Research On Statics Of The Thermoelastic Materials Laminated Plates And Shells

Based upon the theories of elastic mechanics and heat transfer, uniting the symplectic theory and state space method, the static mechanics problems of the laminated plates and laminated shells of thermoelastic composites and piezothermoelastic composites were studied.First, deduced the non-homogenous state equations of thermoelastic composites with mechanic-heat coupling effect and piezothermoelastic composites with mechanic-electric-heat coupling effect respectively. Secondly, according to the symplectic theory, a corresponding augment dimensions constitutive relationships was established by combining the heat exchange equations with the constitutive relationships of thermoelastic composite materials and piezothermoelastic composite materials. The homogenous state equations of thermoelastic composites with mechanic-heat coupling effect and piezothermoelastic composites with mechanic-electric-heat coupling effect, wer directly derived by the augment dimensions constitutive relationships and the state space method.The treatment avoided the solution of the second order differential equation on the thermal equilibrium equations and thermal gradient relationships, which was necessary performed to solving non-homogeneous state equations, greatly simplified the solution procedure of laminated structures, and improved numerical precision. Notably the homogenous state equations could be straightly discreted in finite element format, presented a new method for the semi-analytical solution of laminated plates and shells with complicated boundary condition in practice.In this paper, non-homogenous state equations and homogenous state equations were detailedly derived of thermoelastic composites laminated plates, cylindrical open shells, orthogonal generic shells, and piezothermoelastic composites laminated plates, cylindrical open shells, and respectively analyzed their exact solution with four simply supported, the results validated the correctness of the homogenous state equations.