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

2015 ◽  
Vol 31 (5) ◽  
pp. 557-572 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
General Solution ◽  
State Space ◽  
Eigenfunction Expansion ◽  
Separation Of Variables ◽  
Transversely Isotropic ◽  
Circular Plates ◽  
Solution Approach ◽  
Space Solution ◽  
Cylindrical Tubes ◽  
Space Formalism

AbstractWe 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.

Three-Dimensional Stress Singularities at Conical Notches and Inclusions in Transversely Isotropic Materials

1986 ◽  
Vol 53 (1) ◽  
pp. 89-96 ◽  
Author(s):  
Nihal Somaratna ◽  
T. C. T. Ting
Keyword(s):  
General Solution ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Solution Procedure ◽  
Legendre Functions ◽  
Spherical Coordinates ◽  
Stress Singularities ◽  
Isotropic Materials ◽  
Transversely Isotropic Materials

This study examines analytically the possible existence of stress singularities of the form σ = ρδf(θ,φ) at the apex of axisymmetric conical boundaries in transversely isotropic materials. (ρ, θ, φ) refer to spherical coordinates with the origin at the apex. The problems of one conical boundary and of two conical boundaries with a common apex are considered. The boundaries are either rigidly clamped or traction free. Separation of variables enables the general solution to be expressed in terms of Legendre functions of the first and second kind. Imposition of boundary conditions leads to an eigenequation that would determine possible values of δ. The degenerate case that arises when the eigenvalues of the elasiticity constants are identical is also discussed. Isotropic materials constitute only a particular case in this class of degenerate materials and previously reported eigenequations corresponding to isotropic materials are shown to be recoverable from the present results. Numerical results corresponding to a few selected cases are also presented to illustrate the solution procedure.

A Cantilever Subjected to Axial Force, Bending Moment, and Shear Force

2014 ◽  
Vol 30 (5) ◽  
pp. 549-559 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn ◽  
C.-C. Chang
Keyword(s):  
State Space ◽  
Axial Force ◽  
Eigenfunction Expansion ◽  
Shear Force ◽  
Bending Moment ◽  
Stress Fields ◽  
Orthotropic Body ◽  
Rigorous Solution ◽  
End Conditions ◽  
Space Formalism

AbstractWe present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

Exact Elasticity Solution for Axisymmetric Deformation of Circular Plates

2015 ◽  
Vol 31 (6) ◽  
pp. 617-629 ◽  
Author(s):  
W.-D. Tseng ◽  
J.-Q. Tarn
Keyword(s):  
Eigenfunction Expansion ◽  
Separation Of Variables ◽  
Axisymmetric Deformation ◽  
Thickness Effect ◽  
Circular Plates ◽  
Elasticity Solution ◽  
Rigorous Solution ◽  
State Space Approach ◽  
Axisymmetric Bending ◽  
Space Approach

ABSTRACTWe present an exact analysis of axisymmetric bending of circular plates according to elasticity theory. On the basis of Hamiltonian state space approach, a rigorous solution of the problem is determined by means of separation of variables and symplectic eigenfunction expansion in a systematic way. The thickness effect on bending of circular plates and the applicability of the classical plate solutions for the problem are evaluated accordingly.

scholarly journals Finite elastic deformations of transversely isotropic circular cylindrical tubes

2014 ◽  
Vol 51 (5) ◽  
pp. 1188-1196 ◽  
Author(s):  
Mustapha El Hamdaoui ◽  
José Merodio ◽  
Ray W. Ogden ◽  
Javier Rodríguez
Keyword(s):  
Transversely Isotropic ◽  
Elastic Deformations ◽  
Cylindrical Tubes ◽  
Finite Elastic Deformations
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