臺灣博碩士論文加值系統

72個自由度高精確度的高階三角形板元素用以探討複合夾心板之氣熱彈特性，Von Karman幾何大變形假設和半穩定空氣動力學理論作為分析的基礎，複合夾心板是由複合層板面板與蜂巢結構心材所組成，夾心板之側向位移由彎矩撓曲及剪力變形疊加而得。研究範疇包括複合夾心板之熱應力挫屈、熱應力後挫屈；熱應力挫屈後複合夾心板之自由振動、線性顫振與非線性顫振等課題，深入研究複合夾心板的幾何形狀、纖維角度、邊界條件、材料係數、疊層順序與溫度分佈等變數。當複合夾心板承受溫度影響時可能發生熱應力挫屈現象，研究發現挫屈模態與複合夾心板之纖維角度和展弦比有關。溫度高於臨界挫屈溫度時，複合夾心板進入熱應力後挫屈階段，幾何大變形引入非線性勁度矩陣，此時非線性平衡方程式可由Newton-Raphson解法求解。結果顯示複合夾心板挫屈模態可能發生轉移，轉移後之模態取決於纖維角度與展弦比。溫度上升時與下降時，熱應力後挫屈之變形路徑可能不同。為了分析溫度高於臨界挫屈溫度時，複合夾心板之自由振動行為，複合夾心板之總位移分別以靜態與動態位移量之和表示，並假設其動態位移量遠小於靜態位移。先以Newton-Raphson解法求取靜態挫屈變形，再於頻率域求得自然頻率與振動模態。結果顯示振動模態的排列順序為溫度的函數，最低模態可能由高模態主宰。挫屈模態發生轉移時，複合夾心板之勁度突然改變，振動模態也會劇烈變化。溫度梯度增強複合夾心板之勁度，沒有振動模態頻率會陡降為零。挫屈模態發生轉移時，振動模態也只會緩慢變化。線性顫振可由頻率域求解，一般而言，顫振耦合發生於(1,1)與(2,1)模態之間。對於較狹長和較厚之格板，顫振耦合發生於(n,1)與(n+1,1)模態之間。非線性顫振問題於時間域求得結果，Newmark數值積分法配合靜態壓縮與模態縮減用以節省計算時間。研究發現溫度上升不一定降低顫振邊界，反而可能因為挫屈模態發生轉移，複合夾心板形成浪板形狀，提供額外勁度，造成顫振邊界上升。溫度梯度使得複合夾心板在溫度低於臨界挫屈溫度時便開始變形，並且明顯穩定複合夾心板之動態行為。五種不同行為─平坦、挫屈、有限循環運動、週期性運動、散漫運動均可有效預測，並有深入剖析。空氣動力與空氣摩擦生熱交互作用所引起的非線性行為有廣泛探討與充分瞭解，本文提供首篇先進複合夾心板氣熱彈行為的完整研究。

By considering the total transverse displacement of a sandwich plate be the sum of the displacement due to bending of the plate and that due to shear deformation of the core, a 72 degree-of-freedom high precision high order triangular plate element is developed for aerothermoelastic analysis of composite sandwich plates. The Von Karman large deflection assumptions and quasi-steady supersonic aerodynamic theory are used for the aerothermoelastic analysis of composite sandwich panel consisting of two laminated face sheets and an orthotropic honeycomb core. The scope of this thesis includes thermal buckling and thermal postbuckling of composite sandwich plates; free vibration, linear flutter, and nonlinear flutter of thermally buckled composite sandwich plates. The effects of plate geometry, fiber orientation, boundary conditions, material properties, stacking sequence, and temperature distribution are discussed in details. The thermal buckling analysis has been represented as the standard eigenvalue problem. Numerical results show that the buckling mode that sandwich plate will buckle into is dependent on the fiber orientation in the plate and aspect ratio of the plate. In the thermal postbuckling analysis of composite sandwich plates. The nonlinear system equation is solved by Newton-Raphson method. Numerical results show that the buckle pattern that sandwich plate with angle-ply laminates faces will change is dependent on the fiber orientation in the plate and aspect ratio of the plate. The path of cooling down process is different from that of heating up process. The buckle pattern change will occur at lower temperature during cooling down process while it will occur at higher temperature in the heating up process. In the free vibration analysis of thermally buckled composite sandwich plates, the total response of the plate is assumed to be the sum of displacement due to static deformation and that due to dynamic deformation. The nonlinear governing equations can be written into two sets of equations. The static deflection of the thermally buckled plate is first solved by Newton-Raphson method. Then, another set of linear equation may determine the dynamic behavior of the thermally buckled plate in frequency domain. By examining the buckling and free vibration modes of the plate, a clear picture of buckle pattern change and lowest vibration mode shift is presented. Numerical results show that the order of the vibration mode is a function of the temperature rise. The higher vibration mode with multiple waves may become the fundamental vibration mode. Due to this buckle pattern change, the stiffness of the plate is also suddenly changed that in turn makes the natural frequency of the plate jump. The higher vibration mode may become the fundamental vibration mode after buckle pattern change. The temperature gradient induces thermal moments and makes the plate stiffer. None of the natural frequencies will drop to zero as the temperature is increased and lowest vibration mode shift induced by buckle pattern change will occur slowly. In the flutter analysis of thermally buckled composite sandwich plates, Newton-Raphson method and Newmark method are used to solve the nonlinear problem in frequency and time domains, respectively. Static condensation and modal reduction are adopted for saving computing time. In general, the coalescence pair usually is between natural modes (1,1) and (2,1). For longer or thicker plates, the flutter mode shape is the combination of (n,1) and (n+1,1) flutter modes. Numerical results show that the elevated temperature may not only decrease flutter boundary in general, but also increase flutter boundary due to the buckling pattern suddenly changes in some special cases. The corrugated deflection pattern will offer additional geometrical nonlinear stiffness. The critical aerodynamic pressure of the buckled plate with high temperature rise may be higher than the one without thermal effect. The temperature gradient makes the plates deflect under the critical buckling temperature and stabilized the dynamic behavior of the thermally buckled composite sandwich plates significantly. All five types of panel behavior such as flat, buckled, limit-cycle, periodic, and chaotic motions can be identified successively. The nonlinear behavior of composite sandwich plates subjected to aerodynamic loading and aerodynamic heating is extensively explored and reasonably understood. This dissertation provides aerothermoelastic analysis of composite sandwich plate that is still lacking. It is the first study devoted to the complete aerothermoelastic analysis of advanced composite sandwich plate.

CONTENTS

ABSTRACT...........................................................................................................................ii
CONTENTS......................................................................................................................xviii
LIST OF TABLES..............................................................................................................xxi
LIST OF FIGURES............................................................................................................xxii
NOMENCLATURE...........................................................................................................xxv

Chapter page
I. INTRODUCTION............................................................................................................1
II. FORMULATION OF FINITE ELEMENT....................................................................14
2.1 Formulation of Composite Sandwich Plates............................................................14
2.2 Strain Energy, Kinematic Energy, and Work...........................................................17
2.3 Triangular Plate Element...........….………………….............................................18
2.4 Element Stiffness, Mass, Aerodynamic Matrices and Thermal Loading Vector….21
III. THERMAL BUCKLING AND POSTBUCKLING ANALYSIS OF COMPOSITE SANDWICH PLATES..................................................................................................24
3.1 Equilibrium Equation...............................................................................................24
3.2 Solution Procedures for Thermal Postbuckling Analysis.........................................26
3.3 Numerical Results....................................................................................................27
3.3.1 Thermal Buckling............................................................................................27
[(0/90)2/core]s Sandwich Plate.......................................................................28
[(±q)2/core]s Sandwich Plate..........................................................................29
3.3.2 Thermal Postbuckling......................................................................................31
[(0/90)2/core]s Sandwich Plate.......................................................................31
[(±q)2/core]s Sandwich Plate..........................................................................33
Temperature Gradient Effect..........................................................................36
IV. FREE VIBRATION ANALYSIS OF THERMALLY BUCKLED COMPOSITE SANDWICH PLATES..................................................................................................38
4.1 Equation of Motion..................................................................................................38
4.2 Solution Procedures..................................................................................................40
4.3 Numerical Results....................................................................................................41
[(0/90)2/core]s Sandwich Plate..................................................................... ...........42
[(±q)2/core]s Sandwich Plate....................................................................................43
Temperature Gradient Effect....................................................................................45
V. FLUTTER ANALYSIS OF THERMALLY BUCKLED COMPOSITE SANDWICH PLATES.........................................................................................................................47
5.1 Equation of Motion..................................................................................................47
5.2 Solution Procedures..................................................................................................49
5.2.1 Frequency Domain Formulation for Linear Flutter.........................................49
5.2.2 Time Domain Modal-Formulation for Nonlinear Flutter................................51
5.3 Numerical Results....................................................................................................55
5.3.1 Linear Panel Flutter.........................................................................................55
5.3.2 Nonlinear Panel Flutter ..................................................................................58
VI. CONCLUSIONS…………………………………........................................................63
REFERENCES.....................................................................................................................66
APPENDIX..........................................................................................................................74
TABLES...............................................................................................................................77
FIGURES.............................................................................................................................79
PUBLICATION LIST........................................................................................................123
VITA...................................................................................................................................124

LIST OF TABLES

Table page
2.1 Material properties for the graphite epoxy laminated face sheet.................................77
2.2 Material properties of aluminum honeycomb core......................................................77
3.1 Critical buckling temperature of conventional sandwich plate...................................78

LIST OF FIGURES

Figure page
2.1 Geometry of a rectangular honeycomb core sandwich panel.....................................79
2.2 72 degree of freedom triangular plate element...........................................................80
2.3 The 8×4 mesh of a rectangular plate with a/b=2.......................................................81
3.1 Critical buckling temperature vs aspect ratio for [(0/90)2/core] s rectangular sandwich plates......................................................................................................82
3.2 Boundary of thermal buckling mode for simply supported sandwich plates....…......83
3.3 Critical buckling temperature vs core thickness for [(0/90)2/core] s square sandwich plates.........................................................................................................................84
3.4 Boundary of thermal buckling mode for simply supported [(±q)2/core] s sandwich plates............................................................................................................................85
3.5 Critical buckling temperature vs aspect ratio for simply supported [(±q)2/core]s sandwich plates............................................................................................................86
3.6 Critical buckling temperature vs fiber orientation for simply supported [(±q)2/core]s sandwich plates............................................................................................................87
3.7 Central deflection vs temperature rise for [(0/90)2/core] s square sandwich plates.....88
3.8 Central deflection vs temperature rise for [(0/90)2/core] s rectangular sandwich plates............................................................................................................................89
3.9 Central line deflection curve for [(0/90)2/core] s sandwich plate (a/b=4)...................90
3.10 Central line deflection curve for [(0/90)2/core] s sandwich plate (a/b=5)...................91
3.11 Central deflection vs temperature for [(±q)2/core] s square sandwich plates...............92
3.12 3-D deflection shape for [(±60) 2/core] s square composite sandwich plate................93
3.13 Boundary of mode shape for [(±q)2/core] s square composite sandwich plates...........94
3.14 Boundary of mode shape for [(±q)2/core] s composite sandwich plates (a/b=2).........95
3.15 Thermal postbuckling behavior of [(±60) 2/core] s square sandwich plate..............…96
3.16 Temperature gradient effect on central deflection of [(±q)2/core]s sandwich plates..97
4.1 Natural frequencies for [(+45/-45/+45) square laminate.........................................…98
4.2 Natural frequencies for [(0/90)2/core]s square composite sandwich plate..............…99
4.3 Natural frequencies for [(0/90)2/core]s composite sandwich plate (a/b=2).............100
4.4 Natural frequencies for [(0/90)2/core]s composite sandwich plate (a/b=3)...........…101
4.5 Boundary of first vibration mode shape for [(±q)2/core]s square sandwich plates....102
4.6 Natural frequencies for [(±60)2/core]s square composite sandwich plate.................103
4.7 Contour plot of first mode for [(±60)2/core]s square composite sandwich plate.......104
4.8 Natural frequencies for [(±75)2/core]s square composite sandwich plate.................105
4.9 Temperature gradient on vibration of thermally buckled [(±60)2/core]s square sandwich plate..............................................................................................…….....106
4.10 Temperature gradient on vibration of thermally buckled [(±75)2/core]s square sandwich plate................................................................................................….......107
5.1 Flutter coalescence plot of [(0/90)2/core]s rectangular sandwich plates....................108
5.2 Critical dynamic pressure vs aspect ratio for [(±q)2/core]s rectangular sandwich plates..........................................................................................................................109
5.3 Critical dynamic pressure vs fiber angle for [(±q)2/core]s rectangular sandwich plates..........................................................................................................................110
5.4 Flutter boundary vs fiber angle for [(±q)2/core]s square sandwich plates.…………111
5.5 Stability boundary of [(±30)2/core]s and [(±45)2/core]s square sandwich plates...…112
5.6 Temperature gradient on flutter boundary of [(±q)2/core]s sandwich plates (DT/DTcr =1).............................................................................................................................113
5.7 Stability boundary of square isotropic plate with uniform temperature....................114
5.8 Temperature gradient on stability boundary of [(±45)2/core]s square sandwich plate...........................................................................................................................115
5.9 Phase plane plot for [(±45)2/core]s square sandwich plate (l=100)..........................116
5.10 Phase plane plot for [(±45)2/core]s square sandwich plate (DT/DTcr=3)...................117
5.11 Response of [(±45)2/core]s square composite sandwich plate (Tt =1.5DT, Tb =0.5DT, l=250).......................................................................................................................118
5.12 Temperature gradient on stability boundary of [(±30)2/core]s square sandwich plate...........................................................................................................................119
5.13 Contour plot of static deflection of [(±30)2/core]s sandwich plate (DT/DTcr=3).......120
5.14 Flutter coalescence plot of [(±30)2/core]s sandwich plate (DT/DTcr=3)....................121
5.15 Temperature gradient on stability boundary of [(0/90)2/core]s square sandwich plate...........................................................................................................................122

Agarwal, B. D., and Broutman, L. J., Analysis and Performance of Fiber Composites, Wiley, New York, pp. 162-164 and pp. 232-236, 1990.
Abbas, J. F., Ibrahim, R. A., and Gibson, R. F. “Nonlinear Flutter of Orthotropic Composite panel Under Aerodynamic Heating,” AIAA Journal, Vol. 31, No. 8, pp. 1478-1488, 1993.
Bisplinghoff, R. L., and Pian, T. H. H., “On the Vibrations of Thermal Buckled Bars and Plates,’ Proceedings of 9th International Congress for Applied Mechanics, Vol. 7, pp. 307-318, 1957.
Bailey, C. D., “Vibration of Thermal Stressed Plates with Various Boundary Conditions,” AIAA Journal, Vol. 11, No. 1, pp. 14-19, 1973.
Birman, V., and Librescu, L., “Supersonic Flutter of Shear Deformable Laminated Composite Flat Panels,” J. of Sound and Vibration, Vol. 139, pp. 265-275, 1990.
Calligeros, J. M., and Dugundji, J., “Effects of Orthotropicity Orientation on Supersonic Panel Flutter,” AIAA Journal, Vol. 1, No. 9, pp. 2180-2182, 1963.
Chen, J. K., and Sun, C. T., “Analysis of Impact Response of Buckled Composite Laminates,” Composite Structures, Vol. 3, pp. 97-118, 1985.
Chen, L. W., and Chen, L. Y. “Thermal Buckling of Laminated Composite Plates,” J. of Thermal Stresses, Vol. 10, pp. 345-356, 1987.
Chen, A. T., and Yang, T. Y., “A 36 DOF Symmetrically Laminated Triangular Element with Shear Deformation and Rotatory Inertia,” J. of Composite Materials, Vol. 22, pp. 341-359, 1988.
Chen, L. W., and Chen, L. Y. “Thermal Buckling Analysis of Composite Laminated Plates by the Finite Element Method,” J. of Thermal Stresses, Vol. 12, pp. 41-56, 1989.
Chen, L. W., and Chen, L. Y., “Thermal Postbuckling Analysis of Laminated Composite Plates by the Finite Element Method,” Composite Structures, Vol. 12, pp. 257-270, 1989.
Chang, J. S., “FEM Analysis of Buckling and Thermal Buckling of Antisymmetric Angle-Ply Laminates According to Transverse Shear and normal Deformation High Order Displacement Theory,” Computers & Structures, Vol. 37, No.6, pp.925-946, 1990.
Chen, L. W., Chen, W. J., and Lin, P. D. “Thermal Buckling Behavior of Thick Composite Laminated Plates under Nonuniform Temperature Distribution,” Computers & Structures, Vol. 41, No.4, pp.637-645, 1991.
Chen, L. W., and Chen, L. Y., “Thermal Postbuckling Behavior of Laminated Composite Plates with Temperature-Dependent Properties,” Composite Structures, Vol. 19, pp. 267-283, 1991.
Chang, J. S., “Overall Buckling and Postbuckling Behavior of Beam-Like Sandwich Plates,” Composite Science and Technology, Vol. 45, pp. 55-63, 1992.
Chen L. W., Lan, T., and Lin, P. D., “Thermal Buckling of Bimodular Sandwich Beam,” Composite Structures, proceedings of the 7th International Conference, Univ. of Paisley, United Kingdom, July 5-7, 1993.
Dowell, E. H., "Panel Flutter: A Review of the Aeroelastic Stability of Plates and Shells," AIAA Journal, Vol. 8, No. 3, pp. 385-399, 1970.
Dowell, E. H., “Flutter of a Buckled Plate as an Example of Chaotic Motion of a Deterministic Autonomous System,” J. of Sound and Vibration, Vol. 85, pp. 333-344, 1982.
Eisley, J. G., and Luessen, G., “Flutter of Thin Plates under Combined Shear and Normal Edge Forces,” AIAA Journal, Vol. 1, No. 3, pp. 620-626, 1963.
Gossard, M. L., Seide, P., and Roberts, W. M., “Thermal Buckling of Plates,” NACA TN -2771, 1952.
Gee, D. J., and Sipcic, S. R., “Coupled Thermal Model for Nonlinear Panel Flutter,” AIAA Journal, Vol. 37, No. 5, pp. 642-650, 1999.
Han, A. D., and Yang, T. Y., “Nonlinear Panel Flutter Using High-Order Triangular Finite Elements,” AIAA Journal, Vol. 21, No. 10, pp. 1453-1461, 1983.
Ibrahim, I. M., Farah, A., and Rizk, M. N. F., “Dynamic Analysis of Unbalanced Anisotropic Sandwich Plates,” J. of the Engineering Mechanics Division, ASCE, Vol. 107, pp. 405-418, 1981.
Ketter, D. J., "Flutter of Flat, Rectangular, Orthotropic Panels," AIAA Journal, Vol. 5, No. 1, pp. 116-124, 1967.
Ko, W. L., and Raymond, H. J., “Thermal Behavior of a Titanium Honeycomb-Core Sandwich Panel,” NASA TM-101732, 1991.
Ko, W. L., “Mechanical and Thermal Buckling Analysis of Sandwich Panels under Different Edge Conditions,” PICAST’1 1993-Pacific International Conference on Aerospace Science and Technology, National Cheng-Kung University, Tainan, Taiwan, Dec. 6-9, 1993, Proceedings, Vol. 1, pp. 318-327, 1993.
Ko, W. L., “Predictions of Thermal Buckling Strengths of Hypersonic Aircraft Sandwich Panels Using Minimum Potential Energy and Finite Element Methods,” NASA TM-4643, 1995.
Ko, W. L., “Thermostructural Behavior of a Hypersonic Aircraft Sandwich Panel Subjected to Heating on One Side,” NASA TM-4769, 1997.
Locke, J., and Mei, C., “Finite Element, Large-Deflection Random Response of Thermal Buckled Beams,” AIAA Journal, Vol. 28, No. 12, pp. 2125-2131, 1990.
Lee, I., and Cho, M. H., “Supersonic Flutter Analysis of Clamped Symmetric Composite Panels Using Shear Deformable Finite Elements,” AIAA Journal, Vol. 29, No. 5, pp. 782-783, 1991.
Liaw, D. G., “Supersonic Flutter of Laminated Thin Plates with Thermal Effects,” J. of Aircraft, Vol. 30, No. 1, pp. 105-111, 1993.
Locke, J. E., “Vibration Analysis of Heated Anisotropic Plates with Free Edge Conditions,” J. of Aircraft, Vol. 31, No. 3, pp. 696-702, 1994.
Lee, C. H., and Sun, C. T., “The Nonlinear Frequency and Large Amplitude of Sandwich Composites with Embedded Shape Memory Alloy,” J. of Reinforced Plastics and Composites, Vol. 14, No. 6, pp. 1160-1173, 1995.
Librescu, L., Lin, W., Nemeth, M. P., and Starnes, J. H. Jr., “Vibration of Geometrically Imperfect Panels subjected to Thermal and Mechanical loads,” J. of Spacecraft and Rockets, Vol. 33, No.2, pp. 285-291, 1996.
Meyers, C. A., and Hyer, C. A., “Thermal Buckling and Postbuckling of Symmetrically Laminated Composite Plates,” J. of Thermal Stresses, Vol. 14, pp. 519-540, 1991.
Moh, J. S., and Hwu, C., “Optimization for Buckling of Composite Sandwich Plates,” AIAA Journal, Vol. 35, No. 5, pp. 863-868, 1997.
Olson, M. D., " Finite Elements Applied to Panel Flutter," AIAA Journal, Vol. 5, No. 12, pp. 2267-2270, 1967.
Olson, M. D., " Some Flutter Solutions Using Finite Elements," AIAA Journal, Vol. 8, No. 4, pp. 747-752, 1970.
Plantema, F. J., Sandwich Construction, Wiley, New York, pp. 3-5, 1966.
Prasad, M. S. R., and Sarma, B. S., “Panel Flutter Analysis Using High Precision Shear Flexible Element,” J. of Sound and Vibration, Vol. 144, pp. 9-16, 1991.
Rossettos, J. N., and Tong, P., "Finite-Element Analysis of Vibration and Flutter of Cantilever Anisotropic Plates," Journal of Applied Mechanics, ASME, Vol. 41, No. 4, pp. 1075-1080, 1974.
Rao, K. M., “Buckling Analysis of Anisotropic Sandwich Plates Faced with Fiber-Reinforced Plastics,” AIAA Journal, Vol. 23, No. 8, pp. 1247-1253, 1985.
Rajagopal, S. V., Singh, G. and Rao, Y. V. K. S., “Large-Deflection and Nonlinear Vibration of Multilayered Sandwich Plates,” AIAA Journal, Vol. 25, No. 1, pp. 130-133, 1987.
Raju, K. K., and Rao, G. V., “Thermal Post-buckling of Thin Simply Supported Orthotropic Square Plates,” Composite Structures, Vol. 12, pp. 149-154, 1989.
Raju, K. K., and Rao, G. V., “Postbuckling of Point Supported Square Plates Resting on Elastic Foundation Subjected to Thermal or Mechanical Loading,” Computers & Structures, Vol. 40, No.4, pp. 1061-1064, 1991.
Rais-Rohani, M., and Marcellier, P., “Buckling and Vibration Analysis of Composite Sandwich Plates with Elastic Rotational Edge Restraints,” AIAA Journal, Vol. 37, No. 5, pp. 579-587, 1999.
Schaeffer, H. G., and Heard, W. L., Jr., “Flutter of a Flat Panel Subjected to a Nonlinear Temperature Distribution,” AIAA Journal, Vol. 3, No. 10, pp. 1918-1923, 1965.
Sander, G. D., Bon, C., and Geradin, M., " Finite Element Analysis of Supersonic Panel Flutter," Int. J. for Numerical Methods in Engineering, Vol. 7, pp. 379-394, 1973.
Sawyer, J. W., " Flutter and Buckling of General Laminated Plates," Journal of Aircraft, Vol. 14, No. 4, pp. 387-393, 1977.
Shiau, L. C., “Supersonic Flutter of Composite Sandwich Panels,” AIAA Journal, Vol. 30, No. 12, pp. 2987-2989, 1992.
Shiau, L. C., and Chang, J. T., “Transverse Shear Effect on Flutter of Composite Panels,” J. of Aerospace Engineering, ASCE, Vol. 5, pp. 465-479, 1992.
Shiau, L. C., and Lu, L. T., " Nonlinear Flutter of Two-Dimensional Simply Supported Symmetric Composite Laminated Plates," Journal of Aircraft, Vol. 29, No. 1, pp. 140-145, 1992.
Singh, G., Rao, G. V., and Iyengar, N. G. R., “Thermal Postbuckling Behavior of Laminated Composite Plates,” AIAA Journal, Vol. 32, No. 6, pp. 1336-1338, 1993.
Shiau, L. C., and Wu, T. Y., “Application of the Finite Element Method to Postbuckling Analysis of Laminated Plates,” AIAA Journal, Vol. 33, No. 12, pp. 2379-2385, 1995.
Shi, Y., and Mei, C., “Coexisting Thermal Postbuckling of Composite Plates with Initial Imperfections using Finite Element Modal Method,” AIAA/ASME/ASCE/AHS /ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 37th, Salt Lake City, UT, Apr. 15-17, 1996, Technical Papers. Pt. 3, Reston, VA, American Institute of Aeronautics and Astronautics, pp. 1355-1362, 1996.
Shiau, L. C., and Wu, T. Y., “Free Vibration of Buckled Laminated Plates by Finite Element Method,” Journal of Vibration and Acoustics, ASME, Vol. 119, pp. 635-640, 1997.
Shiau, L. C., and Wu, T. Y., “Nonlinear Flutter of Laminated Plates with In-plane Force and Transverse Shear Effects,” Mechanics of Structures and Machines, Vol. 29, pp. 121-142, 2001.
Tang, S., “Natural Vibration of Isotropic Plates with Temperature-Dependent Properties,” AIAA Journal, Vol. 7, No. 4, pp. 725-727, 1969.
Tomar J. S., and Gupta, A. K., “Thermal Effect on Frequencies of an Orthotropic Rectangular Plate of Linear Varying Thickness,” J. of Sound and Vibration, Vol. 90, No. 3, pp. 325-331, 1983.
Tauchert, T. R., “Thermal Buckling of Thick Antisymmetric Angle-Ply Laminates,” J. of Thermal Stresses, Vol. 10, pp. 113-1124, 1987.
Thangaratnam, K. R., and Ramachandran, J., “Thermal Buckling of Composite Laminated Plates,” Computers & Structures, Vol. 32, No.5, pp.1117-1124, 1989.
Tenneti, R., and Chandrashekhara, K., “Nonlinear Thermal Dynamic Analysis of Graphite/Aluminum Composite Plates,” AIAA Journal, Vol. 32, No. 9, pp. 1931-1933, 1994.
Voss, H. M., and Dowell, E. H., “Effect of Aerodynamic Damping on Flutter of Thin Panels,” AIAA Journal, Vol. 2, No. 1, pp. 119-120, 1964.
Whitney, J. M., and Ashton, J. E., “Effect of Environment on the Elastic Response of layered Composite Plate,” AIAA Journal, Vol. 9, No. 9, pp. 1708-1713, 1971.
Xue, D. Y., and Mei, C., “Finite Element Nonlinear Flutter and Fatigue Life of Two-Dimensional Panels with Temperature Effects,” J. of Aircraft, Vol. 30, No. 6, pp. 993-1000, 1993.
Xue, D. Y., and Mei, C., “Finite Element Nonlinear Panel Flutter with Arbitrary Temperatures in Supersonic Flow,” AIAA Journal, Vol. 31, No. 1, pp. 154-162, 1993.
Yang, T. Y., and Han, A. D., “Flutter of Thermally Buckled Finite Element Panels,” AIAA Journal, Vol. 14, No. 7, pp. 975-977, 1976.
Yang, T. Y., and Han, A. D., “Buckled Plate Vibration and Large Amplitude Vibrations Using High-Order Triangular Elements,” AIAA Journal, Vol. 21, No. 5, pp. 758-766, 1983.
Yang, T. Y., Finite Element Structural Analysis, Prentice-Hall, pp. 450-455, 1986.
Zhou, R. C., Xue, D. T., Mei, C., and Gray, C. C., “Vibration of Thermally Buckled Composite Plates with Initial Deflections Using Triangular Elements,” AIAA paper 93-1321, 1993.
Zhou, R. C., Xue, D. Y., and Mei, C., “Finite Element Time Domain-Modal Formulation for Nonlinear Flutter of Composite Panels,” AIAA Journal, Vol. 32, No. 10, pp. 2044-2052, 1994.
Zhou, R. C., Mei, C., and Huang, J. K., “Suppression of Nonlinear Panel Flutter at Supersonic Speeds and Elevated Temperatures,” AIAA Journal, Vol. 34, No. 2, pp. 347-354, 1996.