hp-Spectral Finite Element Analysis of Shear Deformable Beams and Plates

Subject Areas : Engineering

R Ranjan ¹ , J.N Reddy ²

1 - Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station
2 - Advanced Computational Mechanics Laboratory, Department of Mechanical Engineering, Texas A&M University, College Station

Received: 2009-11-25 Accepted : 2009-11-30 Published : 2009-09-30

Keywords:

References:

 [1] Reddy J.N., 2004, Mechanics of Laminated Composite Plates and Shells, CRC Press, Boca Raton, FL, Second Edition.

[2] Reddy J.N., 2007, Theory and Analysis of Elastic Plates and Shells, CRC Press, Boca Raton, FL, Second Edition.

[3] Reddy J.N., 2004, An Introduction to Non-Linear Finite Element Analysis, Oxford University Press, Oxford, UK.

[4] Donning B.M., Liu W.K., 1998, Meshless methods for shear-deformable beams and plates, Computer Methods in Applied Mechanical Engineering 152: 47-71.

[5] Maenghyo C., Parmerter R., 1994, Finite Element for composite bending based on efficient higher order theory, AIAA Journal 32: 2241-2248.

[6] Pontaza J.P., Reddy J.N., 2004, Mixed plate bending elements based on least squares formulations, International Journal for Numerical Methods in Engineering 60: 891-922.

[7] Urathaler Y., Reddy J.N., 2008, A mixed finite element for nonlinear bending analysis of laminated composite plates based on FSDT, Mechanics of Advanced Materials and Structures 15: 335-354.

[8] Archiniega R.A., Reddy J.N., 2007, Large deformation analysis of functionally graded shells, International Journal for Solids and Structures 44: 2036-2052.

[9] Karniadakis G.K., Sherwin S., 2004, Spectral/hp element methods for computational fluid dynamics, Oxford Science Publications, London, Second Edition.

[10] Melenk J.M., 2002, On condition numbers in hp-fem with Gauss-Lobatto-based shape functions, Journal of Computational and Applied Mathematics 139: 21-48.

[11] Maitre J.F., Pourquier O., 1996, Condition number and diagonal preconditioning: comparison of the p-version and the spectral element methods, Numerical Methods 74: 69-84.

[12] Reddy J.N., 1997, On Locking-free shear deformable beam finite elements, Computer Methods in Applied Mechanics and Engineering 149: 113-132.

[13] Reddy J.N., Wang, C.M., Lam, K.Y., 1997, Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates, Communications in Numerical Methods in Engineering 13: 495-510.

[14] Reddy J.N., 2006, An Introduction to the Finite Element Method, McGraw-Hill, New York, Third Edition.

[15] Prabhakar V., Reddy, J.N., 2007, Orthogonality of modal basis in hp finite element models, International Journal for Numerical Methods in Fluids 54: 1291-1312.

[16] Osilenker B., 1999, Fourier Series in Orthogonal Polynomials, World Scientific, Singapore, Second Edition.

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