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
We say that a variety ${\mathcal V}$ of algebras has the Compact Intersection Property (CIP), if the family of compact congruences of every $A\in {\mathcal V}$ is closed under intersection. We investigate the congruence lattices of algebras in locally finite, congruence-distributive CIP varieties and obtain a complete characterization for several types of such varieties. It turns out that our description only depends on subdirectly irreducible algebras in ${\mathcal V}$ and embeddings between them. We believe that the strategy used here can be further developed and used to describe the congruence lattices for any (locally finite) congruence-distributive CIP variety.