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Elastostatic problems in multicomponent, multilayered periodic composites

Wągrowska M., Szlachetka O., Bagdasaryan V.

Przegląd Naukowy Inżynieria i Kształtowanie Środowiska

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2018

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Vol. 27, No. 1

9--18

EN

The object of the analysis is a two-dimensional elastostatic problem for multicomponent, multilayered periodic composites. The equations of equilibrium for this composite are obtained within the framework of tolerance modelling procedure. The paper presents two examples of solutions of

boundary value problems.

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2

Elastostatic problem for an interface rigid inclusion in a periodic two-layer space

Kaczyński A., Kozłowski W.

Acta Mechanica et Automatica

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2010

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Vol. 4, no. 4

42-50

EN

The article is devoted to the elastostatic three-dimensional problem of an interface sheet-like inclusion (anticrack) embedded into a periodic two-layered unbounded composite. An approximate analysis is carried out within the framework of the homogenized model with microlocal parameters. The

formulation and the method of solving the general problem for an arbitrarily shaped inclusion is presented. As an example illustrating this method, the problem for a rigid circular inclu- sion under perpendicular tension is solved explicitly and discussed from the point of view of failure theory.

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3

Fast multipole boundary element method for the analysis of plates with many holes

Ptaszny J., Fedeliński P.

Archives of Mechanics

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2007

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Vol. 59, nr 4-5

385-401

EN

A three-node quadratic element version of the fast multipole boundary element method (FMBEM) for two-dimensional elastostatic problems is presented. The method is applied to the analysis of perforated plates. A comparison of convergence and accuracy of the present method using quadratic

elements with the method using constant elements, presented by other authors, is given. Stress results for a square plate with a circular hole are investigated. Effective material properties of plates with many holes are estimated and compared to analytical results. Implementation of quadratic-element version of the FMBEM resulted in a lower number of degrees of freedom and expansion terms, and similar accuracy to constant-element version of the method, for the same structures. Influence of boundary conditions on the convergence of the iterative solver is investigated. The effectiveness of the FMBEM in relation to the conventional BEM is presented.

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4

The two-actions theorem and its application to composite materials.

Stampouloglou J.H., Theotokoglou E.E.

Archive of Mechanical Engineering

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2002

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Vol. XLIX, nr 4

298-315

EN

In the present study a new energy theorem is proposed, "The two actions theorem", which is valid in linear elastostatic problems. A new formalism concerning the works done by external actions is introduced. Known energy theorems are proved using the proposed two-action theorem. A composite

materials problem is confronted in terms of the two actions theorem and energy relations are formulated. Finally, it is presented a study on the problems of a composed two material below cylinder under internal and external pressure, and of stretching of an infinite plate with an inserted elastic disc of a different material. The proposed energy relations are veryfied in these applications.

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PL

W pracy przedstawiono nowe twierdzenie, "Twierdzenie o podwójnych oddziaływaniach", które ma zastosowanie w liniowych zagadnieniach elastostatycznych. Wprowadzono nowy formalizm dla wyrażenia pracy wykonanej przez oddziaływania zewnętrzne. Twierdzenie o podwójnych oddziaływaniach może

posłużyć do weryfikacji znanych twierdzeń związanych z energią. Twierdzenie wykorzystano w zagadnieniu dotyczącym materiałów kompozytowych formułując zależności energetyczne. Ponadto, zaprezentowano dwa przykłady aplikacji twierdzenia: w zastosowaniu do cylindra złożonego z dwu cylindrów z różnych materiałów poddanego ciśnieniu wewnętrznemu i zewnętrznemu, oraz w zagadnieniu rozciągania nieskończonej płyty z wbudowanym elastycznym dyskiem z innego materiału. W aplikacjach tych zweryfikowano zaproponowane związki energetyczne.

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