Hostname: page-component-8448b6f56d-tj2md Total loading time: 0 Render date: 2024-04-25T02:19:07.069Z Has data issue: false hasContentIssue false

A State Space Solution Approach for Problems of Cylindrical Tubes and Circular Plates

Published online by Cambridge University Press:  15 July 2015

W.-D. Tseng*
Affiliation:
Department of Construction Engineering Nan Jeon University of Science and Technology Tainan, Taiwan
J.-Q. Tarn
Affiliation:
Department of Civil Engineering National Cheng Kung University Tainan, Taiwan
*
* Corresponding author (wdtseng@mail.nju.edu.tw)
Get access

Abstract

We present a general solution approach for analysis of transversely isotropic cylindrical tubes and circular plates. On the basis of Hamiltonian state space formalism in a systematic way, rigorous solutions of the twisting problems are determined by means of separation of variables and symplectic eigenfunction expansion.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Flugge, W. and Kelkar, V. S., “The Problem of an Elastic Circular Cylinder,” International Journal of Solids and Structures, 4, pp. 397420 (1968).Google Scholar
2.Knowles, J. K. and Horgan, C. O., “On the Exponential Decay of Stress in Circular Elastic Cylinders Subject to Axisymmetric Self-equilibrated End Loads,” International Journal of Solids and Structures, 59, pp. 3350 (1969).Google Scholar
3.Power, L. D. and Childs, S. B., “Axisymmetric Stresses and Displacements in a Finite Circular Bar,” International Journal of Engineering Science, 9, pp. 241255 (1971).CrossRefGoogle Scholar
4.Moore, I. D., “Three-dimensional Response of Elastic Tubes,” International Journal of Solids and Structures, 26, pp. 391400 (1990).Google Scholar
5.Tarn, J. Q., “A State Space Formalism for Anisotropic Elasticity, Part I: Rectilinear Anisotropy,” International Journal of Solids and Structures, 39, pp. 51435155 (2002).Google Scholar
6.Tarn, J. Q., “A State Space Formalism for Anisotropic Elasticity, Part II: Cylindrical Anisotropy,” International Journal of Solids and Structures, 39, pp. 51575172 (2002).Google Scholar
7.Tarn, J. Q., “A State Space Formalism for Piezothermoelasticity,” International Journal of Solids and Structures, 39, pp. 51735184 (2002).CrossRefGoogle Scholar
8.Tarn, J. Q., Chang, H. H. and Tseng, W. D., A Hamiltonian State Space Approach for 3D Problems of Anisotropic Elasticity and Piezoelectricity, Proceedings of the Second Asian Conference on Mechanics of Functional Materials and Structures (2010).Google Scholar
9.Tarn, J. Q. and Chang, H. H., “Torsion of Cylindrically Orthotopic Elastic Circular Bars with Radial Inhomogeneity: Some Exact Solutions and End Effects,” International Journal of Solids and Structures, 45, pp. 303319 (2008).CrossRefGoogle Scholar
10.Tarn, J. Q., Tseng, W. D. and Chang, H. H., “A Circular Elastic Cylinder under its Own Weight,” International Journal of Solids and Structures, 46, pp. 28862896 (2009).Google Scholar
11.Tarn, J. Q., Chang, H. H. and Tseng, W. D., “Axisymmetric Deformation of a Transversely Isotropic Cylindrical Body: A Hamiltonian State-space Approach,” Journal of Elasticity, 97, pp. 131154 (2009).Google Scholar
12.Tarn, J. Q., Chang, H. H. and Tseng, W. D., “A Hamiltonian State Space Approach for 3D Analysis of Circular Cantilevers,” Journal of Elasticity, 101, pp. 207237 (2010).Google Scholar
13.Tseng, W. D. and Tarn, J. Q., “A Circular Elastic Cylinder Under Extension,” Journal of Mechanics, 27, pp. 399407 (2011).Google Scholar
14.Tseng, W. D., Tarn, J. Q. and Chang, J. H., “Laminated Tubes under Extension, Internal and External Pressure,” Journal of Mechanics, 30, pp. 455466 (2014).Google Scholar
15.Tseng, W. D. and Tarn, J. Q., Three-Dimensional Solution for the Stress Field Around a Circular Hole in a Plate, Journal of Mechanics, 30, pp. 611624 (2014).Google Scholar
16.Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, MIR, Moscow (1981).Google Scholar
17.Hildebrand, F. B., Advanced Calculus for Applications, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1976).Google Scholar
18.Hildebrand, F. B., Methods of Applied Mathematics, 2nd Ed., Prentice-Hall, Englewood Cliffs, New Jersey (1965).Google Scholar