Thermo-Elastic Study of Sandwich Plates by Alternative Hierarchical Finite Element Method Based on Reddy’s C1HSDT

Abstract

The dynamic behavior of a structure is influenced by the environment in which it is located it among the community seeking more structure, we have the thermal loading, this work investigates a plate sandwich subjected to thermal stress, the modeling of the plate is made by a third order model developed by Reddy TSDT (Third Order Shear Deformation Theory), while the TLT theory (Theory Thermal Layers) is used to transform the three-dimensional problem to a two-dimensional thermal problem. Next, a rectangular-p element with four nodes at the vertices and four sides is used to model the structure, and the thermal conduction. In the structure part, the forms used functions are trigonometric family C0 type for membrane displacements and rotations and type C1 for inflected movements, the thermal portion is modeled by C0 types of shape functions where the degrees of freedom to the nodes are the temperature, the temperature gradient and the temperature curve, the thermoelastic study to determine the displacements of the submerged plate by the method of integration time PTIM (Precis Time Integration Method). Finally, a study of convergence of the developed numerical code is made, the found results are validated with those found in the literature, and different parametric studies are made for the sandwich plates in different situations, structure, and thermo- elastic.

Keywords

• : Free vibration,thick composites plates,sandwich plate,hierarchical finite element method,C1 HSDT,heat conduction,thermo-elastic analysis

References

1. Nelson RB. Lorch DR. A refined theory for laminated orthotropic plates. ASME, J Appl Mech 1974; 41: 177-183.
2. Lo KH, Christen RM, Wu EM. A higher order rheory of plate deformation – Part 1: Homogeneous plates. ASME, J Appl Mech 1979; 44: 663-668.
3. Nayak AK, Moy SSJ, Shenoi RA. Free vibration analysis of composite sandwich plates based on reddy's higher order theory. Composites Part B: Engineering 2002; 33 (7): 505-519.
4. Nayak AK, Shenoi RA, Moy SSJ. Transient response of composite sandwich plates. Comput Struct 2004; 64: 249-267.
5. Batra RC, Aimmanee S. Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories. Comput Struct 2005; 83: 934-955.
6. Ambartsumian SA. On the Theory of Bending Plates. Izv Otd Tech Nauk. AN SSSR 1958; 5:69–77.
7. Soldatos KP, Timarci T. A unified formulation of laminated composites, shear deformable, five-degrees-of-freedom cylindrical shell theories. Compos Struct 1993; 25: 165–171.
8. Reddy JN. Energy and variational methods in applied mechanics. Wiley, London 1984.

9. Padovan J. Steady conduction of heat in linear and nonlinear fully anisotropic media by finite elements. Journal of Heat Transfer 1974;96:313-8.
10. Tamma KK, Yurko AA. A unified finite element modelling/analysis approach for thermal structural response in layered composites. Computers & Structures 1988;29:743-54.
11. Bose A, Surana KS. Piecewise hierarchical p-version axisymmetric shell element for non-linear heat conduction in laminated composites. Computers & Structures 1993;47:1-18.
12. [12] R. Rolfes, K. Rohwer, Integrated thermal and mechanical analysis of composite plates and shells, Composites Science and Technology 2000; 60 2097-2106
13. Heemskerk JF, Delil AAM, Daniels DHW. Thermal conductivity of honeycomb sandwich panels for space application. Technical report, National Aerospace Laboratory NLR, The Netherlands, 1971.
14. J. Noack, R. Rolfes, J. Tessmer, New layer wise theories and finite elements for efficient thermal analysis of hybrid structures, Computers and Structures 2003; 81, 2525–2538.
15. Brischetto, S, Effect of the through-the-thickness temperature distribution on the response of layered and composite shells. International Journal of Applied Mechanics 2009; 1 (4), 1–25.
16. Brischetto S, Carrera E, Thermal stress analysis by refined multilayered composite shell theories. Journal of Thermal Stresses 2009; 32 (1), 165–186.
17. Khare, R.K, Kant, T, Garg, A.K. Closed-form thermo-mechanical solutions of higher-order theories of cross-ply laminated shallow shells. Composite Structures 2003; 59 (3), 313–340.
18. Khdeir, A.A. Thermoelastic analysis of cross-ply laminated circular cylindrical shells. International Journal of Solids and Structures 1996; 33 (27), 4007–4017.
19. Birsan, M. Thermal stresses in cylindrical Cosserat elastic shells. European Journal of Mechanics - A/Solids 2009; 28 (1), 94–101.
20. Carrera, E., An assessment of mixed and classical theories for the thermal stress analysis of orthotropic multilayered plates. Journal of Thermal Stresses 23 (9), 797–831.
21. Carrera, E., (2002). Temperature profile influence on layered plates response considering classical and advanced theories. AIAA Journal 2000; 40 (9), 1885–1896.
22. Rolfes, R., Noack, J., Taeschner, M. High performance 3D-analysis of thermo-mechanically loaded composite structures. Composite Structures 1999;46 (4), 367–379.
23. [23] Brischetto, S. Effect of the through-the-thickness temperature distribution on the response of layered and composite shells. International Journal of Applied Mechanics 2009;1 (4), 1–25.
24. Brischetto, S., Leetsch, R., Carrera, E., Wallmersperger, T., Kröplin, B. Thermomechanical bending of functionally graded plates. Journal of Thermal Stresses 2008; 31 (3), 286–308.
25. Tungikar V, Rao, B.K.M. Three dimensional exact solution of thermal stresses in rectangular composite laminates. Composite Structures 1994; 27 (4), 419–430.
26. Asadi E, Fariborz SJ, Free vibration of composite plates with mixed boundary conditions based on higher-order shear deformation theory. Arch Appl Mech 2012; 82, 755–766.
27. Houmat A. An alternative hierarchical finite element formulation applied to plate vibrations. J Sound Vib 1997; 206(2): 201-215.
28. Reddy JN. A simple higher-order theory for laminated composite plates. ASME, J Appl Mech 1984; 51, 745-752.
29. Senthilnalhan NR, Lim KH, Lee KH. Chow ST. Buckling of shear deformable plates. AIAA J 1987; 25(9), 1268-71.
30. Kant T, Swaminathan K. Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Composite structures 2001, 53, 73-85.
31. Whitney JM, Pagano NJ. Shear deformation in heterogeneous anisotropic plates. ASME, J Appl Mech 1970; 37(4), 1031-1036.