A dimensional splitting method for the linearly elastic shell

2007 ◽  
Vol 84 (6) ◽  
pp. 807-824 ◽  
Author(s):  
Kaitai Li ◽  
Xiaoqin Shen
Keyword(s):  
Elastic Shell ◽  
Splitting Method ◽  
Dimensional Splitting

scholarly journals A finite element dimensional splitting method for 3D rotating Navier-Stokes equations

2015 ◽  
Vol 45 (8) ◽  
pp. 1299-1318
Author(s):  
Wu ZHANG ◽  
HongZhou FAN ◽  
Jian SU ◽  
KaiTai LI ◽  
AiXiang HUANG
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Splitting Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Dimensional Splitting

scholarly journals Transonic flow calculations using a dimensional splitting method

2000 ◽  
Vol 42 ◽  
pp. 752
Author(s):  
Hing Hung ◽  
John A. Gear ◽  
Natalie J. T. Phillips
Keyword(s):  
Transonic Flow ◽  
Splitting Method ◽  
Dimensional Splitting

scholarly journals Runge-Kutta Discontinuous Local Evolution Galerkin Methods for the Shallow Water Equations on the Cubed-Sphere Grid

2017 ◽  
Vol 10 (2) ◽  
pp. 373-419 ◽  
Author(s):  
Yangyu Kuang ◽  
Kailiang Wu ◽  
Huazhong Tang
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Evolution Operator ◽  
Splitting Method ◽  
Galerkin Methods ◽  
Dimensional Splitting ◽  
Runge Kutta ◽  
And Performance ◽  
Cubed Sphere ◽  
Cell Interface

AbstractThe paper develops high order accurate Runge-Kutta discontinuous local evolution Galerkin (RKDLEG) methods on the cubed-sphere grid for the shallow water equations (SWEs). Instead of using the dimensional splitting method or solving one-dimensional Riemann problem in the direction normal to the cell interface, the RKDLEG methods are built on genuinely multi-dimensional approximate local evolution operator of the locally linearized SWEs on a sphere by considering all bicharacteristic directions. Several numerical experiments are conducted to demonstrate the accuracy and performance of our RKDLEG methods, in comparison to the Runge-Kutta discontinuous Galerkin method with Godunov's flux etc.

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.

scholarly journals Target metric and Shell Shaping

2021 ◽  
Vol 8 (1) ◽  
pp. 13-25
Author(s):  
Gloria Rita Argento ◽  
Stefano Gabriele ◽  
Luciano Teresi ◽  
Valerio Varano
Keyword(s):  
Elastic Energy ◽  
Elastic Shell ◽  
The Other ◽  
The One

Abstract We exploit the possibility of deforming a shell by assigning a target metric, which, for 2D structures, is decomposed into the first and second target fundamental-forms. As well known, an elastic shell may change its shape under two different kinds of actions: one are the loadings, the other one are the distortions, also known as the pre-strains. Actually, the target fundamental forms prescribe a sought shape for the solid, and the metric effectively realized is the one that minimizes the distance, measured through an elastic energy, between the target and the actual fundamental forms. The proposed method is very effective in deforming shells.

scholarly journals A Finite Element Splitting Method for a Convection-Diffusion Problem

2020 ◽  
Vol 20 (4) ◽  
pp. 717-725 ◽  
Author(s):  
Vidar Thomée
Keyword(s):  
Finite Element ◽  
Splitting Method ◽  
Diffusion Problem ◽  
Euler Method ◽  
Euler Approximation ◽  
Convection Diffusion ◽  
Time Stepping ◽  
Backward Euler ◽  
Spatially Periodic ◽  
Forward Euler

AbstractFor a spatially periodic convection-diffusion problem, we analyze a time stepping method based on Lie splitting of a spatially semidiscrete finite element solution on time steps of length k, using the backward Euler method for the diffusion part and a stabilized explicit forward Euler approximation on {m\geq 1} intervals of length {k/m} for the convection part. This complements earlier work on time splitting of the problem in a finite difference context.

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