Curvature and Out-of-Plane-Strain for Generalized Plane Strain

1972 ◽  
Vol 39 (3) ◽  
pp. 827-829 ◽  
Author(s):  
V. J. Parks
Keyword(s):  
Plane Strain ◽  
Cross Section ◽  
Central Region ◽  
Transverse Cross Section ◽  
Infinite Length ◽  
Out Of Plane ◽  
Plane Solution ◽  
Generalized Plane Strain

Out-of-plane strains and stresses are determined using reciprocity for the central region of very long bars (approaching infinite length) of uniform transverse cross section subjected to the same in-plane loads on every cross section. The loading explicitly specifies no end loads on the bars. The results are obtained without recourse to the in-plane solution. Conversely the end force and moment are determined for the case where the out-of-plane strain is zero.

Generalized plane strain analysis of a bimaterial composite containing a free surface normal to the interface

1991 ◽  
Vol 6 (12) ◽  
pp. 2609-2622 ◽  
Author(s):  
V.K. Tewary ◽  
R.D. Kriz
Keyword(s):  
Free Surface ◽  
Grain Boundary ◽  
Integral Representation ◽  
Plane Strain ◽  
Displacement Field ◽  
Strain Analysis ◽  
Elastic Plane ◽  
Surface Normal ◽  
Out Of Plane ◽  
Generalized Plane Strain

The elastic plane strain Green's function calculated in earlier papers is modified to account for generalized plane strain and applied to calculating the stress and the displacement field in a bimaterial composite containing a free surface normal to the interface and subjected to an out-of-plane load. The result is obtained in terms of a closed integral representation which is evaluated numerically as well as analytically. The method is applied to a cubic solid containing a Σ-5 grain boundary and to fiber-reinforced laminated composites. The singularities in the stress are identified and discussed.

On the Use of a Plane-Strain Model to Solve Generalized Plane-Strain Problems

1997 ◽  
Vol 64 (1) ◽  
pp. 236-238 ◽  
Author(s):  
Shoufeng Hu ◽  
N. J. Pagano
Keyword(s):  
Finite Element ◽  
Plane Strain ◽  
Three Dimensional ◽  
Element Analysis ◽  
Out Of Plane ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element ◽  
Strain Model ◽  
Generalized Plane Strain ◽  
Plane Strain Model

Many composite problems are generalized plane strain in nature. They are often solved using three-dimensional finite element analyses. We propose a technique to solve these problems with a plane-strain model, which is achieved by introducing some artificial out-of-plane thermal strains in a two-dimensional finite element analysis. These artificial thermal strains are chosen such that an identical stress field is obtained, while the actual strains and displacements can also be determined.

Stress concentration factors for the torsion of curved beams of arbitrary cross-section

2006 ◽  
Vol 220 (12) ◽  
pp. 1709-1726 ◽  
Author(s):  
R E Cornwell
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Cross Section ◽  
Cross Sections ◽  
Shear Stresses ◽  
Curved Beams ◽  
Finite Element Implementation ◽  
Out Of Plane ◽  
Concentration Factors ◽  
Stress Concentration Factors

There are numerous situations in machine component design in which curved beams with cross-sections of arbitrary geometry are loaded in the plane of curvature, i.e. in flexure. However, there is little guidance in the technical literature concerning how the shear stresses resulting from out-of-plane loading of these same components are effected by the component's curvature. The current literature on out-of-plane loading of curved members relates almost exclusively to the circular and rectangular cross-sections used in springs. This article extends the range of applicability of stress concentration factors for curved beams with circular and rectangular cross-sections and greatly expands the types of cross-sections for which stress concentration factors are available. Wahl's stress concentration factor for circular cross-sections, usually assumed only valid for spring indices above 3.0, is shown to be applicable for spring indices as low as 1.2. The theory applicable to the torsion of curved beams and its finite-element implementation are outlined. Results developed using the finite-element implementation agree with previously available data for circular and rectangular cross-sections while providing stress concentration factors for a wider variety of cross-section geometries and spring indices.

Piezoelectric T-Beam Microactuators

2008 ◽  
Author(s):  
Hareesh K. R. Kommepalli ◽  
Andrew D. Hirsh ◽  
Christopher D. Rahn ◽  
Srinivas A. Tadigadapa
Keyword(s):  
Cross Section ◽  
Fabrication Process ◽  
Mems Fabrication ◽  
Out Of Plane ◽  
Cantilevered Beam ◽  
Piezoelectric Mems ◽  
The Cross ◽  
T Beam ◽  
Cross Section Geometry

This paper introduces a novel T-beam actuator fabricated by a piezoelectric MEMS fabrication process. ICP-RIE etching from the front and back of a bulk PZT chip is used to produce stair stepped structures through the thickness with complex inplane shapes. Masked electrode deposition creates active and passive regions in the PZT structure. With a T-shaped crosssection, and bottom and top flange and web electrodes, a cantilevered beam can bend in-plane and out-of-plane with bimorph actuation in both directions. One of these T-beam actuators is fabricated and experimentally tested. An experimentally validated model predicts that the cross-section geometry can be optimized to produce higher displacement and blocking force.

Adaptation of Cardinal Points Symmetry Landmarks Distribution Model to in-vivo B-Mode Ultrasound Images of Transverse Cross-section of Carotid Arteries

2021 ◽  
Vol 6 (7) ◽  
pp. 107-113
Author(s):  
Charles Nnamdi Udekwe ◽  
Akinlolu Adediran Ponnle
Keyword(s):  
Carotid Artery ◽  
Cross Section ◽  
Carotid Arteries ◽  
Region Of Interest ◽  
Transverse Cross Section ◽  
Transverse Plane ◽  
Distribution Model ◽  
Ultrasound Images ◽  
Symmetry Line

The geometry of the imaged transverse cross-section of carotid arteries in in-vivo B-mode ultrasound images are most times irregular, unsymmetrical, full of speckles and usually non-uniform. We had earlier developed a technique of cardinal point symmetry landmark distribution model (CPS-LDM) to completely characterize the Region of Interest (ROI) of the geometric shape of thick-walled simulated B-mode ultrasound images of carotid artery imaged in the transverse plane, but this was based on the symmetric property of the image. In this paper, this developed technique was applied to completely characterize the region of interest of the geometric shape of in-vivo B-mode ultrasound images of non-uniform carotid artery imaged in the transverse plane. In order to adapt the CPS-LD Model to the in-vivo carotid artery images, the single VS-VS vertical symmetry line common to the four ROIs of the symmetric image is replaced with each ROI having its own VS-VS vertical symmetry line. This adjustment enables the in-vivo carotid artery images possess symmetric properties, hence, ensuring that all mathematical operations of the CPS-LD Model are conveniently applied to them. This adaptability was observed to work well in segmenting the in-vivo carotid artery images. This paper shows the adaptive ability of the developed CPS-LD Model to successfully annotate and segment in-vivo B-mode ultrasound images of carotid arteries in the transverse cross-sectional plane either they are symmetrical or unsymmetrical.

Stress Distribution in a Uniformly Rotating Equilateral Triangular Shaft

1955 ◽  
Vol 22 (2) ◽  
pp. 255-259
Author(s):  
H. T. Johnson
Keyword(s):  
Approximate Solution ◽  
Stress Distribution ◽  
Boundary Conditions ◽  
Plane Strain ◽  
Cross Section ◽  
Plane Stress ◽  
Biharmonic Equation ◽  
Approximate Solutions ◽  
Distribution Of Stresses ◽  
General Method

Abstract An approximate solution for the distribution of stresses in a rotating prismatic shaft, of triangular cross section, is presented in this paper. A general method is employed which may be applied in obtaining approximate solutions for the stress distribution for rotating prismatic shapes, for the cases of either generalized plane stress or plane strain. Polynomials are used which exactly satisfy the biharmonic equation and the symmetry conditions, and which approximately satisfy the boundary conditions.

scholarly journals Out-of-plane strain effect on silicon-based flexible FinFETs

2015 ◽  
Author(s):  
Mohamed T. Ghoneim ◽  
Nasir Alfaraj ◽  
Galo A. Torres Sevilla ◽  
Hossain M. Fahad ◽  
Muhammad M. Hussain
Keyword(s):  
Plane Strain ◽  
Strain Effect ◽  
Out Of Plane ◽  
Silicon Based

Shear-Driven Flow in a Toroid of Square Cross Section

2003 ◽  
Vol 125 (1) ◽  
pp. 130-137 ◽  
Author(s):  
J. A. C. Humphrey ◽  
J. Cushner ◽  
M. Al-Shannag ◽  
J. Herrero ◽  
F. Giralt
Keyword(s):  
Cross Section ◽  
Finite Length ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Radius Of Curvature ◽  
Infinite Length ◽  
Core Flow ◽  
Reynolds Number Flow ◽  
End Wall

The two-dimensional wall-driven flow in a plane rectangular enclosure and the three-dimensional wall-driven flow in a parallelepiped of infinite length are limiting cases of the more general shear-driven flow that can be realized experimentally and modeled numerically in a toroid of rectangular cross section. Present visualization observations and numerical calculations of the shear-driven flow in a toroid of square cross section of characteristic side length D and radius of curvature Rc reveal many of the features displayed by sheared fluids in plane enclosures and in parallelepipeds of infinite as well as finite length. These include: the recirculating core flow and its associated counterrotating corner eddies; above a critical value of the Reynolds (or corresponding Goertler) number, the appearance of Goertler vortices aligned with the recirculating core flow; at higher values of the Reynolds number, flow unsteadiness, and vortex meandering as precursors to more disorganized forms of motion and eventual transition to turbulence. Present calculations also show that, for any fixed location in a toroid, the Goertler vortex passing through that location can alternate its sense of rotation periodically as a function of time, and that this alternation in sign of rotation occurs simultaneously for all the vortices in a toroid. This phenomenon has not been previously reported and, apparently, has not been observed for the wall-driven flow in a finite-length parallelepiped where the sense of rotation of the Goertler vortices is determined and stabilized by the end wall vortices. Unlike the wall-driven flow in a finite-length parallelepiped, the shear-driven flow in a toroid is devoid of contaminating end wall effects. For this reason, and because the toroid geometry allows a continuous variation of the curvature parameter, δ=D/Rc, this flow configuration represents a more general paradigm for fluid mechanics research.

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