Thermal Buckling Analysis of Laminated Composite Plate

Thermal Buckling Analysis of Laminated Composite Plate

Kandi. Ashok

P. G. student, Aerospace Engineering

MLR Institute of Technology Hyderabad, India

Dr. S. Srinivas Prasad Professor & Head, Department of Aeronautical Engineering

MLR Institute of Technology Hyderabad, India

Srikanth Sikhakolli Post Graduate, Aerospace Engineering

MLR Institute of Technology Hyderabad, India

Abstract Aerospace in one such field where the structural components undergo through various combinations of loads always. So coupled field analysis in this field of application has become quite compulsory. One such kind of analysis is thermal buckling analysis. Thermal buckling analysis of laminated smart composite plates subjected to uniform temperature distribution has been presented in this paper. Shape memory alloy (SMA) fibers whose material properties depend on temperature is used as smart material. Finite Element Analysis (FEA) tool ANSYS

1. was used to observe the effects of thickness ratio, fiber orientation on the critical buckling temperature.

   Keywords Shape Memory Alloys, Thermal buckling, FEA, thickness ratio, fiber orientation

   1. INTRODUCTION

      A structure or a material is defined smart if they are able to perceive external stimulus and to act on that a real time active control. Recently the development of new Aeronautical Structures and the implementation of innovative materials have been mandatory for succeeding in critical tasks in terms of weight, fuel consumption, aerodynamic efficiency, cost reduction and so on. [1]

      The SMAs are a class of materials that exhibit a martensitic transformation when cooled from the higher- temperature austenite state. The interaction of temperature and applied stress in driving the martensitic and reverse transformations can be used to exploit the phenomena such as the shape memory effect SME and pseudo-elasticity. The two main types of shape-memory alloys are the copper- aluminum-nickel, and nickel-titanium and (NiTi) alloys but SMAs can also be created by alloying zinc, copper, gold and iron. NiTi alloys are generally more expensive and change from austenite to martensite upon cooling [2].

      In the last years aeronautic civil sector has signed a considerable economic growth due to an increase of 6% every year [6]. So that many companies like Boeing and Airbus have the intent to develop new aircraft concept and design for the development of cargo and passenger transport for the next 25 years [3].

      Figure 1. Transition of nitinol (SMA) from the marten site phase to the austenite phase

      Boeing, General Electric Aircraft Engines, Goodrich Corporation, NASA, and All Nippon Airways developed the Variable Geometry Chevron using shape-memory alloy that reduces aircraft's engine noise.

   2. CRITICAL BUCKLING TEMPERATURE CALCULATIONS

      The buckling behavior due to the uniform temperature is calculated non-dimensionally using the formula

      Laminate	Critical buckling temperature
      Without SMA	1.12
      With SMA	1.96

      Table 1. Hand calculation values of critical buckling temperature

      Where,

      T Change in temperature

      Coefficient of thermal expansion

      Critical buckling temperature parameter

   3. METHODOLOGY

      A 2-D SMA fiber- reinforced composite plates using layer- wise model is to be developed. The composite plates are subjected to uniform temperature; an incremental load technique is used for the analysis. The buckling temperature results of the laminated plates with SMA and without SMA fibers are compared for the cases kept in table 2.

      Varying thickness ratio (a/h)	Fiber orientation
      20	-10/0/10
      40	-45/0/45
      60	-90/0/90
      80
      100

      Table 2. various cases considered for the analysis

   4. FINITE ELEMENT MODELLING AND ANALYSIS

      1. Modeling

         a = 0.5 m

         1

         ELEMENTS

         TYPE NUM SEP 12 2014

         01:34:04

         Y

         Z X

         b = 0.8 m

         Elastic Modulus	E11 = 1.55 GPa	E22 = 8.07 GPa	E33 = 8.07 GPa
         Poissons ratio	12 = 0.22	23 = 0.348	31 = 0.22
         Modulus of Rigidity	G12 = 4.55 GPa	G23 = 3.25 GPa	G31 = 4.555 GPa
         Coe. of thermal expansion	x=-1017e-6	y=30e-6	z=30e-6
         Density	1.59e-3
         Thermal conductivity	8.3075
         Specific heat	1.3

      2. Analysis

      Figure 3. Meshed layer-wise model

      Table 3. Properties of graphite epoxy

      Elastic Modulus	83 GPa
      Poissons ratio	0.33
      Coe. Of thermal expansion	11e-6
      Density	6.45e3
      Thermal conductivity	18
      Specific heat	200

      Table 4.. Properties of Nitinol

      Figure 2. layer-wise model

      Length along X-axis is denoted as a Length along y-axis is denoted as b Thickness along z-axis as h

      The thermal and static analysis is done on the composite plate by applying material properties. The thermal analysis is done by applying temperature of 274 k on the surface of the plate.

      ELEMENTS

      U NFOR NMOM RFOR

      TEMPERATURES TMIN=274 TMAX=274

      SEP 12 2014

      01:31:42

      Y

      Z X

      1

      Figure-4: Applied Boundary Conditions

   5. RESULTS AND DISCUSSION

      The below figures shows the results of the nodal solution for the deformed + Un-deformed shape, displacement vector sum and von-mises stress.

      1

      DISPLACEMENT

      STEP=1 SUB =1

      FACT=16.3554 DMX =.432E-07

      OCT 11 2014

      19:58:06

      Y

      Z X

      1

      Figure 5. Deformed + Undeformed shape for a/h = 60 (without SMA)

      DISPLACEMENT

      STEP=1 SUB =1

      FACT=16.3554 DMX =.663E-08

      SEP 12 2014

      15:30:39

      Y

      Z X

      Figure 6. Deformed + Undeformed shape for a/h = 60 (with SMA)

      1

      NODAL SOLUTION

      STEP=1 SUB =1

      FACT=16.3554 USUM (AVG) RSYS=0

      DMX =.432E-07 SMX =.432E-07

      Y MX

      ZMN X

      OCT 11 2014

      0.707e-18

      Thickness ratio a/h	Orientation [-10/0/10]	Orientation [-45/0/45]	Orientation [-90/0/90]
      20	0.912e-08	0.198e-08	0.708e-18
      40	0.486e-08	0.101e-08	0.708e-18
      60	0.318e-08	0.663e-08	0.708e-18
      80	0.245e-08	0.503e-08	0.708e-18
      100	0.195e-08	0.403e-08

      20:01:19

      0 .961E-08 .192E-07 .288E-07 .384E-07

      .480E-08 .144E-07 .240E-07 .336E-07 .432E-07

      Figure 7. Displacement vector shape for a/h= 60(with out SMA)

      1

      NODAL SOLUTION

      STEP=1 SUB =1

      FACT=16.3554 USUM (AVG) RSYS=0

      DMX =.663E-08 SMX =.663E-08

      OCT 11 2014

      19:47:56

      Y MX

      MZN X

      0

      .737E-09 .221E-08 .369E-08 .516E-08 .663E-08

      .590E-08

      .442E-08

      .295E-08

      .147E-08

      Figure 8. Displacement vector shape for a/h= 60(with SMA)

      Table 6. Comparison of deformation results for different thickness ratios and orientation for with SMA

      From the results we can understand that the 90/0/90 orientation is not at all suitable in concern of stiffness criterion in both the cases of using SMA and without using SMA. While coming to other cases, the -45/0/45 lay-up case is showing considerable stiffness when compared to -10/0-10 lay-up case. And when compared to with and without SMA usage, the plate with SMA has shown considerable less deformation.

      As per the strength criterion, the stresses result that we got will again depend on the material properties that we are using. But from the results we got we can say that the material is safe in both the conditions.

      1

      NODAL SOLUTION STEP=1

      OCT 11 2014

   6. CONCLUSION

      SUB =1

      FACT=16.3554 SEQV (AVG) DMX =.432E-07 SMN =87026.8

      SMX =342820

      87026.8

      115448

      Y

      MX

      ZMN X

      143870

      172291

      200712

      229134

      257555

      285977

      314398

      20:13:00

      342820

      The displacement at the each point along the different thickness and lamina orientations are found out and the results are compared with the composite laminates alone and the laminates with SMA fibers. With the incorporation of the SMA fibers into the composite laminate, the thermal buckling temperature has been enhanced and hence SMA composites can withstand higher temperatures and can be

      used in the environments where the structures are exposed

      Figure 9. von- misses stress for a/h = 60(without SMA)

      1

      NODAL SOLUTION

      STEP=1 SUB =1

      FACT=16.3554 SEQV (AVG) DMX =.663E-08 SMN =184209

      SMX =313999

      OCT 11 2014

      19:51:12

      MX

      MZN X

      184209

      198630 227472 256315 285157 313999

      299578

      270736

      241893

      213051

      Y

      Figure 10. von- misses stress for a/h = 60(with SMA)

      Thickness ratio a/h	Orientation [-10/0/10]	Orientation [-45/0/45]	Orientation [-90/0/90]
      20	0.506e-07	0.200e0-7	0.105e-17
      40	0.289e-07	0.108e-07	0.105e-17
      60	0.182e-07	0.0752e-07	0.105e-17
      80	0.132e-07	0.0568e-07	0.105e-17
      100	0.102e-07	0.0450e-07	0.105e-17

      Table 5. Comparison of deformation results for different thickness ratios and orientation for with out SMA

      to high temperatures.

   7. REFERENCES

1. Pecora R., Analisi della lamina ortotropa e teoria classica dei laminati, Italy (2006) 2-10

2. Davidson, B.D., Hu, H., and Schapery, R.A., An Analytical Crack Tip Element for Layered Elastic Structures, Journal of Applied Mechanics, (1995) 294-305.

3. M. Granito, A cooling system for S.M.A. (shape memory alloy) based on the use of peltier cells, Philosophy thesis, University of Naples Federico II ITALY.

4. A.L. Martins and F.M. Catalano, Viscous Drag Optimization for a Transport Aircraft Mission Adaptive Wing, 21st ICAS Congress, Melbourne, Australia Paper A98-31499 (1998).