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961.
李逸豪徐典陈一鸣安东琦李锐 《应用数学和力学》2023,(9):1112-1121
Analytical solutions, with unique research value, can serve as benchmarks for empirical formulas and numerical methods, a tool for rapid parameter analysis and optimization, and a theoretical basis for experimental designs. Conventional analytical methods, e.g., the Lévy solution method, are only applicable to mechanical problems of plates and shells with opposite simply-supported edges, which, however, may fail to obtain analytical solutions for the issues with complex boundary constraints. In recent years, the finite integral transform method for plate and shell problems was developed to deal with non-Lévy-type plates and shells, but it is still infeasible to solve the mixed boundary constrains-induced complex boundary value problems of higher-order partial differential equations. Herein, for the first time, the finite integral transform method was combined with the sub-domain decomposition technique to solve the free vibrations of rectangular thin plates with mixed boundary constraints. The rectangular plate was first divided into 2 sub-domains according to the mixed boundary constraints, and the 2 sub-domains were solved analytically with the finite integral transform method. Finally, the continuity conditions were introduced to obtain the analytical solution of the original problem. Based on the side spot-welded cantilever plates commonly used in engineering, the free vibration problem of a rectangular thin plate with 1 edge subjected to clamped-simply supported constraints and the other 3 edges free, was analyzed. The obtained natural frequencies and mode shapes are in good agreement with those from the finite element method as well as the solutions in literature, thus verifying the accuracy of the proposed method. The solution procedure of the finite integral transform method can be implemented based on the governing equations without any assumption of the solution form. Therefore, this strict analytical method is widely applicable to complex boundary value problems of higher-order partial differential equations for such mechanical problems of plates and shells. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved. 相似文献
962.
本文根据平面问题的复变函数理论推导了含界面裂纹双金属胶接件满足微分方程、开裂界面边界条件与未开裂界面连续条件的应力与位移本征函数展开式,并建立了不可压缩双金属界面裂纹的复合型守恒积分及其与应力强度因子之关系,进而利用分区广义变分原理满足其余边界条件确定包含应力强度因子在内的展开式系数,得到守恒积分并求出应力强度因子.数值计算表明,沿不同回路的在恒积分具有很好的守恒性而且由这两种方法所得应力强度因子具有很好的一致性. 相似文献
963.
A. V. Shenoy 《Transport in Porous Media》1993,11(3):219-241
The governing equation for Darcy-Forchheimer flow of non-Newtonian inelastic power-law fluid through porous media has been derived from first principles. Using this equation, the problem of Darcy-Forchheimer natural, forced, and mixed convection within the porous media saturated with a power-law fluid has been solved using the approximate integral method. It is observed that a similarity solution exists specifically for only the case of an isothermal vertical flat plate embedded in the porous media. The results based on the approximate method, when compared with existing exact solutions show an agreement of within a maximum error bound of 2.5%.Nomenclature
A
cross-sectional area
-
b
i
coefficient in the chosen temperature profile
-
B
1
coefficient in the profile for the dimensionless boundary layer thickness
-
C
coefficient in the modified Forchheimer term for power-law fluids
-
C
1
coefficient in the Oseen approximation which depends essentially on pore geometry
-
C
i
coefficient depending essentially on pore geometry
-
C
D
drag coefficient
-
C
t
coefficient in the expression forK
*
-
d
particle diameter (for irregular shaped particles, it is characteristic length for average-size particle)
-
f
p
resistance or drag on a single particle
-
F
R
total resistance to flow offered byN particles in the porous media
-
g
acceleration due to gravity
-
g
x
component of the acceleration due to gravity in thex-direction
-
Grashof number based on permeability for power-law fluids
-
K
intrinsic permeability of the porous media
-
K
*
modified permeability of the porous media for flow of power-law fluids
-
l
c
characteristic length
-
m
exponent in the gravity field
-
n
power-law index of the inelastic non-Newtonian fluid
-
N
total number of particles
- Nux,D,F
local Nusselt number for Darcy forced convection flow
- Nux,D-F,F
local Nusselt number for Darcy-Forchheimer forced convection flow
- Nux,D,M
local Nusselt number for Darcy mixed convection flow
- Nux,D-F,M
local Nusselt number for Darcy-Forchheimer mixed convection flow
- Nux,D,N
local Nusselt number for Darcy natural convection flow
- Nux,D-F,N
local Nusselt number for Darcy-Forchheimer natural convection flow
-
pressure
-
p
exponent in the wall temperature variation
-
Pe
c
characteristic Péclet number
-
Pe
x
local Péclet number for forced convection flow
-
Pe
x
modified local Péclet number for mixed convection flow
-
Ra
c
characteristic Rayleigh number
-
Ra
x
local Rayleigh number for Darcy natural convection flow
-
Ra
x
local Rayleigh number for Darcy-Forchheimer natural convection flow
- Re
convectional Reynolds number for power-law fluids
-
Reynolds number based on permeability for power-law fluids
-
T
temperature
-
T
e
ambient constant temperature
-
T
w,ref
constant reference wall surface temperature
-
T
w(X)
variable wall surface temperature
- T
w
temperature difference equal toT
w,ref–T
e
-
T
1
term in the Darcy-Forchheimer natural convection regime for Newtonian fluids
-
T
2
term in the Darcy-Forchheimer natural convection regime for non-Newtonian fluids (first approximation)
-
T
N
term in the Darcy/Forchheimer natural convection regime for non-Newtonian fluids (second approximation)
-
u
Darcian or superficial velocity
-
u
1
dimensionless velocity profile
-
u
e
external forced convection flow velocity
-
u
s
seepage velocity (local average velocity of flow around the particle)
-
u
w
wall slip velocity
-
U
c
M
characteristic velocity for mixed convection
-
U
c
N
characteristic velocity for natural convection
-
x, y
boundary-layer coordinates
-
x
1,y
1
dimensionless boundary layer coordinates
-
X
coefficient which is a function of flow behaviour indexn for power-law fluids
-
effective thermal diffusivity of the porous medium
-
shape factor which takes a value of/4 for spheres
-
shape factor which takes a value of/6 for spheres
-
0
expansion coefficient of the fluid
-
T
boundary-layer thickness
-
T
1
dimensionless boundary layer thickness
-
porosity of the medium
-
similarity variable
-
dimensionless temperature difference
-
coefficient which is a function of the geometry of the porous media (it takes a value of 3 for a single sphere in an infinite fluid)
-
0
viscosity of Newtonian fluid
-
*
fluid consistency of the inelastic non-Newtonian power-law fluid
-
constant equal toX(2
2–n
)/
-
density of the fluid
-
dimensionless wall temperature difference 相似文献
964.
本文提出了一种水平成层介质中弹性波粘弹性波计算的新方法,分别研究了线源和点源作用情况。该方法适用于各种粘弹性模型,数值计算简单,可模拟任意震源及所产生的各种体波、面波,数值结果表明具有很高的计算精度和计算效率。 相似文献
965.
966.
In the present paper we consider interior and exterior mixed boundary value problems of anti-plane shear in the static theory of linear piezoelectricity. Using the boundary integral equation method we reduce the problems to systems of singular integral equations with discontinuous coefficients to which the classical Nöether’s theorems on existence of the solution can be applied. This allows us to establish well-posedness results and to obtain integral solutions of the corresponding mixed boundary value problems for a rather general class of piezoelectric materials.
Mathematics Subject Classifications (2000) 45E05, 45F15, 74F15. 相似文献
967.
A. M. Zenkour 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(3-4):262-276
Summary The static and dynamic responses of anisotropic spherical shells under a uniformly distributed transverse load are investigated.
Analytical solutions using the mixed variational formulation are presented for spherical shells subjected to various boundary
conditions. Numerical results of a refined mixed first-order shear deformation theory for natural frequencies, critical buckling,
center deflections and stresses are compared with those obtained using the classical shell theory. A variety of simply-supported
and clamped boundary conditions are considered and comparisons with the existing literature are made. The sample numerical
results presented herein for global structural behaviour of monoclinic spherical shells should serve as references for future
comparisons. 相似文献
968.
A boundary layer analysis has been presented for the interaction of mixed convection with thermal radiation in laminar boundary flow from a vertical wedge in a porous medium saturated with a power-law type non-Newtonian incorporating the variation of permeability and thermal conductivity. The transformed conservation laws are solved numerically for the case of variable surface temperature conditions. The combined convection non-similar parameter we note that =0 and 1 correspond to pure free and forced convection cases. The Rosseland approximation is used to describe the radiative heat flux in energy equation. Velocity and temperature profiles as well as the local Nusselt number are presented. 相似文献
969.
AUNIFORMLYDIFFERENCESCHEMEOFSINGULARPERTURBATIONPROBLEMFORASEMILINEARORDINARYDIFFERENTIALEQUATIONWITHMIXEDBOUNDARYVALUECONDIT... 相似文献
970.