New Formula for Geometric Stiffness Matrix Calculation

Show more

References

[1] Bathe, K.-J. (1996) Finite Element Procedures. Prentice Hall, Upper Saddle River.

[2] Belytschko, T., Liu, W.K., Moran, B. and Elkhodary, K. (2000) Nonlinear Finite Elements for Continua and Structures. John Wiley & Sons, Hoboken.

[3] Bonet, J. and Wood, R.D. (2008) Nonlinear Continuum Mechanics for Finite Element Analysis. Cambridge University Press, Cambridge.

[4] Cook, R.D., Malkus, D.S., Plesha, M.E. and Witt, R.J. (2002) Concepts and Applications of Finite Element Analysis. John Wiley & Sons, Hoboken.

[5] Němec I., et al. (2010) Finite Element Analysis of Structures: Principles and Praxis. Shaker-Verlag, Aachen.

[6] Reddy, J.N. (2004) Nonlinear Finite Element Analysis. Oxford University Press, Oxford.

[7] Zienkiewicz, O.C. and Taylor, R.L. (2000) The Finite Element Method. Butterworth Heinemann, Oxford.

[8] de Souza Neto, E.A., Periæ, D. and Owen, D.R.J. (2008) Computational Methods for Plasticity: Theory and Applications. John Wiley & Sons, Hoboken.

[9] Simo, J.C. & Hughes, T.J.R. (2008) ComputationalInelasticity. Springer, New York, 392 p.

[10] Wriggers, P. (2008) Nonlinear Finite Element Methods. Springer-Verlag, New York.

[11] Lacarbonara, W. and Pacitti, A. (2008) Nonlinear Modeling of Cables with Flexural Stiffness. Mathematical Problems in Engineering, 2008, Article ID: 370767.

http://dx.doi.org/10.1155/2008/370767

[12] Xiao, H. and Chen, L.S. (2002) Hencky’s Elasticity Model and Linear Stress-Strain Relations in Isotropic Finite Hyperelasticity. Acta Mechanica, 157, 51-60.

http://dx.doi.org/10.1007/BF01182154

[13] Xiao, H., Bruhns, O.T. and Meyers, A. (1998) Objective Corotational Rates and Unified Work-Conjugacy Relation between Eulerian and Lagrangean Strain and Stress Measures. Archives of Mechanics, 50, 1015-1045.

[14] Meyers, A. (1999) On the Consistency of Some Eulerian Strain Rates. Zeitschrift fur Angewandte Mathematik und Mechanik, 79, 171-177.

http://dx.doi.org/10.1002/(SICI)1521-4001(199903)79:3<171::AID-ZAMM171>3.0.CO;2-6

[15] Simo, J.C. and Pister, K.S. (1984) Remarks on Rate Constitutive Equations for Finite Deformation Problem: Computational Implications. Computer Methods in Applied Mechanics and Engineering, 46, 201-215.

http://dx.doi.org/10.1016/0045-7825(84)90062-8

[16] Curnier, A. and Rakotomanana, L. (1991) Generalized Strain and Stress Measures: Critical Survey and New Results. Engineering Transactions, 39, 461-538.

[17] Chiskis, A. and Parnes, R. (2000) Linear Stress-Strain Relations in Nonlinear Elasticity. Acta Mechanica, 146, 109-113.

http://dx.doi.org/10.1007/BF01178798

[18] Farahani, K. and Naghdabadi, R. (2000) Conjugate Stresses of the Seth-Hill Strain Tensors. International Journal of Solids and Structures, 37, 5247-5255.

http://dx.doi.org/10.1016/S0020-7683(99)00209-7

[19] Darijani, H. and Naghdabadi, R. (2010) Constitutive Modeling of Solids at Finitede Formation Using a Second-Order Stress-Strain Relation. International Journal of Engineering Science, 48, 223-236.

http://dx.doi.org/10.1016/j.ijengsci.2009.08.006

[20] Hill, R. (1978) Aspects of Invariance in Solid Mechanics. Advances in Applied Mechanics, 18, 1-75.

http://dx.doi.org/10.1016/S0065-2156(08)70264-3

[21] Farahani, K. and Bahai, H. (2004) Hyper-Elastic Constitutive Equations of Conjugate Stresses and Strain Tensors for the Seth-Hill Strain Measures. International Journal of Engineering Science, 42, 29-41.

http://dx.doi.org/10.1016/S0020-7225(03)00241-6