Transverse Normal Stress Effects in Multilayered Plates

1999 ◽  
Vol 66 (4) ◽  
pp. 1004-1012 ◽  
Author(s):  
E. Carrera
Keyword(s):  
Normal Stress ◽  
Plate Thickness ◽  
Transverse Displacement ◽  
Multilayered Plate ◽  
Stress Effects ◽  
Transverse Normal Stress ◽  
Classical Models ◽  
Multilayered Plates ◽  
Plate Analysis ◽  
Transversely Anisotropic

An evaluation of transverse normal stress σzz effects in multilayered plate modeling is given in this paper. Mixed theories with continuous interlaminar transverse shear and normal stresses have been formulated on the basis of Reissner's theorem (Reissner, 1984). The case in which the number of the displacement variables preserves independence by the number of constitutive layers, N1, has been investigated. Classical models based on standard displacement formulations have been discussed for comparison purposes. The analysis of transverse stress effects has been conducted by allowing a constant, linear, and higher-order distribution of the transverse displacement components in the plate thickness directions. Related two-dimensional models are compared for the static response of symmetrically and unsymmetrically layered, simply supported plates made of isotropic as well as orthotropic layers. The conducted numerical investigation and comparison with available results have above all led to the following conclusions. The possibility of including σzz makes the used mixed theories more attractive that other available modelings. σzz plays a fundamental role in thick laminate plates analysis. Such a role increases in transversely anisotropic multilayered plate analysis. With an increase of the plate thickness, a very accurate description of σzz requires modelings whose number of independent variables depends on N1.

Large-Amplitude Oscillations of Unsymmetrically Laminated Anisotropic Rectangular Plates Including Shear, Rotatory Inertia, and Transverse Normal Stress

1985 ◽  
Vol 52 (3) ◽  
pp. 536-542 ◽  
Author(s):  
K. S. Sivakumaran ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Normal Stress ◽  
Transverse Shear ◽  
Plate Theory ◽  
Orientation Angle ◽  
Nonlinear Frequency ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Transverse Normal Stress

This paper is concerned with nonlinear free vibrations of generally laminated anisotropic elastic plates. Based on Reissner’s variational principle a nonlinear plate theory is developed. The effects of transverse shear, rotatory inertia, transverse normal stress, and transverse normal contraction or extension are included in this theory. Using the Galerkin procedure and principle of harmonic balance, approximate solutions to governing equations of unsymmetrically laminated rectangular plates including transverse shear, rotatory inertia, and transverse normal stress are formulated for various boundary conditions. Numerical results for the ratio of nonlinear frequency to linear frequency of unsymmetric angle-ply and cross-ply laminates are presented graphically for various values of elastic properties, fiber orientation angle, number of layers, and aspect ratio and for different boundary conditions. Present results are also compared with available data.

Normal stress effects on Knudsen flow

2018 ◽  
Vol 30 (1) ◽  
pp. 013103
Author(s):  
Byung Chan Eu
Keyword(s):  
Normal Stress ◽  
Knudsen Flow ◽  
Stress Effects

Analysis of normal stress effects in a squeeze film porous bearing

Wear ◽  
1987 ◽  
Vol 116 (2) ◽  
pp. 237-248 ◽  
Author(s):  
N.M. Bujurke ◽  
M. Jagadeeswar ◽  
P.S. Hiremath
Keyword(s):  
Normal Stress ◽  
Squeeze Film ◽  
Stress Effects ◽  
Porous Bearing

Historical review of Zig-Zag theories for multilayered plates and shells

2003 ◽  
Vol 56 (3) ◽  
pp. 287-308 ◽  
Author(s):  
Erasmo Carrera
Keyword(s):  
English Language ◽  
Plate Thickness ◽  
Historical Review ◽  
Axiomatic Approach ◽  
Multilayered Structures ◽  
Anisotropic Plates ◽  
Plate And Shell ◽  
Multilayered Plates ◽  
Plates And Shells ◽  
Transverse Stresses

This paper gives a historical review of the theories that have been developed for the analysis of multilayered structures. Attention has been restricted to the so-called Zig-Zag theories, which describe a piecewise continuous displacement field in the plate thickness direction and fulfill interlaminar continuity of transverse stresses at each layer interface. Basically, plate and shell geometries are addressed, even though beams are also considered in some cases. Models in which the number of displacement variables is kept independent of the number of constitutive layers are discussed to the greatest extent. Attention has been restricted to those plate and shell theories which are based on the so-called method of hypotheses or axiomatic approach in which assumptions are introduced for displacements and/or transverse stresses. Mostly, the work published in the English language is reviewed. However, an account of a few articles originally written in Russian is also given. The historical review conducted has led to the following main conclusions. 1) Lekhnitskii (1935) was the first to propose a Zig-Zag theory, which was obtained by solving an elasticity problem involving a layered beam. 2) Two other different and independent Zig-Zag theories have been singled out. One was developed by Ambartsumian (1958), who extended the well-known Reissner-Mindlin theory to layered, anisotropic plates and shells; the other approach was introduced by Reissner (1984), who proposed a variational theorem that permits both displacements and transverse stress assumptions. 3) On the basis of historical considerations, which are detailed in the paper, it is proposed to refer to these three theories by using the following three names: Lekhnitskii Multilayered Theory, (LMT), Ambartsumian Multilayered Theory (AMT), and Reissner Multilayered Theory (RMT). As far as subsequent contributions to these three theories are concerned, it can be remarked that: 4) LMT although very promising, has almost been ignored in the open literature. 5) Dozens of papers have instead been presented which consist of direct applications or particular cases of the original AMT. The contents of the original works have very often been ignored, not recognized, or not mentioned in the large number of articles that were published in journals written in the English language. Such historical unfairness is detailed in Section 3.2. 6) RMT seems to be the most natural and powerful method to analyze multilayered structures. Compared to other theories, the RMT approach has allowed from the beginning development of models which retain the fundamental effect related to transverse normal stresses and strains. This review article cites 138 references.

scholarly journals Normal stress effects in the gravity driven flow of granular materials

2017 ◽  
Vol 92 ◽  
pp. 84-91 ◽  
Author(s):  
Wei-Tao Wu ◽  
Nadine Aubry ◽  
James F. Antaki ◽  
Mehrdad Massoudi
Keyword(s):  
Normal Stress ◽  
Granular Materials ◽  
Stress Effects ◽  
Gravity Driven ◽  
Gravity Driven Flow
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