Weak Formulation Study for Thermoelastic Analysis of Thick Open Laminated Shell

Abstract

Weak formulations of mixed state equations including boundary conditions of open laminated cylindrical shells is presented in a cylindrical coordinate system. Thermal stresses mixed state equation of open cylindrical shell is established. Mixed equation is changed into Hamilton canonical equation. For applying the transfer matrix method and taking advantage of the Hamiltonian matrix in the calculation, three-dimensional thermoelastic solutions are obtained for open laminated cylindrical shell of arbitrary thickness subjected to mechanical loading and temperature variation. Every equation of elasticity can be satisfied, and all elastic constants can be taken into account. The principle and method suggested here have clear physical concepts. In the present study, the equations weaken without special treatment, so this method would be easily popularized in dynamic analysis of elasticity. The solutions and results given here may serve as a benchmark for other numerical procedures.

Keywords:

• open laminated cylindrical shell
• weak formulation
• mixed state equations
• thermal stresses
• Hamilton canonical equation
• three-dimensional solutions

ACKNOWLEDGMENT

This project supported by Anhui ProvinceNationalNatural Science Foundation through grantNo. 050440506,No. KJ2007A004 and ZD2008001-1.