Two-Dimensional Approximation of Piezoelectric Shallow Shells with Variable Thickness

2014 ◽  
Vol 84 (1) ◽  
pp. 71-81
Author(s):  
J. Raja ◽  
N. Sabu
Keyword(s):  
Variable Thickness ◽  
Two Dimensional ◽  
Shallow Shells ◽  
Dimensional Approximation

THE SUPPORT BONDS RIGIDITY INFLUENCES ON THE CARRYING CAPACITY REDUCTION OF THE SHALLOW SHELLS ON A RECTANGULAR PLAN

2020 ◽  
Vol 92 (6) ◽  
pp. 3-12
Author(s):  
A.G. KOLESNIKOV ◽  
Keyword(s):  
Variable Thickness ◽  
Carrying Capacity ◽  
Geometric Nonlinearity ◽  
Progressive Collapse ◽  
Geometrically Nonlinear ◽  
Loss Of Stability ◽  
Shallow Shells ◽  
Capacity Reduction ◽  
Internal Forces ◽  
Hinged Support

Geometric nonlinearity shallow shells on a square and rectangular plan with constant and variable thickness are considered. Loss of stability of a structure due to a decrease in the rigidity of one of the support (transition from fixed support to hinged support) is considered. The Bubnov-Galerkin method is used to solve differential equations of shallow geometrically nonlinear shells. The Vlasov's beam functions are used for approximating. The use of dimensionless quantities makes it possible to repeat the calculations and obtain similar dependences. The graphs are given that make it possible to assess the reduction in the critical load in the shell at each stage of reducing the rigidity of the support and to predict the further behavior of the structure. Regularities of changes in internal forces for various types of structure support are shown. Conclusions are made about the necessary design solutions to prevent the progressive collapse of the shell due to a decrease in the rigidity of one of the supports.

Wake Flow of Single and Multiple Yawed Cylinders

2004 ◽  
Vol 126 (5) ◽  
pp. 861-870 ◽  
Author(s):  
A. Thakur ◽  
X. Liu ◽  
J. S. Marshall
Keyword(s):  
Computational Study ◽  
Three Dimensional ◽  
Side Wall ◽  
Wake Flow ◽  
Upstream Region ◽  
Two Dimensional ◽  
Cylinder Wake ◽  
Dimensional Approximation ◽  
The Face ◽  
Drag And Lift

An experimental and computational study is performed of the wake flow behind a single yawed cylinder and a pair of parallel yawed cylinders placed in tandem. The experiments are performed for a yawed cylinder and a pair of yawed cylinders towed in a tank. Laser-induced fluorescence is used for flow visualization and particle-image velocimetry is used for quantitative velocity and vorticity measurement. Computations are performed using a second-order accurate block-structured finite-volume method with periodic boundary conditions along the cylinder axis. Results are applied to assess the applicability of a quasi-two-dimensional approximation, which assumes that the flow field is the same for any slice of the flow over the cylinder cross section. For a single cylinder, it is found that the cylinder wake vortices approach a quasi-two-dimensional state away from the cylinder upstream end for all cases examined (in which the cylinder yaw angle covers the range 0⩽ϕ⩽60°). Within the upstream region, the vortex orientation is found to be influenced by the tank side-wall boundary condition relative to the cylinder. For the case of two parallel yawed cylinders, vortices shed from the upstream cylinder are found to remain nearly quasi-two-dimensional as they are advected back and reach within about a cylinder diameter from the face of the downstream cylinder. As the vortices advect closer to the cylinder, the vortex cores become highly deformed and wrap around the downstream cylinder face. Three-dimensional perturbations of the upstream vortices are amplified as the vortices impact upon the downstream cylinder, such that during the final stages of vortex impact the quasi-two-dimensional nature of the flow breaks down and the vorticity field for the impacting vortices acquire significant three-dimensional perturbations. Quasi-two-dimensional and fully three-dimensional computational results are compared to assess the accuracy of the quasi-two-dimensional approximation in prediction of drag and lift coefficients of the cylinders.

scholarly journals Magnetoconvection in a horizontal duct flow at very high Hartmann and Grashof numbers

2021 ◽  
Vol 931 ◽  
Author(s):  
R. Akhmedagaev ◽  
O. Zikanov ◽  
Y. Listratov
Keyword(s):  
Magnetic Field ◽  
Magnetic Field Effect ◽  
Dimensional Structure ◽  
Two Dimensional ◽  
Duct Flow ◽  
Mean Flow ◽  
Horizontal Magnetic Field ◽  
Nuclear Fusion Reactor ◽  
Dimensional Approximation ◽  
Very High

Direct numerical simulations and linear stability analysis are carried out to study mixed convection in a horizontal duct with constant-rate heating applied at the bottom and an imposed transverse horizontal magnetic field. A two-dimensional approximation corresponding to the asymptotic limit of a very strong magnetic field effect is validated and applied, together with full three-dimensional analysis, to investigate the flow's behaviour in the previously unexplored range of control parameters corresponding to typical conditions of a liquid metal blanket of a nuclear fusion reactor (Hartmann numbers up to $10^4$ and Grashof numbers up to $10^{10}$ ). It is found that the instability to quasi-two-dimensional rolls parallel to the magnetic field discovered at smaller Hartmann and Grashof numbers in earlier studies also occurs in this parameter range. Transport of the rolls by the mean flow leads to magnetoconvective temperature fluctuations of exceptionally high amplitudes. It is also demonstrated that quasi-two-dimensional structure of flows at very high Hartmann numbers does not guarantee accuracy of the classical two-dimensional approximation. The accuracy deteriorates at the highest Grashof numbers considered in the study.

scholarly journals Quasi-two-dimensional approximation for numerical simulation of flows in engine ducts

2019 ◽  
Author(s):  
V. Vlasenko ◽  
A. Shiryaeva
Keyword(s):  
High Speed ◽  
Fuel Injection ◽  
Three Dimensional ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Combustion Chambers ◽  
New Approach ◽  
One Dimensional ◽  
Dimensional Approximation ◽  
3D Flows

New quasi-two-dimensional (2.5D) approach to description of three-dimensional (3D) flows in ducts is proposed. It generalizes quasi-one-dimensional (quasi-1D, 1.5D) theories. Calculations are performed in the (x; y) plane, but variable width of duct in the z direction is taken into account. Derivation of 2.5D approximation equations is given. Tests for verification of 2.5D calculations are proposed. Parametrical 2.5D calculations of flow with hydrogen combustion in an elliptical combustor of a high-speed aircraft, investigated within HEXAFLY-INT international project, are described. Optimal scheme of fuel injection is found and explained. For one regime, 2.5D and 3D calculations are compared. The new approach is recommended for use during preliminary design of combustion chambers.

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