Theoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers

Subject Areas : Engineering

J.N Reddy ¹ , S Doshi ² , A Muliana ³

1 - Department of Mechanical Engineering, Texas A&M University, College Station
2 - Department of Civil Engineering, Texas A&M University, College Station
3 - Department of Mechanical Engineering, Texas A&M University, College Station

Received: 2011-10-25 Accepted : 2011-11-30 Published : 2011-12-30

Keywords:

References:

[1] Hasselman D.P.H., Youngblood G.E., 1978, Enhanced Thermal Stress Resistance of Structural Ceramics with Thermal Conductivity Gradient, Journal of the American Ceramic Society 61(1, 2): 49-53.

[2] Yamanouchi M., Koizumi M., Hirai T., Shiota I., (Editors), 1990, Proceedings of the First International Symposium on Functionally Gradient Materials, Japan.

[3] Koizumi M., 1993, The Concept of FGM, Ceramic Transactions, Functionally Gradient Materials 34: 3-10.

[4] Noda N., 1991, Thermal stresses in materials with temperature-dependent properties, Applied Mechanics Reviews 44: 383-397.

[5] Zhang Q.J., Zhang L.M., Yuan R.Z., 1993, A coupled thermoelasticity model of functionally gradient materials under sudden high surface heating, Ceramic Transactions, Functionally Gradient Materials 34: 99-106.

[6] Tanigawa Y., 1995, Some basic thermoplastic problems for nonhomogeneous structural material, Journal Applied Mechanics 48: 377–389.

[7] Sankar B.V., T Tzeng J., 2002, Thermal stresses in functionally graded beams, AIAA Journal 40: 1228-1232.

[8] Praveen G.N., Reddy J.N., 1998, Nonlinear Transient Thermoelastic Analysis of Functionally Graded Ceramic-Metal Plates, Journal of Solids and Structures 35(33):4457-4476.

[9] Praveen G.N., Chin C.D., Reddy J.N., 1999, Thermoelastic Analysis of Functionally Graded Ceramic-Metal Cylinder, ASCE Journal Engineering Mechanics 125(11): 1259-1266.

[10] Reddy J.N., 2000, Analysis of Functionally Graded Plates, International Journal for Numerical Methods in Engineering 47: 663–684.

[11] Shen H.-S., 2009, Functionally Graded Materials. Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton, FL.

[12] Bonet J., Wood R.D., 2008, Nonlinear Continuum Mechanics for Finite Element Analysis, 2nd ed., Cambridge University Press, Cambridge, UK .

[13] Reddy J. N., 2008, An Introduction to Continuum Mechanics with Applications, Cambridge University Press, New York.

[14] Gurtin M.E., Fried E., Anand L., 2010, The Mechanics and Thermodynamics of Continua, Cambridge University Press, New York.

[15] Tiersten H.F., 1969, Linear Piezoelectric Plate Vibrations, Plenum, New York.

[16] Penfield P., Jr., Hermann A.H., 1967, Electrodynamics of Moving Media, Research Monograph No. 40, The M.I.T. Press, Cambridge, MA.

[17] Ballas R.G., 2007, Piezoelectric Multilayer Beam Bending Actuators, Springer, Berlin.

[18] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd ed., CRC Press, Boca Raton, Florida .

[19] Reddy J.N., Gartling D. K., 2008, The Finite Element Method in Heat Transfer and Fluid Dynamics, 3rd ed., CRC Press, Boca Raton, FL.

[20] Reddy J.N., 2002, Energy Principles and Variational Methods in Applied Mechanics, 2nd ed., John Wiley & Sons, New York.

[21] Reddy J.N., 2006, An Introduction to the Finite Element Method, 3rd ed., McGraw–Hill, New York.