Abstract
The development of a shear-deformable laminated plate element, based on the Mindlin plate theory, for use in large reference displacement analysis is presented. The element is sufficiently general to accept an arbitrary number of layers and an arbitrary number of orthotrophic material property sets. Coordinate mapping is utilized so that non-rectangular elements may be modeled. The Gauss quadrature method of numerical integration is utilized to evaluate volume integrals. A comparative study is done on the use of full Gauss quadrature, reduced Gauss quadrature, mixed Gauss quadrature, and closed form integration techniques for the element. Dynamic analysis is performed on the RSSR (Revolute-Spherical-Spherical-Revolute) mechanism, with the coupler modeled as a flexible plate. The results indicate the differences in the dynamic response of the transverse shear deformable eight-noded element as compared to a four-noded plate element. Dynamically induced stresses are examined, with the results indicating that the primary deformation mode of the eight-noded Mindlin plate model being bending.
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References
Bhumbla, R., Kostmatka, J. B., and Reddy, J. N., ‘Free vibration behavior of spinning shear-deformables plates composed of composite materials’, AIAA Journal 28, 1990, 1962–1970.
Chandrashekhara, K., ‘Free vibrations of anisotropic laminated doubly curved shells’, Computers & Structures 33, 1989, 435–440.
Chang, B. and Shabana, A. A., ‘Total Lagrangian formulation for the large displacement analysis of rectangular plates’, International Journal for Numerical Methods in Engineering 29, 1990, 73–103.
Cook, R. D., Concepts and Applications of Finite Element Analysis, John Wiley & Sons, New York, NY, 1981.
Jones, R. M., Mechanics of Composite Materials, McGraw-Hill, New York, NY, 1975.
Kant, T. and Mallikarjuna, ‘Vibrations of unsymmetrically laminated plates analyzed by using a higher order theory with C 0 finite element formulation’, Journal of Sound and Vibration 134, 1989, 1–16.
Khulief, Y. A. and Shabana, A. A., ‘Impact responses of multi-body systems with consistent and lumped masses’, Journal of Sound and Vibration 104, 1986, 187–207.
Kremer, J. M., ‘Large reference displacement analysis of composite plates’, Ph.D. Dissertation, University of Illinois at Chicago, Department of Mechanical Engineering, Chicago, IL, 1991.
Kremer, J. M., Shabana, A. A., and Widera, G. E. O., ‘Large reference displacement analysis of composite plates part I: finite element formulation’, International Journal for Numerical Methods in Engineering 36(1), 1993, 1–16.
Kremer, J. M., Shabana, A. A., and Widera, G. E. O., ‘Large reference displacement analysis of composite plates part II: computer implementation’, International Journal for Numerical Methods in Engineering 36(1), 1993, 17–42.
Lowen, G. G. and Chassapis, C., ‘The elastic behavior of linkages: an update’, Mechanism and Machine Theory 21, 1986, 33–42.
Lowen, G. G. and Jandrasits, W. G., ‘Survey of investigations into the dynamic behavior of mechanisms containing links with distributed mass and elasticity’, Mechanism and Machine Theory 7, 1972, 13–17.
Panda, S. C. and Natarajan, R., ‘Finite element analysis of laminated composite plates’, International Journal for Numerical Methods in Engineering 14, 1979, 69–79.
Pillasch, D. W., Majerus, J. N., and Zak, A. R., ‘Dynamic finite element model for laminated structures’, Computers & Structures 16, 1983, 449–455.
Reddy, J. N., Energy and Variational Methods in Applied Mechanics, John Wiley & Sons, New York, NY, 1984.
Sanders, J. L., ‘An improved first-approximation theory for thin shells’, NASA Technical Report R-24, 1959.
Schwartz, M. M., Composite Materials Handbook, McGraw-Hill, New York, NY, 1984.
Shabana, A. A., Dynamics of Multibody Systems, John Wiley & Sons, New York, NY, 1989.
Timoshenko, S. and Goodier, J., Theory of Elasticity, McGraw-Hill, New York, NY, 1970.
Widera, G. E. O. and Moumene, M., ‘Cutouts in laminated plates and shells’, Advances in Macro-Mechanics of Composite Material Vessels and Components PVP-146, Pd-18, 1988, 155–158.
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Kremer, J.M., Shabana, A.A. & Widera, G.E.O. An eight noded composite plate element for the dynamic analysis of spatial mechanism systems. Nonlinear Dyn 5, 459–476 (1994). https://doi.org/10.1007/BF00052454
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DOI: https://doi.org/10.1007/BF00052454