Theoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers
محورهای موضوعی : EngineeringJ.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
کلید واژه: Bending, Functionally graded material, Timoshenko Beam Theory, Piezoelectricity, Bernoulli–Euler beam theory, PZT,
چکیده مقاله :
In this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed using the principle of virtual displacements. The formulation is based on a power-law variation of the material in the core with piezoelectric layers at the top and bottom. Virtual work statements of the two theories are also developed and their finite element models are presented. The theoretical formulations and finite element models presented herein can be used in the analysis of piezolaminated and adaptive structures such as beams and plates.
[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.