A state space formalism for anisotropic elasticity. Part I: Rectilinear anisotropy

2002 ◽  
Vol 39 (20) ◽  
pp. 5143-5155 ◽  
Author(s):  
Jiann-Quo Tarn
Keyword(s):  
State Space ◽  
Anisotropic Elasticity ◽  
Space Formalism ◽  
Rectilinear Anisotropy

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.

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.

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