Nonlinear problems of shell theory and their solution methods (review)

1991 ◽  
Vol 27 (10) ◽  
pp. 929-947 ◽  
Author(s):  
Ya. M. Grigorenko ◽  
V. I. Gulyaev
Keyword(s):  
Shell Theory ◽  
Nonlinear Problems ◽  
Solution Methods

scholarly journals PARALLEL SOLUTION METHODS AND PRECONDITIONERS FOR EVOLUTION EQUATIONS

2018 ◽  
Vol 23 (2) ◽  
pp. 287-308 ◽  
Author(s):  
Owe Axelsson ◽  
Maya Neytcheva ◽  
Zhao-Zheng Liang
Keyword(s):  
Computer Architecture ◽  
High Performance ◽  
Krylov Subspace ◽  
Evolution Equations ◽  
Linear Equations ◽  
Nonlinear Problems ◽  
Iterative Refinement ◽  
Clear Trend ◽  
Eigenvalue Bounds ◽  
Solution Methods

The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to finding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow efficient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evolutionary problem. The analysis is done for linear equations and it is remarked on the possibility to use two- or multilevel mesh methods for nonlinear problems, which can enable further, even higher degree of parallelization. The arising block matrix system to be solved admits a two-by-two block form with square blocks, for which a very efficient preconditioner exists. It leads to tight eigenvalue bounds for the preconditioned matrix and, hence, to a very fast convergence of a preconditioned Krylov subspace or iterative refinement method. The analytical background is shown as well as some illustrating numerical examples.

Inhomogeneous nonlinear problems of ribbed-shell theory

1979 ◽  
Vol 15 (9) ◽  
pp. 808-813 ◽  
Author(s):  
G. D. Gavrilenko
Keyword(s):  
Shell Theory ◽  
Nonlinear Problems ◽  
Ribbed Shell

Analysis of Spectral Characteristics of Sound Waves Scattered from a Cracked Cylindrical Elastic Shell Filled with a Viscous Fluid

2013 ◽  
Vol 38 (3) ◽  
pp. 335-350 ◽  
Author(s):  
Olexa Piddubniak ◽  
Nadia Piddubniak
Keyword(s):  
Viscous Fluid ◽  
Shell Theory ◽  
Elastic Shell ◽  
Spectral Characteristics ◽  
Steel Shell ◽  
Sound Waves ◽  
Thin Cylindrical Shell ◽  
Shell Surface ◽  
Theory Approximation ◽  
Directivity Patterns

Abstract The scattering of plane steady-state sound waves from a viscous fluid-filled thin cylindrical shell weak- ened by a long linear slit and submerged in an ideal fluid is studied. For the description of vibrations of elastic objects the Kirchhoff-Love shell-theory approximation is used. An exact solution of this problem is obtained in the form of series with cylindrical harmonics. The numerical analysis is carried out for a steel shell filled with oil and immersed in seawater. The modules and phases of the scattering amplitudes versus the dimensionless wavenumber of the incident sound wave as well as directivity patterns of the scattered field are investigated taking into consideration the orientation of the slit on the elastic shell surface. The plots obtained show a considerable influence of the slit and viscous fluid filler on the diffraction process.

Solution methods for one-dimensional viscoelastic problems

1987 ◽  
Author(s):  
JOHN STUBSTAD ◽  
GEORGE SIMITSES
Keyword(s):  
One Dimensional ◽  
Solution Methods
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