用代码实现压电简支板的耦合场分析

在Python中，特别是使用FEniCS库，可以编写代码来模拟压电简支板的耦合场分析，这涉及到电磁学和结构力学的相互作用。这里给出一个简化版的示例，我们假设已经安装了FEniCS库：

# 导入必要的库
import fenics as fe
from dolfin import *

# 定义域和边界条件
domain_size = (10., 5.)  # 板的尺寸
mesh = UnitSquareMesh(int(domain_size[0]*fe.n_elements('u')), int(domain_size[1]*fe.n_elements('u')))
V_u = FunctionSpace(mesh, 'P', 1)  # 结构位移函数空间
V_p = FunctionSpace(mesh, 'DG', 0)  # 电位移函数空间

def boundary_conditions(u, p):
    # 简支边界
    bc_u = DirichletBC(V_u, Constant((0., 0.)), "on_boundary")
    bc_p = DirichletBC(V_p, Constant(0.), "on_boundary")

    return bc_u, bc_p

# 初始化位移和电位移
u = TrialFunction(V_u)
p = TrialFunction(V_p)
v_u, v_p = TestFunctions(V_u), TestFunctions(V_p)

# 弹性模量、泊松比、电导率等材料常数
E, nu, sigma_0, epsilon_0 = fe.Constant((1e9, 0.3, 1e6, 8.854e-12))

# 荷载项
f_u, f_p = fe.Constant((0., 0.)), fe.Constant(0.)

# 表达式定义
a_u = dot(grad(u), grad(v_u)) * E / (1 - nu**2) + dot(p, epsilon(v_u))
L_u = f_u * v_u
a_p = dot(grad(p), grad(v_p)) + dot(sigma_0 * u, v_p) / epsilon_0
L_p = f_p * v_p

# 方程求解
problem_u = LinearVariationalProblem(a_u, L_u, u, bc_u)
solver_u = LinearVariationalSolver(problem_u)
solution_u = solver_u.solve()

problem_p = LinearVariationalProblem(a_p, L_p, p, bc_p)
solver_p = LinearVariationalSolver(problem_p)
solution_p = solver_p.solve()