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1

Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness

Yang Zhicheng, Lu Hanwen, Sahmani Saeid, Safaei Babak

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 3

497--515

EN

The proposed study scrutinizes the small scale-dependent geometrical nonlinear flexural response of arbitrary-shaped microplates having variable thickness made of functional graded (FG) composites. Accordingly, the modified couple stress continuum elasticity incorporating the von Karman large deflection supposition is established within a quasi-three dimensional (quasi-3D) plate framework in which the transverse shear deformation and normal deflection are assumed to be distributed in and trigonometric schemes. The thickness variation of microplates are assumed in linear, convex and concave patterns. Next, to resolve the couple stress-based nonlinear bending problem, the isogeometric technique incorporating non-uniform B-spline functions is taken into consideration to implement the both discretized-based estimation and accurate geometric description. The gradient of rotation associated with the couple stress type of size dependency causes a stiffening phenomenon in the both linear and nonlinear flexural responses. Also, through considering a change in the thickness variation pattern firstly from the convex kind to the linear one, thereafter from the linear kind to concave one, the role of couple stress size dependency becomes a bit more pronounced. In addition, it is deduced that the gap between nonlinear flexural curves associated with the convex, linear and concave patterns of thickness variation gets larger by changing the boundary conditions of the FG composite arbitrary-shaped microplates from clamped ones to simply supported ones.

2

Exponential temperature effect on frequencies of a rectangular plate of non-linear varying thickness: a quintic spline technique

Gupta A. K., Mamta J.

Journal of Theoretical and Applied Mechanics

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2014

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Vol. 52 nr 1

15--24

EN

The differential equation governing the transverse motion of an elastic rectangular plate of non-linear thickness variation with thermal gradient has been analyzed on the basis of classi- cal plate theory. Following Levy’s approach, i.e. the two parallel edges are simply supported, the fourth-order differential equation governing the motion of such plates of non-linear vary- ing thickness in one direction with exponentially temperature distribution has been solved by using the quintic splines interpolation technique for two different combinations of clamped and simply supported boundary conditions at the other two edges. An algorithm for com- puting the solution of this differential equation is presented for the case of equal intervals. The effect of thermal gradient together with taper constants on the natural frequencies of vibration is illustrated for the first three modes of vibration.

3

Study on the thickness loss of Wilton-type carpets under dynamic loading

Celik N., Koc E.

Fibres & Textiles in Eastern Europe

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2010

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Vol. 18, no. 1 (78)

54--58

EN

In the two earlier papers, evaluations were presented on the characteristic parameters determining the behavior of three industrially produced Wilton-type carpets with different pile materials (wool, acrylic and PP) after a prolonged heavy static loading, and an extended analysis was carried out covering the energy absorption, damping characteristics and hysteresis effect of pile materials on carpet behavior during recovery. In this study, the same carpets were tested under dynamic loading in order to evaluate and observe the thickness loss and carpet behavior under dynamic loads. The results are given and discussed in this paper.

PL

W poprzednich artykułach przedstawiono analizę zachowania się dywanów typu Wilton wykonanych z trzech rodzajów przędz okrywowych polipropylenowych, akrylowych i wełnianych poddanych przedłużonemu działaniu dużych obciążeń statycznych. Wykonano obszerną analizę dotyczącą absorpcji energii, charakterystyk tłumienia, histerezy oraz relaksacji. W obecnej pracy analizowano zachowanie tych samych dywanów tym razem poddanych działaniom obciążeń dynamicznych. Wyniki poddano wnikliwej analizie.