Python进行有限元仿真的使用及创建

pip install fenics pyfem

from fenics import *
import matplotlib.pyplot as plt
# 创建一个网格
mesh = UnitSquareMesh(8, 8)
# 定义边界条件
def boundary(x, on_boundary):
    return on_boundary
bc = DirichletBC(mesh, Constant(0), boundary)
# 定义变量和函数空间
V = FunctionSpace(mesh, 'P', 1)
u = TrialFunction(V)
v = TestFunction(V)
# 定义方程
f = Constant(-6.0)
a = dot(grad(u), grad(v))*dx
L = f*v*dx
# 求解方程
u = Function(V)
solve(a == L, u, bc)
# 绘制结果
plot(u)
plt.show()

python复制代码from pyfem import Problem
from pyfem.utils.meshGenerator import createRectangleMesh
from pyfem.utils.output import printMatrix
from pyfem.materials.linearElasticity import LinearElasticity
from pyfem.boundaryConditions.dirichlet import Dirichlet
from pyfem.solvers.linearSolver import solveLinearSystem
# 创建问题实例
problem = Problem()
# 创建网格
mesh = createRectangleMesh([0, 1], [0, 1], [0, 1], [10, 10])
problem.setMesh(mesh)
# 定义材料属性
elasticity = LinearElasticity(E=1, nu=0.3)
problem.setMaterialProperties(elasticity)
# 定义边界条件
dirichlet = Dirichlet(u=0)
problem.addBoundaryCondition(dirichlet, 'left')
problem.addBoundaryCondition(dirichlet, 'right')
problem.addBoundaryCondition(dirichlet, 'bottom')
problem.addBoundaryCondition(dirichlet, 'top')
# 构建系统矩阵和右侧向量
A, b = problem.buildSystem()
# 求解线性系统
u = solveLinearSystem(A, b)
# 打印结果
printMatrix(A)
printMatrix(b)
printMatrix(u)