scholarly journals Vibration of multilayered beams using sinus finite elements with transverse normal stress

2010 ◽  
Vol 92 (6) ◽  
pp. 1524-1534 ◽  
Author(s):  
P. Vidal ◽  
O. Polit
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Transverse Normal Stress

The Various Approximations of the Bimetallic Thermostatic Strip

1991 ◽  
Vol 58 (4) ◽  
pp. 1015-1020 ◽  
Author(s):  
Christopher D. Pionke ◽  
Gerald Wempner
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Edge Effects ◽  
Degrees Of Freedom ◽  
Dissimilar Materials ◽  
Interfacial Shear ◽  
Thin Strip ◽  
Reasonable Accuracy ◽  
Interfacial Stresses ◽  
Transverse Normal Stress

A thin strip, formed by bonding two dissimilar materials, constitutes a simple thermostatic element. If edge effects are neglected, then the strip is reduced to a uniform beam, or plate, with two degrees-of-freedom. The flexure occurs only because of the bond and interfacial shear which is also accompanied by transverse normal stress. These latter stresses are very localized at the end and edges. Here, the elementary approximations, and refinements via finite elements, are presented and compared. Deflections are given with reasonable accuracy by the simple approximations, but the severe interfacial stresses are revealed only by the refinements.

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.

New mixed finite elements for the discretization of piezoelectric structures or macro-fiber composites

2018 ◽  
Vol 29 (16) ◽  
pp. 3266-3283 ◽  
Author(s):  
Astrid S Pechstein ◽  
Martin Meindlhumer ◽  
Alexander Humer
Keyword(s):  
Finite Elements ◽  
Normal Stress ◽  
Degrees Of Freedom ◽  
Piezoelectric Materials ◽  
Normal Component ◽  
Mixed Finite Elements ◽  
Fiber Composites ◽  
Tangential Component ◽  
Tangential Displacement ◽  
Thin Elements

We propose a new three-dimensional formulation based on the mixed tangential-displacement normal-normal-stress method for elasticity. In elastic tangential-displacement normal-normal-stress elements, the tangential component of the displacement field and the normal component of the stress vector are degrees of freedom and continuous across inter-element interfaces. Tangential-displacement normal-normal-stress finite elements have been shown to be locking-free with respect to shear locking in thin elements, which makes them suitable for the discretization of laminates or macro-fiber composites. In the current paper, we extend the formulation to piezoelectric materials by adding the electric potential as degree of freedom.

Analytical Simulation of the Composite Ice Wall

1989 ◽  
Vol 111 (3) ◽  
pp. 174-180 ◽  
Author(s):  
P. Corder ◽  
T. Kozik
Keyword(s):  
Shear Stress ◽  
Closed Form ◽  
Normal Stress ◽  
Transverse Shear ◽  
Parametric Study ◽  
Beam Theory ◽  
Transverse Shear Stress ◽  
Transverse Normal Stress ◽  
Analytical Simulation ◽  
Sandwich Configuration

A system of linear, closed-form stress equations for a steel-concrete-steel sandwich configuration, i.e., the “Composite Ice Wall,” was derived incorporating a formulation of classical beam theory. The stress terms include the longitudinal normal stress, the transverse shear stress and the transverse normal stress. These equations were programmed using Pascal and a parametric study was conducted. Some of the results are included herein. The analytical model produces principal stress contours and centerline deflections very similar to those in the classical beam for comparable pressure loadings.

The Contradicting Assumptions of Zero Transverse Normal Stress and Strain in the Thin Plate Theory: A Justification

1999 ◽  
Vol 68 (4) ◽  
pp. 660-662 ◽  
Author(s):  
K. Bhaskar and ◽  
T. K. Varadan
Keyword(s):  
Normal Stress ◽  
Thin Plate ◽  
Test Problem ◽  
Plate Theory ◽  
Stress And Strain ◽  
Elasticity Solution ◽  
Classical Plate Theory ◽  
Transverse Normal Stress ◽  
Thin Plate Theory

The need and validity of the contradicting assumptions of zero transverse normal stress and the corresponding strain in the classical plate theory are critically examined here. This is done by studying the relative magnitudes of these quantities with respect to other stresses and strains for a test problem amenable to an exact elasticity solution.

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.

Influence of transverse normal stress on sheet metal formability

2003 ◽  
Vol 19 (10) ◽  
pp. 1567-1583 ◽  
Author(s):  
L.M. Smith ◽  
R.C. Averill ◽  
J.P. Lucas ◽  
T.B. Stoughton ◽  
P.H. Matin
Keyword(s):  
Normal Stress ◽  
Sheet Metal ◽  
Transverse Normal Stress
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