Abstract
In this paper, an analytic method is presented for the research of nonlinear three-dimensional problems of composite laminated plates. The perturbation method and the variational principle are used to satisfy the basic differential equations and the boundary conditions of the three-dimensional theory of elasticity. The nonlinear three-dimensional problems are studied for composite anisotropic circular laminas and laminates subjected to transverse loading. The perturbation series solutions of high accuracy are obtained. A large number of results show that transverse normal stress and transverse shear stresses are very important in the nonlinear three-dimensional analysis of laminated plates.
Similar content being viewed by others
References
C. I. Wu and J. R. Vinson, Influence of large amplitude transverse shear deformation and rotatory inertia on lateral vibrations of transversely isotropic plates, ASME J. Appl. Mech., 36 (1969), 254–260.
C. I. Wu and J. R. Vinson, On the nonlinear oscillations of plates composed of composite materials, J. Composite Materials, 3 (1969), 548–561.
C. I. Wu and J. R. Vinson, Nonlinear oscillations of laminated specially orthotropic plates with clamped and simply supported edges, J. Acoust. Soc. Am, 49 (1971), 1561–1567.
M. Sathyamoorthy, Shear and rotatory inertia effects on large amplitude vibration of skew plates, J. Sound Vib., 52 (1977), 155–163.
M. Sathyamoorthy, Vibration of plates considering shear and rotatory inertia, AIAA J., 16 (1978), 285–286.
M. Sathyamoorthy, Shear and rotatory inertia effects on the large amplitude vibration of plates, J. Eng. Mech. Div., Proc. ASCE, 104, 5 (1978), 1288–1293.
M. Sathyamoorthy, Shear effects on vibration of plates, J. Sound Vib., 60 (1978), 308–311.
K. N Ahmed and W. S. Burton, Three-dimensional solutions for antisymmetrically laminated anisotropic plates, ASME J. Appl. Mech., 57 (1990), 182–188.
N. J. Pagano and S. J. Hatfield, Elastic behavior of multilayered bidirectional composites, AIAA J., 10 (1970), 931–933.
Chia Chuenyuan, Nonlinear Analysis of Plates, McGraw-Hill Inc., New York (1980).
A. H. Nayfen, Introduction to Perturbation Techniques, John Wiley and Sons., (1981).
C. W. Lee, Three-dimensional solution for simply-supported thick retangular plates, Nuclear Engineering and Design, 6 (1967), 155–162.
Z. L. Xue, Mechanics of Elasticity, Higher Education Publisher, Beijing (1987). (in Chinese)
Jiang Xiaoyu, The three-dimensional linear and nonlinear, static and dynamic analysis of composite laminated plates and shells, Doctor's Degree Thesis of Northwestern Polytechnical University, Xi'an (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Xiaoyu, J., Xiangzhou, Z. Nonlinear three-dimensional analysis of composite laminated plates. Appl Math Mech 17, 621–632 (1996). https://doi.org/10.1007/BF00123106
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00123106