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On tolerance averaged model of the propagation of boundary displacement fluctuations in FGM-type laminated composite

100%

Łacińska L. , Wierzbicki E.

2007

tom Vol. 6, nr 1

133-140

The object of the contribution is the analysis of a certain initial-boundary problems in elastodynamics of FGM-type multiphased laminated composites. The aim of the paper is to formulate an answer to the question what kind of assumptions are enough to be taken into account in the framework of the simplified tolerance model for the elastodynamics of the considered laminates the boundary effect will be observed.

On the boundary effect in elastodynamics of laminated solids

75%

Wierzbicki E. , Łacińska L.

2007

tom Z. 6

45-54

The object of the contribution is the analysis of a certain aspects of the boundary effect behaviour in elastodynamics of FGM-type multiphase laminated composites. The aim of the paper is to answer the question what kind of assumptions are enough to be taken into account in the framework of the simplified tolerance model for the elastodynamics of the considered laminates the boundary effect will be observed. The answer to this question is obtained for a certain class of two-phased FGM-type laminates and for tolerance description based on the exclusively one arbitrary shape function.

Przedmiotem rozważań jest analiza zjawisk typu warstwy brzegowej w elastodynamice wielofazowych laminatów z gradacją własności efektywnych. Celem pracy jest odpowiedź na pytanie, przy jakich założeniach przyjętych w ramach uproszczonego tolerancyjnego modelu elastodynamiki takich laminatów efekt brzegowy jest obserwowany. Odpowiedź na to pytanie uzyskano dla pewnej klasy dwufazowych laminatów typu FGM i tolerancyjnego modelu z jedną funkcją kształtu, której postać nie musi być precyzowana dla realizacji celu pracy.

On the null condition for nonlinearly elastic solids

51%

Domański W. , Ogden R. W.

tom Vol. 58, nr 4-5

339-361

Smooth solutions to the Cauchy problem for the equations of nonlinear elastodynamics exist typically only locally in time. However, under the assumption of small initial data and an additional restriction, the so-called null condition, global existence and uniqueness of a classical solution can be proved. In this paper, we examine this condition for the elastodynamic equations and study its connection with the property of genuine nonlinearity as well as its relation with the phenomenon of self-resonance of nonlinear elastic waves. Using a special structure of plane waves elastodynamics [13], we provide an alternative and simple formulation of the null condition. This condition is then evaluated for some examples of elastic constitutive laws in order to determine the nature of the restrictions that it imposes.

Boundary layer phenomena in elastodynamics of functionally graded laminates

51%

Rychlewska J. , Woźniak C.

tom Vol. 58, nr 4-5

431-444

The object of considerations are micro-laminated two-phase solids having macroscopic properties continuously varying in the direction normal to the layering (functionally graded laminates, FGL). The main question posed in this contribution is how to investigate both micro- and macro- dynamic response of the linear-elastic FGL. To answer this question, a new approximate mathematical model of FGL is proposed. This model is represented by a certain refined homogenized equation of motion for averaged displacements and a boundary-layer equation for intrinsic displacement fluctuations. Main attention is given to the investigations of near-initial and near-boundary dynamic phenomena in FGL, which are related to the specific form of initial and boundary conditions. For a periodically laminated medium the obtained results reduce to those derived in [7].