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Some remarks on the tolerance averaged model of uniperiodic composites

Augustowska L., Wierzbicki E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2003

Vol. 2, nr 1

7--13

The subject of this note are tolerance averaged models. These models can be obtained either by the mode shape functions approach or the basis functions approach [1]. The aim of this contribution is to present a comparison between two simplest versions of such models, i.e. models based on only one shape function. In the case of the basis function approach such model is named in the note as the heuristic tolerance averaged model and in the case of the mode shape functions approach as the tolerance averaged mode shape model. As a comparison criterion is taken into account the problem of free-vibration of an unbounded two-layered laminate.

Vibrations and waves in a fibre-reinforced composite

Augustowska L., Siedlecka U., Wierzbicki E.

Vibrations in Physical Systems

2002

Vol. 20

86--87

Two approaches to the formation of a tolerance averaged equations for elastodynamics of periodic solids

Augustowska L., Wierzbicki E.

Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej

2002

Vol. 1, nr 1

5--13

The aim of this contribution is to formulate two different approaches to the computation of averaged moduli in the equations of the tolerance averaged model of microperiodic linear-elastic composites. In the first approach, which will be called basis function approach, we shall use some of the FEM concepts in order to establish the basis functions in the Galerkin approximation to the non-stationary periodic cell problem of elastodynamics. In the second approach, which will be called mode shape function approach, we shall also use FEM concepts in order to determine functions describing the character of free vibrations of the periodicity cell. This approach makes it possible to reduce a large number of unknowns occuring in the first approach.