Composite (FGM’s) Beam Finite Elements
The composite structures (e.g. laminate, sandwich structures, or FGM’s) are often used in engineering applications. Their FE analyses require creating very fine mesh of elements even for relatively small sized bodies, what increases computational time, particularly in nonlinear analyses. Macro-mechanical modelling of the composites is based on material properties homogenisation. The homogenisation of the material properties is made for three layers sandwich bar with constant material properties of middle layer and polynomial variation of effective elasticity modulus and volume fraction of fibre and matrix at the top/bottom layer. In derivation of the bar element matrices the effective longitudinal elasticity modulus have been considered. The uni-axially polynomial variation fibre elasticity modulus E f and the matrix elasticity modulus E m are given as polynomials. In the numerical examples/analyses we assume a three-layers two-node sandwich bar with double symmetric rectangular cross-section. As a typical example of geometric nonlinear behaviour the three-hinge mechanism was analysed. Two different approaches have been considered for calculation of the effective longitudinal elasticity modulus of the composite (FGM’s) bar with both polynomial variation of constituent’s volume fraction and polynomial longitudinal variation of the elasticity modulus. Stiffness matrix of the composite bar contains transfer constants, which accurately describe the polynomial uni-axially variation of effective Young’s modulus. The obtained results are compared with 3D analysis in the ANSYS simulation program. Findings show good accuracy and effectiveness of this new finite element. The results obtained with this element do not depend on the mesh density.
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- 1.Y. Bansal, M.J. Pindera, Efficient Reformulation of the Thermoelastic Higher-Order Theory for FGMs, NASA, 2002.Google Scholar
- 2.M. Koizumi, FGM activity in Japan, Composites, Part B(28B), 1997.Google Scholar
- 3.M. Koizumi, M, Niino, Overview of FGM Research in Japan, MRS Bulletin (20), 19–21, 1995.Google Scholar
- 7.W.K. Liu, E.G. Karpov, H.S. Park, Nano Mechanics and Materials: Theory, Multiple Scale Analysis, and Applications. Wiley, 2005.Google Scholar
- 10.J. Murín, V. Kutiš, M. Masný, An effective solution of electro-thermo-structural problem of uni-axially graded material, Structural Engineering and mechanics, 28, 695–713, 2007.Google Scholar
- 11.J. Murín, V. Kutiš, Extended mixture rules for the composite (FGM’s) beam finite elements, prepared for publication, 2007.Google Scholar
- 14.J. Murín, Implicit non-incremental FEM equations for non-linear continuum. Strojnícky časopis 52(3), 2001.Google Scholar
- 15.H. Rubin, Analytische Lösung linearer Differentialgleichungen mit veränderlichen Koeffizienten und baustatische Anwendung. Bautechnik, 76, 1999.Google Scholar
- 16.V. Kutiš, Beam element with variation of cross-section satisfying local and global equilibrium conditions, Ph.D. thesis, Slovak University of Techno1ogy, Bratislava, 2001.Google Scholar
- 17.H. Altenbach, J. Altenbach, W. Kissing, Mechanics of Composite Structural Elements, Springer, 2004.Google Scholar
- 18.J. Murín, V. Kutiš, Geometrically non-linear truss element with varying stiffness, Engineering Mechanics 13(6), 435–452, 2006.Google Scholar
- 19.Ansys Theory Manual 2004.Google Scholar
- 20.J. Murín, V. Kutiš, Improved mixture rules for the composite (FGM’s) sandwich beam finite element. In: IX International Conference on Computational Plasticity COMPLAS IX, E. Onate and D.R.J. Owen (eds.), CIMNE, Barcelona, 2007.Google Scholar