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.
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.
出处
《同济大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2014年第11期1665-1669,共5页
Journal of Tongji University:Natural Science
基金
国家自然科学基金(50578121)
关键词
解析层元
温度应力
平面应变
稳定温度场
层状路面体系
analytical layer-element
thermal stress
planestrain
stable temperature field
layered pavement system
