Quasi-3D analysis of free vibration of anisotropic plates

The subject of the present work is multilayered finite elements that are able to furnish an accurate description of both strain and stress fields. The formulation of the finite elements is based upon Reissners mixed variational theorem (RMVT), which allows one to assume two independent fields for displacements and transverse stress variables. The resulting advanced finite elements can describe, a priori, the interlaminar continuous transverse shear and normal stress fields, and the so called C 0 -requirements can be satisfied. This paper is mainly concerned about the vibrations of multilayered plates. The present FEM formulation is validated by comparing the results with both the literature and the commercial code NASTRAN. To conduct the assessment, five challenging benchmarks with different boundary conditions and lamination schemes are considered. For each benchmark, the first four nondimensional frequencies are calculated and a few modes are presented. It can be concluded that the present quasi-3D layer-wise formulation has a very good agreement with respect to the more computationally expensive three-dimensional FEM formulations. Moreover, the displacement and transverse stresses are computed a priori without any operation of post-processing. Therefore, the present results can be used as reference numbers for testing other new FEM models. � 2005 Elsevier Ltd. All rights reserved.

[1]  Erasmo Carrera,et al.  CZ° requirements—models for the two dimensional analysis of multilayered structures , 1997 .

[2]  Erasmo Carrera,et al.  Assessment of Plate Elements on Bending and Vibrations of Composite Structures , 2002 .

[3]  N. J. Pagano,et al.  Stress fields in composite laminates , 1978 .

[4]  Erasmo Carrera,et al.  Classical and advanced multilayered plate elements based upon PVD and RMVT. Part 1: Derivation of finite element matrices , 2002 .

[5]  Raphael Loewy,et al.  On vibrations of heterogeneous orthotropic cylindrical shells. , 1971 .

[6]  Erasmo Carrera,et al.  Multilayered Finite Plate Element based on Reissner Mixed Variational Theorem. Part II: Numerical Analysis, , 2002 .

[7]  N. J. Pagano,et al.  Elastic Behavior of Multilayered Bidirectional Composites , 1972 .

[8]  G. Kirchhoff,et al.  Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. , 1850 .

[9]  E. Reissner.  The effect of transverse shear deformation on the bending of elastic plates , 1945 .

[10]  J. Whitney,et al.  The Effect of Transverse Shear Deformation on the Bending of Laminated Plates , 1969 .

[11]  N. Pagano,et al.  Exact Solutions for Composite Laminates in Cylindrical Bending , 1969 .

[12]  E. Carrera.  Historical review of Zig-Zag theories for multilayered plates and shells , 2003 .

[13]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[14]  E. Reissner.  On a mixed variational theorem and on shear deformable plate theory , 1986 .

[15]  M. Poisson.  Mémoire sur l'équilibre et le mouvement des corps élastiques , 1828 .

[16]  E. Carrera.  On the use of the Murakami's zig-zag function in the modeling of layered plates and shells , 2004 .

[17]  J. Reddy.  Mechanics of laminated composite plates : theory and analysis , 1997 .

[18]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[19]  N. Pagano,et al.  Exact Solutions for Rectangular Bidirectional Composites and Sandwich Plates , 1970 .

[20]  E. Reissner.  On a certain mixed variational theorem and a proposed application , 1984 .

[21]  Erasmo Carrera,et al.  Multilayered Finite Plate Element based on Reissner Mixed Variational Theorem. Part I: Theory., , 2002 .

[22]  E. Reissner.  On a Variational Theorem in Elasticity , 1950 .