Exact Solution of Laminated Orthogonal Hyperbolic Shells of Thermoelastic with Four Simply Supported

Abstract:

The exact solution of laminated Orthogonal Hyperbolic shell of thermoelastic composite is very important to investigate it’s the mechanical properties. Therefore, many studies were completed in this paper. Firstly, the non-homogeneous state equation in generic coordinates is derived for thermoelastic composites including thermal gradient relationships by the basic equations and state space method. Secondly, an augmented dimension constitutive relationship was obtained by combining thermal gradient relationships into constitutive relationships of composite constitutive relationships based on the theory of symplectic variable and precise time-integration with dimension expanding method. Lastly, uniting state space method and the augmented dimension constitutive relationships, a homogeneous state equation which can be solely solved was deduced by eliminating the stresses in plane. The homogeneous state equation can simplify greatly the solution process of the laminated Orthogonal Hyperbolic shell, improve the calculation accuracy. What’s more, it can be discrete straightly in finite element format. So, the homogeneous state equation, derived in the paper, can supply a new method for the exact solution of laminated structures with complicated boundary condition in practice.

• Periodical: Applied Mechanics and Materials (Volumes 727-728)
• Pages: 529-540
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.727-728.529
• Online since: January 2015
• Authors: Jian Hai Xue, Jia Yu Li
• Keywords: Exact Solution, Homogenous State Equation, Laminated Orthogonal Hyperbolic Shells, State Space Method, Thermoelastic Composites

References

[1] Fan J R. Exact theory of thick laminated plate and shell[M]. Beijing: Science Press, 1996 (In Chinese).

[2] Zou G P, Tang L M. A semi-analytical solution for thermal stress analysis of laminated composite cylindrical shells[J]. Acta Mechanica Sinica, 1995, 27(3): 336-342 (In Chinese).

[3] Zou G P, Tang L M. The state equations and a semi-analytical solution for thick composite double curved shells[J]. Acta Aeronautica et Astronautica Sinica, 1994, 15(2): 1424-1432 (In Chinese).

[4] Ding K W, Tang L M. Thermal stresses for open laminated cylindrical shell of arbitrary thickness[J]. Chinese Journal of Applied Mechanics, 1999, 16(2): 68-74 (In Chinese).

[5] Ding K W, Tang L M. Analytical solution of thermal stresses for open laminated cylindrical shell[J]. Engineering Mechanics, 1999, 16(3): 1-6 (In Chinese).

[6] SHU X F, LAN J X, WU Y Z. Analysis of thermal-elastic coupling vibration of large deflection cylindrical shell[J]. Applied Mathematics and Mechanics, 2004, 25(9): 994-1000.

DOI: 10.1007/bf02438348

[7] LI J Y, CHENG X Q, QING G H. Exact solution laminated piezothermoelastic generic shells with four simply supported edges[J]. Engineering Mechanics, 2010, 27(8): 83-89 (In Chinese).

[8] THANYAWALAI S. ZHEN H X. Coupled thermal-mechanical modeling of carbon fibers reinforced polymer composites for damage detection Coupled thermal-mechanical modeling of carbon fibers reinforced polymer composites for damage detection[J], Composites: Part B, 2012, 43: 1631-1636.

DOI: 10.1016/j.compositesb.2011.11.041

[9] Zhong W X. Symplectic system of applied mechanicas[M]. Beijing: Science Press, 2003 (In Chinese).

[10] GU Y X, CHENG B S, ZHANG H W. precise time-integration with dimension expanding method[J], ACTA MECHANICA SINICA, 2000, 32(4): 447-456 (In Chinese).