The additive mixture rules have been extended for calculation of the effective longitudinal elasticity modulus of the composite (Functionally Graded Materials - FGM's) beams with both the polynomial longitudinal variation of the constituent's elasticity modulus. Stiffness matrix of the composite Bernoulli-Euler beam has been established which contains the transfer constants. These transfer constants describe very accurately the polynomial uni-axially variation of the effective longitudinal elasticity modulus, which is calculated using the extended mixture rules.
The mixture rules have been extended for calculation of the effective elasticity modulus for stretching and flexural bending of the layer-wise symmetric composite (FGM's) sandwich beam finite element as well. The polynomial longitudinal and transversally symmetric layer-wise variation of the sandwich beam stiffness has been taken into the account. Elastic behaviour of the sandwich beam will be modelled by the laminate theory. Stiffness matrix of such new sandwich beam element has been established. The nature and quality of the matrix reinforcement interface have not been considered. Four examples have been solved using the extended mixture rules and the new composite (FGM's) beam elements with varying stiffness. The obtained results are evaluated, discussed and compared. and Obsahuje seznam literatury
In this paper a new truss element with variation of the cross-sectional area and/or Young modulus along its axis is presented which can be used for geometrically non-linear analysis of uniaxially graded bars. The non-linear stiffness matrices of
this element contain the unknown nodal displacements. The non-incremental Lagrangian approach, without any linearisation, has been used for deriving the stiffness matrices. The new shape functions of the beam element have been established which
describe the stiffness variation along the element length very accurately. Numerical experiments have been performed - the large displacement of Von Mises two truss structure with varying stiffness, which results confirm the effectiveness and accuracy
of the new truss element. In addition, this element fulfils the equilibrium equations in both the global and local sense. and Obsahuje seznam literatury