稳定温度场下层状路面体系的解析层元解

Analytical Layer element Solution for Layered Pavement in Stable Temperature Field

摘要:

从热弹性力学平面应变问题的控制方程出发，利用Fourier变换及Laplace变换推导其解析解，进而得出稳定温度场下平面应变问题的精确刚度矩阵，即解析层元；根据边界条件和层间连续条件对各层元进行组装，得到总刚度矩阵；求解总刚度矩阵方程，得到积分变换域内的解；应用Laplace Fourier逆变换技术，得到物理域内的解.编制相应的计算程序进行验证及分析，结果表明，该解答与有限元软件模拟结果吻合，分层特性对层状路面体系温度应力和竖向位移量影响显著.

Abstract:

Starting from the governing equations of thermoelasticity for the plane strain problem, the analytical solution of the problem is obtained by using the Fourier transform and Laplace transform. And then, the exact stiffness matrix for the multi layered plane strain problem in stable temperature field is established, which is called analytical layer element. The global stiffness matrix is assembled by considering the boundary conditions and the continuity between adjacent layers, and the solution in the transform domain are obtained by solving the equations of the global stiffness matrix. The actual solutions in the physical domain are acquired by inverting the Laplace Fourier transform. Numerical calculation and analysis are carried out by corresponding computer program whose results agree well with those by finite element analysis software, and numerical calculation shows the layered characteristics has a significant effect on the thermal stress and vertical displacement in layered pavement system.