Asymptotic analysis and numerical solution of the two-level boundary equations of a plane problem of stationary hydroelasticity

1993 ◽  
Vol 57 (1) ◽  
pp. 105-115 ◽  
Author(s):  
S.V. Sorokin
Keyword(s):  
Asymptotic Analysis ◽  
Numerical Solution ◽  
Plane Problem ◽  
Boundary Equations

scholarly journals Asymptotic analysis of an anti-plane dynamic problem for a three-layered strongly inhomogeneous laminate

2018 ◽  
Vol 25 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Ludmila Prikazchikova ◽  
Yağmur Ece Aydın ◽  
Barış Erbaş ◽  
Julius Kaplunov
Keyword(s):  
Asymptotic Analysis ◽  
Plane Problem ◽  
Dynamic Problem ◽  
Composite Structures ◽  
Vibration Mode ◽  
Low Frequency ◽  
Layered Plate ◽  
Dynamic Shear ◽  
Frequency Range ◽  
Asymptotic Equation

Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is analysed. Two types of contrast are considered, including those for composite structures with thick or thin stiff outer layers. In both cases, the value of the cut-off frequency corresponding to the lowest antisymmetric vibration mode tends to zero. For this mode, the shortened dispersion relations and the associated formulae for displacement and stresses are obtained. The latter motivate the choice of appropriate settings, supporting the limiting forms of the original anti-plane problem. The asymptotic equation derived for a three-layered plate with thick faces is valid over the whole low-frequency range, whereas the range of validity of its counterpart for another type of contrast is restricted to a narrow vicinity of the cut-off frequency.

scholarly journals ASYMPTOTIC ANALYSIS AND NUMERICAL MODELING OF MASS TRANSPORT IN TUBULAR STRUCTURES

2010 ◽  
Vol 20 (03) ◽  
pp. 397-421 ◽  
Author(s):  
GIUSEPPE CARDONE ◽  
GRIGORY P. PANASENKO ◽  
YVAN SIRAKOV
Keyword(s):  
Numerical Modeling ◽  
Asymptotic Expansion ◽  
Diffusion Equation ◽  
Asymptotic Analysis ◽  
Numerical Solution ◽  
Tubular Structures ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Thin Structure ◽  
Asymptotic Expansion Of Solution

In this paper the flow in a thin tubular structure is considered. The velocity of the flow stands for a coefficient in the convection-diffusion equation set in the thin structure. An asymptotic expansion of solution is constructed. This expansion is used further for justification of an asymptotic domain decomposition strategy essentially reducing the memory and the time of the code. A numerical solution obtained by this strategy is compared to the numerical solution obtained by a direct FEM computation.

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