Keywords: geometric non-linear analyses, FGM, bar element, sandwich structure.

Structures made of composite, sandwich or functionally graded materials (FGMs) are often used in many areas and applications. The simplest mixture rules, which determine average effective material properties, are based on the assumption that the composite material property is the sum of the material properties of each constituent multiplied by its volume fraction. To increase the accuracy of calculation of the composite material properties, extended mixture rules [1,2] are applied in this article.

In this paper a new more effective and accurate truss element with continuous variation of the stiffness along its axis suitable for the solution of geometric and/or physical nonlinear problems is presented. A new shape function for the truss element [3,4] was used to overcome the problems associated with using an inaccurate description of the stiffness variation along the element length. The homogenisation of the material properties is made for multilayered sandwich bar with constant material properties of middle layer and polynomial variation of elasticity modulus and volume fraction of fibre and matrix at the top/bottom layers. The volume fraction of the fibre is constant along the width and height of each face layer, but it changes linearly along the layer length i.e. the mechanical properties are changed along the width and length of the specimen. As a typical example of geometrically non-linear behaviour the three-hinge mechanism was chosen and analysed. To examine the accuracy of the new bar element, a code for the MATHEMATICA programme was writen. Only one our new finite element was used for the solution of the chosen problem. The results obtained by this new element were compared with beam and solid element analysis in the ANSYS simulation programme.

The results of numerical experiments are presented in this contribution using the one new sandwich link element and the above mentioned extended mixture rules. The results obtained show good accuracy of our bar finite element. The results obtained with this element do not depend on the mesh density.

1

J. Murín, V. Kutiš, M. Masný, "An effective multiphysical FGM's beam/link finite element with transversal symmetric and longitudinal continuous variation of material properties", Proceedings of the Ninth International Conference on Computational Structures Technology, B.H.V. Topping, M. Papadrakakis, (Editors), Civil-Comp Press, UK, 2008. doi:10.4203/ccp.88.24

2

J. Murín, V. Kutiš, "Improved mixture rules for the composite (FGM's) sandwich beam finite element", In: Computational Plasticity IX. Fundamentational and Applications. Part 2., 9th International Conference, 647-650, 2007.

3

J. Murín, V. Kutiš, "Beam element with continuous variation of the cross-sectional area", Computers & Structures, 80, 329-338, 2002. doi:10.1016/S0045-7949(01)00173-0

4

J. Murín, "Implicit non-incremental FEM equations for non-linear continuum", Strojnícky casopis, Vol. 52, No. 3, 2001.

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