官网：https://doc.cfd.direct/openfoam/user-guide-v9/platehole
$FOAM_TUTORIALS/stressAnalysis/solidDisplacementFoam下的案例
1、网格划分
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
object blockMeshDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
convertToMeters 1;
vertices
(
(0.5 0 0)
(1 0 0)
(2 0 0)
(2 0.707107 0)
(0.707107 0.707107 0)
(0.353553 0.353553 0)
(2 2 0)
(0.707107 2 0)
(0 2 0)
(0 1 0)
(0 0.5 0)
(0.5 0 0.5)
(1 0 0.5)
(2 0 0.5)
(2 0.707107 0.5)
(0.707107 0.707107 0.5)
(0.353553 0.353553 0.5)
(2 2 0.5)
(0.707107 2 0.5)
(0 2 0.5)
(0 1 0.5)
(0 0.5 0.5)
);
blocks
(
hex (5 4 9 10 16 15 20 21) (10 10 1) simpleGrading (1 1 1)
hex (0 1 4 5 11 12 15 16) (10 10 1) simpleGrading (1 1 1)
hex (1 2 3 4 12 13 14 15) (20 10 1) simpleGrading (1 1 1)
hex (4 3 6 7 15 14 17 18) (20 20 1) simpleGrading (1 1 1)
hex (9 4 7 8 20 15 18 19) (10 20 1) simpleGrading (1 1 1)
);
edges
(
arc 0 5 (0.469846 0.17101 0)
arc 5 10 (0.17101 0.469846 0)
arc 1 4 (0.939693 0.34202 0)
arc 4 9 (0.34202 0.939693 0)
arc 11 16 (0.469846 0.17101 0.5)
arc 16 21 (0.17101 0.469846 0.5)
arc 12 15 (0.939693 0.34202 0.5)
arc 15 20 (0.34202 0.939693 0.5)
);
boundary
(
left
{
type symmetryPlane; // 对称边界条件
faces
(
(8 9 20 19)
(9 10 21 20)
);
}
right
{
type patch; // 对称边界条件
faces
(
(2 3 14 13)
(3 6 17 14)
);
}
down
{
type symmetryPlane; // 对称边界条件
faces
(
(0 1 12 11)
(1 2 13 12)
);
}
up
{
type patch;
faces
(
(7 8 19 18)
(6 7 18 17)
);
}
hole
{
type patch;
faces
(
(10 5 16 21)
(5 0 11 16)
);
}
frontAndBack
{
type empty; // 表示一个2D算例
faces
(
(10 9 4 5)
(5 4 1 0)
(1 4 3 2)
(4 7 6 3)
(4 9 8 7)
(21 16 15 20)
(16 11 12 15)
(12 13 14 15)
(15 14 17 18)
(15 18 19 20)
);
}
);
mergePatchPairs
(
);
// ************************************************************************* //
2、边界条件
2.1 位移量D
对于无热应力的单纯应力分析，只有位移量D需要指定。0/D
- 关键词traction：指定牵引力边界。指定牵引力边界矢量和大小；
- pressure：如果这个边界面法向牵引力的压力指向表面之外，就被定义为负值。
- right边界牵引力为（10000 0 0）Pa，pressure为0
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class volVectorField;
object D;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
dimensions [0 1 0 0 0 0 0];
internalField uniform (0 0 0);
boundaryField
{
left
{
type symmetryPlane;
}
right
{
type tractionDisplacement;
traction uniform (10000 0 0); // 牵引力
pressure uniform 0;
value uniform (0 0 0);
}
down
{
type symmetryPlane;
}
up
{
type tractionDisplacement;
traction uniform (0 0 0);
pressure uniform 0;
value uniform (0 0 0);
}
hole
{
type tractionDisplacement;
traction uniform (0 0 0);
pressure uniform 0;
value uniform (0 0 0);
}
frontAndBack
{
type empty;
}
}
// ************************************************************************* //
2.2 物理特性
constant/thermophysicalProperties
- planeStress yes; // 物理特性指定为yes
- thermalStress no; // 不求解热物理方程
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "constant";
object thermalProperties;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
rho // 密度
{
type uniform;
value 7854;
}
nu // 泊松比
{
type uniform;
value 0.3;
}
E // 杨氏模量
{
type uniform;
value 2e+11;
}
Cp // 比热容
{
type uniform;
value 434;
}
kappa // 热传导
{
type uniform;
value 60.5;
}
alphav // 热膨胀系数
{
type uniform;
value 1.1e-05;
}
planeStress yes; // 物理特性指定为yes
thermalStress no; // 不求解热物理方程
// ************************************************************************* //
2.3 控制
- 如果求解器是SIMPLE算法，deltaT设定为多少是无关紧要的。
- ？ timeFormat general;
- ？ timePrecision 6;
- ？ graphFormat raw;
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object controlDict;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
application solidDisplacementFoam; // 求解器
startFrom startTime;
startTime 0;
stopAt endTime;
endTime 100;
deltaT 1;
writeControl timeStep; // 使用步长控制输出
writeInterval 20;
purgeWrite 0; // 文件数量上限，0表示不激活。设置为2只会输出最后2个
writeFormat ascii; // 文件格式
writePrecision 6; // 文件的有效数字
writeCompression off; // 文件格式是否时压缩格式
timeFormat general;
timePrecision 6;
graphFormat raw;
runTimeModifiable true; // 运行中途修改配置文件是否有意义。如果true，则会读取修改文件
// ************************************************************************* //
2.4 离散格式和求解器
- 稳态求解：timeScheme为SteadyState，用于屏蔽掉时间离散项；
- 有限体积离散相建立与高斯定律上，对于大部分模拟高斯定律足够精准。但是在这个案例中没使用least squares；
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object fvSchemes;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
d2dt2Schemes
{
default steadyState;
}
ddtSchemes
{
default Euler;
}
gradSchemes
{
default leastSquares;
grad(D) leastSquares;
grad(T) leastSquares;
}
divSchemes
{
default none;
div(sigmaD) Gauss linear;
}
laplacianSchemes
{
default none;
laplacian(DD,D) Gauss linear corrected;
laplacian(kappa,T) Gauss linear corrected;
}
interpolationSchemes
{
default linear;
}
snGradSchemes
{
default none;
}
// ************************************************************************* //
fvSolution用于控制求解线性方程组使用的矩阵求解器
- stressAnalysis：求解所需要的控制参数；
- nCorrectors：整个方程组求解的外循环数，包括每个时间步长的拉伸边界条件；这里是稳态问题，时间步长代表迭代数以直到收敛，设置为1。
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
FoamFile
{
format ascii;
class dictionary;
location "system";
object fvSolution;
}
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
solvers
{
"(D|T)"
{
solver GAMG; // D的矩阵求解器GAMG
tolerance 1e-06; // 容差
relTol 0.9; // 相对误差，控制每次迭代的残差最小量
smoother GaussSeidel;
nCellsInCoarsestLevel 20;
}
}
stressAnalysis
{
compactNormalStress yes;
nCorrectors 1;
D 1e-06;
}
// ************************************************************************* //
3、运行
solidDisplacementFoam > log && cat log
最终残差始终小于最初残差的0.9倍。
4、后处理
计算张量分量
postProcess -func "components(sigma)"
4.1 对比解析解与数值解
需要把计算域中的对称面的左边的求解出来，可以使用sample生成。需要调用system下的sampleDict字典。
/*--------------------------------*- C++ -*----------------------------------*\
========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Version: 9
\\/ M anipulation |
\*---------------------------------------------------------------------------*/
interpolationScheme cellPoint;
setFormat raw;
sets
(
leftPatch
{
type uniform;
axis y;
start (0 0.5 0.25);
end (0 2 0.25);
nPoints 100;
}
);
fields (sigmaxx);
生成解析解
postProcess -func graphUniform
调用GnuPlot（需要安装）的plot命令
plot [0.5:2] [0:] "postProcessing/graphUniform/100/line_sigmaxx.xy",
1e4*(1+(0.125/(x**2))+(0.09375/(x**4)))
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