Static Axisymmetric End Problems in Semi-infinite and Finite Solid Cylinders

1992 ◽  
Vol 59 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Yoon Young Kim ◽  
Charles R. Steele
Keyword(s):  
Asymptotic Analysis ◽  
Stiffness Matrix ◽  
Present Approach ◽  
Infinite Strip ◽  
Matrix Approach ◽  
Corner Singularities ◽  
End Conditions ◽  
Finite Cylinders

Our earlier technique for a semi-infinite strip (Kim and Steele, 1990) is extended to study general end problems and corner singularities for semi-infinite and finite solid cylinders with free walls. For handling general end conditions, we expand the displacement and stress in term of the Dini series which are the solutions of the cylinders with mixed wall conditions. The relation between the harmonic coefficients of the end displacement and stress is then formed, which we call the end stiffness matrix. One advantage of the end stiffness matrix approach is that the procedure for finite cylinders can be easily built up from that of semi-infinite cylinders. For some end conditions which may yield singular stresses, the nature of the singularity is investigated by the asymptotic analysis of the Dini series coefficients of the stresses. The problems studied by Benthem and Minderhoud (1972) and Robert and Keer (1987) are solved with the present approach.

Modifications of Series Expansions for General End Conditions and Corner Singularities on the Semi-Infinite Strip

1990 ◽  
Vol 57 (3) ◽  
pp. 581-588 ◽  
Author(s):  
Yoon Young Kim ◽  
Charles R. Steele
Keyword(s):  
Stiffness Matrix ◽  
Harmonic Wave ◽  
Infinite Cylinder ◽  
Series Expansions ◽  
Infinite Strip ◽  
Corner Singularities ◽  
Numerical Examples ◽  
Time Harmonic ◽  
End Conditions ◽  
Expansion Coefficients

Modified series expansions are used to study semi-infinite isotropic elastic strip problems for general end conditions and corner singularities. The solutions of strips with mixed lateral edges are used as the expansion sets of the end displacement and stress, and an end stiffness matrix, the relation of harmonics of the end displacement and stress, is formed. The present end stiffness matrix approach, an extension to static strip problems of the method by Kim and Steele (1989, 1990) for time-harmonic wave propagation in a semi-infinite cylinder, is effective due to the asymptotic behavior of the stiffness matrix. Also presented is a technique for handling the corner singularities, which is based on the asymptotic analysis of the expansion coefficients of the end stresses. With this, the order and strength of the singularities are determined, local oscillations are virtually suppressed, and converging solutions are obtained. Some numerical examples are given to demonstrate the effectiveness of the approach.

Computation of rigid body scattering by spheroids and finite cylinders using T‐matrix approach

1980 ◽  
Vol 68 (S1) ◽  
pp. S80-S80
Author(s):  
V. K. Varadan ◽  
V. V. Varadan ◽  
T. A. K. Pillai ◽  
L. R. Dragonette ◽  
L. Flax
Keyword(s):  
Rigid Body ◽  
Matrix Approach ◽  
T Matrix ◽  
Finite Cylinders

Matrix development of the calculus of relations

1948 ◽  
Vol 13 (4) ◽  
pp. 193-203 ◽  
Author(s):  
Irving M. Copilowish
Keyword(s):  
Present Approach ◽  
Matrix Approach ◽  
Matrix Notation ◽  
The Matrix ◽  
Elementary Calculus

In his very interesting address On the calculus of refations, Professor Tarski discussed alternative bases for that calculus. He was there interested in “…different methods of setting up the foundations of this elementary calculus in a rigorously deductive way…” and so did not discuss the method of developing the calculus of relations with which this paper is concerned. Our purpose here is to show how the use of matrix notation for relations permits an algorithmic rather than a postulational-deductive development of the calculus of relations. One limitation of the present approach is to be admitted at the very outset: to enjoy the full benefits of the matrix approach, we are obliged to confine our investigations to Universes of Discourse which are finite. The reason for this restriction will become apparent presently.

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