽  
pp. 33-37
Author(s):  
Vadim Krys'ko ◽  
Olga Saltykova ◽  
Alexey Tebyakin
Keyword(s):  
Analytical Solution ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Solution Method ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Two Dimensional ◽  
Various Boundary Conditions ◽  
The Finite Difference Method

The aim of the work is to obtain an analytical solution of the heat equation for various boundary conditions in the case of a two-dimensional body. As a solution method, the method of variational iterations is used. In the work, both an analytical and a numerical solution of the problem are obtained for the boundary conditions of various types and taking into account the internal heat source. To obtain a numerical solution, the finite difference method was used. The results are compared and the conclusion is made on the reliability of the decisions.

Some Results on the Analytical Solution of Cylindrical Shells With Large Openings

1991 ◽  
Vol 113 (2) ◽  
pp. 297-307 ◽  
Author(s):  
M.-D. Xue ◽  
Y. Deng ◽  
K.-C. Hwang
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Stress Analysis ◽  
Shallow Shell ◽  
Cylindrical Shells ◽  
Geometric Description ◽  
Present Solution ◽  
Approximate Boundary Conditions ◽  
Shell Equation ◽  
Good Agreement

An analytical solution for cylindrical shells with large openings has been developed by the asymptotic method. In comparison with previous analytical solutions obtained by Eringen, Van Dyke and Lekkerkerker, the following three areas have been improved by the present method: 1) The modified Morley’s equation, which is applicable to ro/RT≫1, is used instead of Donnell’s shallow shell equation. 2) The accurate expression of boundary curve of hole is expanded in terms of powers of ρo = ro/R, while the previous approximate geometric description corresponds to the first term of the expansion. 3) The accurate boundary conditions for generalized forces are expanded in terms of powers of ρo and truncated after the terms of ρo3; the previous approximate boundary conditions correspond to the terms of order up to ρo, in the asymptotic expansions. The present solutions are in good agreement with Van Dyke’s solutions for small openings. The analytical results show that the error caused by the previous approximate boundary conditions is significant and has the order O(ρo); the error caused by the previous approximate geometric description of hole boundary has the order O(ρo2); and finally, the error caused by using Donnell’s shallow shell equation is very small for ρo ≤ 0.7. For openings with ρo > 0.25, say, noticeable differences exist between the present and the previous results. The stress analysis of cylindrical shells connected with nozzles has been developed by using the present solution. For increasing the accuracy of stress analysis in the nozzle, the exact description of the edge of nozzle is given and the near-edge boundary layer stress state in the nozzle is considered. The results obtained are in good agreement with those by Eringen for small openings and with those by F.E.M. and experiments for large openings.

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