Abstract
The dynamic analysis of composite shell structures is carried out by an explicit finite element code employing 4-node one-point quadrature elements. The anisotropic Hoffman yield criterion is adopted to model the laminates. The formulation for stress update using a backward Euler scheme is presented in the plane stress subspace. Several numerical examples are presented. The issue of implementing single-iteration schemes for stress update is also investigated.
Similar content being viewed by others
References
Aravas, N. 1987: On the numerical integration of a class of pressure-dependent plasticity models. Int. J. Num. Meth. Engng. 25: 1395–1416
Argyris, J.; Tenek, L. 1994: Linear and geometrically nonlinear bending of isotropic and multilayered composite plates by the natural mode method. Comp. Meth. Appl. Engng. 113: 207–251
Belytschko, T.; Lin, J. L.; Tsay, C.-S. 1984: Explicit algorithms for the nonlinear dynamics of shells. Comp. Meth. Appl. Mech. Engng. 42: 225–251
Belytschko, T.; Plaskacz, E. J. 1992a: SIMD implementation of a non-linear transient shell program with partially structured meshes. Int. J. Num. Meth. Engng. 33: 997–1026
Belytschko, T.; Wong, B. L.; Chiang, H.-Y. 1992b: Advances in one-point quadrature shell elements. Comp. Meth. Appl. Mech. Engng. 96: 93–107
Belytschko, T.; Leviathan, I. 1994: Physical stabilization of the 4-node shell element with one point quadrature. Comp. Meth. Appl. Mech. Engng. 113: 321–350
Burgoyne, C. J.; Crisfield, M. A. 1990: Numerical integration strategy for plates and shells. Int. J. Num. Meth. Engng. 29: 105–121
Hill, R. 1950: The mathematical theory of plasticity. Oxford: Clarendon Press
Hoffman, O. 1967: The brittle strength of orthotropic materials. J. Composite Mater. 1: 200–206
Hughes, T. J. R.; Taylor, R. L.; Kanoknukulchai, W. 1977: A simple and efficient finite element for plate bending. Int. J. Num. Meth. Engng. 11: 1529–1547
Hughes, T. J. R.; Cohen, M.; Haroun, M. 1978: Reduced and selective integration techniques in finite element analysis of plates. Nucl. Engng. Design. 46: 203–222
Iu, V. P.; Cheung, Y. K. 1986: Non-linear vibration analysis of multilayer sandwich plates by incremental finite elements: 1. Theoretical development. Engng. Comput. 3: 36–42
Kapania, R. K. 1988: Analysis of laminated shells, In: Hui, D.; Vinson, J. R. (eds.). Recent Advances in the macro-and micro-mechanics of composite materials structures. 177–187, AD-Vol. 13, ASME
Lee, J. H.; Zhang, Y. 1991: On the numerical integration of a class of pressure-dependent plasticity models with mixed hardening. Int. J. Num. Meth. Engng. 32: 419–438
Li, Z. H. 1988: A refined finite element analysis of anisotropic laminated plates and shells, Ph. D. Thesis, Swansea: University College of Swansea
Liu, G. Q. 1985: Nonlinear and transient finite element analysis of general reinforced concrete plates and shells. Ph. D. Thesis, Swansea: University College of Swansea
Noor, A. K.; Burton, W. S. 1990: Three-dimensional solutions for antisymmetrically laminated anisotropic plates. J. Appl. Mech. 57: 182–188
Owen, D. R. J.; Li, Z. H. 1989: A refined analysis of laminated plates by finite element displacement methods-I. Fundamentals and static analysis. Comput. Struct. 26: 907–914
Owen, D. R. J.; Li, Z. H. 1989: Elastic-plastic dynamic analysis of anisotropic laminated plates. Comp. Meth. Appl. Mech. Engng. 70: 349–365
Owen, D. R. J.; Liu, G. Q. 1985: Elasto-viscoplastic analysis of anisotropic laminated plates and shells. In: Middleton, J.; Pande, G. N. (eds.): Proc. Num. Meth. in Engng. Theory and Appl.-NUMETA 85, Vol. 2. 577–586, Rotterdam: Balkema
Owen, D. R. J.; Liu, G. Q. 1986: Ultimate load behaviour of reinforced concrete plates and shells under dynamic transient loading. Int. J. Num. Meth. Engng. 22: 189–208
Perić, D. 1993: On a class of constitutive equations in viscoplasticity: Formulation and computational issues. Int. J. Num. Meth. Engng. 36: 1365–1393
Reddy, J. N.; Phan, N. D. 1985: Stability and vibration of isotropic and laminated plates according to a higher-order shear deformation theory. J. Sound Vibr. 98: 157–170
Sacco, E.; Reddy, J. N. 1992: On first-and second-order moderate rotation theories of laminated plates. Int. J. Num. Meth. Engng. 33: 1–17
Savoia, M.; Reddy, J. N. 1992: A variational approach to three-dimensional elsticity solutions of laminated composite plates. ASME, J. Appl. Mech. 59: S166-S175
Schellekens, J. C. 1992: Computational strategies for composite structures. PhD Thesis. Delft: Delft University of Technology
Schoenfeld, S.; Benson, D. 1993: Quickly convergent integration methods for plane stress plasticity, Comm. Num. Meth. Engng. 9: 293–305
Simo, J. C.; Taylor, R. L. 1986: A return mapping algorithm for plane stress elastoplasticity. Int. J. Num. Meth. Engng. 22: 649–670
Tessler, A.; Saether, E. 1991: A computationally viable higher-order theory for laminated composite plates. Int. J. Num. Meth. Engng. 31: 1069–1086
Tsai, S. W.; Wu, E. M. 1971: A general theory of strength for anisotropic materials. J. Comp. Mater. 5: 58–80
Tsui, T. Y.; Tong, P. 1971: Stability of transient solution of moderately thick plate by finite difference method. AIAA J. 9: 2062–2063
Author information
Authors and Affiliations
Additional information
Communicated by S. N. Atluri, 4 April 1995
Rights and permissions
About this article
Cite this article
Koh, C.G., Owen, D.R.J. & Perić, D. Explicit dynamic analysis of elasto-plastic laminated composite shells: implementation of non-iterative stress update schemes for the HOFFMAN yield criterion. Computational Mechanics 16, 307–314 (1995). https://doi.org/10.1007/BF00350720
Issue Date:
DOI: https://doi.org/10.1007/BF00350720