Simultaneously with the production of such materials, new numerical methods have been developed and the existing methods have been enhanced for their numerical simulation. For example in [1], the new beam finite element for analysis of beam structures with varying thermal and elastic properties along the beam high was developed. In [2] the linear elastic 3D-beam element of composite cross-section has been presented including warping and shear deformation effect. The conventional finite element programs contain the multiphysical link and solid elements with average values of the real constants and material properties. These elements can be also used for the analysis of FGMs with the spatial variation of material properties, but the solution accuracy depends very much on the mesh fineness and the data preparation is very time consuming.

To avoid these difficulties, a new beam element was developed to study the electric-thermal-elastic behaviour of the longitudinally graded links-beams [3]. In the theoretical part of this contribution, which is continuation of the work [3], we present the effective stiffness matrix of the electric-thermal-structural two-dimensional link-beam finite element with constant cross-section (which is predominantly rectangular) with variation of the effective material properties. This variation of effective material properties is caused with both the continuous longitudinal and layer-wise symmetric transversal variation of the constituents volume fractions and constituents material properties. All the variations are included in the stiffness matrix through the transfer constants. The effective material properties have been calculated with the extended mixture rules and with the laminate theory, but this finite element can be also used in the case when the effective material properties have been obtained with another homogenisation techniques. This new finite element can be used not only for analysis of the symmetric multilayered sandwich beams which are built from layers with longitudinal variation of material properties, but also for two-dimensional beams with both the continuous longitudinal and transversal symmetric variation of material properties. The theoretical part of this contribution is completed by numerical validation, which documents high accuracy and effectiveness of our proposed multiphysical composite (FGMs) link-beam finite element.

1

A. Chakraborty, S. Gopalakrishnan, J.N. Reddy, "A new beam finite element for the analysis of functionally graded materials", International Journal of Mechanical Sciences, Vol. 45, pp. 519, 2003. doi:10.1016/S0020-7403(03)00058-4

2

E.J. Sapountzakis, V.G. Mokos, "3D-beam element of variable composite cross-section including warping and shear deformation effect", Computers and Structures, 85, p. 102, 2007. doi:10.1016/j.compstruc.2006.09.003

3

J. Murín, V. Kutiš, M. Masný, "Composite (FGM's) beam finite elements", In: Composites with Micro- and Nano-Structure, Edited by: V. Kompiš, Springer Science+Business Media B.V., in press, 2007. doi:10.1007/978-1-4020-6975-8_12

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