A Layer-Wise Laminate Theory Rationally Deduced From the Three-Dimenstonal Elasticity

1997 ◽  
Vol 64 (3) ◽  
pp. 538-545 ◽  
Author(s):  
P. Bisegna ◽  
E. Sacco
Keyword(s):  
Lagrange Multipliers ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Stress Fields ◽  
Simultaneous Presence ◽  
Numerical Application ◽  
Piecewise Constant ◽  
Laminate Theory ◽  
The Difference ◽  
Three Dimensional Elasticity

A layer-wise theory of laminated plates, which accounts for piecewise constant shear strain in the thickness, is derived from the three-dimensional elasticity theory by imposing suitable constraints on the strain and stress fields. At this aim, the functional of the three-dimensional elasticity is modified according to the Lagrange multipliers theory. In fact, a nonstandard application of the Lagrange theory is presented, because of the simultaneous presence of constraints on dual spaces. The imposed constraints make reactive strain and stress fields arise. Thus, it is necessary to distinguish between elastic and total strain and stress fields. The difference between them is emphasized in a numerical application.

scholarly journals Deleterious localized stress fields: the effects of boundaries and stiffness tailoring in anisotropic laminated plates

2016 ◽  
Vol 472 (2194) ◽  
pp. 20160391 ◽  
Author(s):  
R. M. J. Groh ◽  
P. M. Weaver
Keyword(s):  
Boundary Layer ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Single Layer ◽  
Variable Stiffness ◽  
Laminated Plates ◽  
Stress Fields ◽  
Relative Significance ◽  
Shear Moduli ◽  
Constant Stiffness

The safe design of primary load-bearing structures requires accurate prediction of stresses, especially in the vicinity of geometric discontinuities where deleterious three-dimensional stress fields can be induced. Even for thin-walled structures significant through-thickness stresses arise at edges and boundaries, and this is especially precarious for laminates of advanced fibre-reinforced composites because through-thickness stresses are the predominant drivers in delamination failure. Here, we use a higher-order equivalent single-layer model derived from the Hellinger–Reissner mixed variational principle to examine boundary layer effects in laminated plates comprising constant-stiffness and variable-stiffness laminae and deforming statically in cylindrical bending. The results show that zigzag deformations, which arise due to layerwise differences in the transverse shear moduli, drive boundary layers towards clamped edges and are therefore critically important in quantifying localized stress gradients. The relative significance of the boundary layer scales with the degree of layerwise anisotropy and the thickness to characteristic length ratio. Finally, we demonstrate that the phenomenon of alternating positive and negative transverse shearing deformation through the thickness of composite laminates, previously only observed at clamped boundaries, can also occur at other locations as a result of smoothly varying the material properties over the in-plane dimensions of the laminate.

Defocus ramp correction in spot-scan imaging

1992 ◽  
Vol 50 (1) ◽  
pp. 130-131
Author(s):  
Kenneth H. Downing
Keyword(s):  
Computer Control ◽  
Three Dimensional ◽  
Sufficient Accuracy ◽  
Objective Lens ◽  
Electron Crystallography ◽  
Contrast Transfer Function ◽  
Tilt Axis ◽  
Specimen Height ◽  
The Difference ◽  
Envelope Functions

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.

The iron content of iron superoxide dismutase: determination by anomalous scattering

1983 ◽  
Vol 218 (1210) ◽  
pp. 119-126 ◽  
Keyword(s):  
Superoxide Dismutase ◽  
Iron Content ◽  
Three Dimensional ◽  
Anomalous Scattering ◽  
Total Iron Content ◽  
Iron Site ◽  
Iron Superoxide Dismutase ◽  
Density Map ◽  
The Difference ◽  
Electron Density Map

The number of iron atoms in the dimeric iron-containing superoxide dismutase from Pseudomonas ovalis and their atomic positions have been determined directly from anomalous scattering measurements on crystals of the native enzyme. To resolve the long-standing question of the total amount of iron per molecule for this class of dismutase, the occupancy of each site was refined against the measured Bijvoet differences. The enzyme is a symmetrical dimer with one iron site in each subunit. The iron position is 9 ņ from the intersubunit interface. The total iron content of the dimer is 1.2±0.2 moles per mole of protein. This is divided between the subunits in the ratio 0.65:0.55; the difference between them is probably not significant. Since each subunit contains, on average, slightly more than half an iron atom we conclude that the normal state of this enzyme is two iron atoms per dimer but that some of the metal is lost during purification of the protein. Although the crystals are obviously a mixture of holo- and apo-enzymes, the 2.9 Å electron density map is uniformly clean, even at the iron site. We conclude that the three-dimensional structures of the iron-bound enzyme and the apoenzyme are identical.

scholarly journals Alternative derivation of the higher-order constitutive model for six-parameter elastic shells

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Mircea Bîrsan
Keyword(s):  
Energy Density ◽  
Constitutive Model ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Shell Theory ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Classical Shell Theory ◽  
Three Dimensional Elasticity ◽  
General Method

AbstractIn this paper, we present a general method to derive the explicit constitutive relations for isotropic elastic 6-parameter shells made from a Cosserat material. The dimensional reduction procedure extends the methods of the classical shell theory to the case of Cosserat shells. Starting from the three-dimensional Cosserat parent model, we perform the integration over the thickness and obtain a consistent shell model of order $$ O(h^5) $$ O ( h 5 ) with respect to the shell thickness h. We derive the explicit form of the strain energy density for 6-parameter (Cosserat) shells, in which the constitutive coefficients are expressed in terms of the three-dimensional elasticity constants and depend on the initial curvature of the shell. The obtained form of the shell strain energy density is compared with other previous variants from the literature, and the advantages of our constitutive model are discussed.

scholarly journals The effect of the outlet angle β2 on the thermomechanical behavior of a centrifugal compressor blade

2020 ◽  
Vol 29 (1) ◽  
pp. 1-8
Author(s):  
Ahmed Allali ◽  
Sadia Belbachir ◽  
Ahmed Alami ◽  
Belhadj Boucham ◽  
Abdelkader Lousdad
Keyword(s):  
Mechanical Behavior ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Complex Form ◽  
Compressor Blade ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Mechanical Fatigue ◽  
Outlet Angle ◽  
The Impact

AbstractThe objective of this work lies in the three-dimensional study of the thermo mechanical behavior of a blade of a centrifugal compressor. Numerical modeling is performed on the computational code "ABAQUS" based on the finite element method. The aim is to study the impact of the change of types of blades, which are defined as a function of wheel output angle β2, on the stress fields and displacements coupled with the variation of the temperature.This coupling defines in a realistic way the thermo mechanical behavior of the blade where one can note the important concentrations of stresses and displacements in the different zones of its complex form as well as the effects at the edges. It will then be possible to prevent damage and cracks in the blades of the centrifugal compressor leading to its failure which can be caused by the thermal or mechanical fatigue of the material with which the wheel is manufactured.

Reduction of Free-Edge Stress Concentration

1985 ◽  
Vol 52 (4) ◽  
pp. 801-805 ◽  
Author(s):  
P. R. Heyliger ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Finite Element Model ◽  
Three Dimensional ◽  
Element Model ◽  
Free Edge ◽  
Shear Stresses ◽  
Normal Stresses ◽  
Interlaminar Shear ◽  
Three Dimensional Elasticity

A quasi-three dimensional elasticity formulation and associated finite element model for the stress analysis of symmetric laminates with free-edge cap reinforcement are described. Numerical results are presented to show the effect of the reinforcement on the reduction of free-edge stresses. It is observed that the interlaminar normal stresses are reduced considerably more than the interlaminar shear stresses due to the free-edge reinforcement.

Sign in / Sign up

Export Citation Format

Share Document