scholarly journals Buckling of chiral rods due to coupled axial and rotational growth

2021 ◽  
pp. 108128652199970
Author(s):  
Satya Prakash Pradhan ◽  
Prashant Saxena
Keyword(s):  
Growth Model ◽  
Cross Sections ◽  
Cosserat Rods ◽  
Out Of Plane

We present a growth model for special Cosserat rods that allows for induced rotation of cross-sections. The growth law considers two controls, one for lengthwise growth and another for rotations. This is explored in greater detail for straight rods with helical and hemitropic material symmetries by introduction of symmetry-preserving growth to account for the microstructure. The example of a guided-guided rod possessing a chiral microstructure is considered to study its deformation due to growth. We show the occurrence of growth-induced out-of-plane buckling in such rods.

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.

Coupled Axial-Flexural-Torsional Vibration of Internally Damped Timoshenko Frames

2010 ◽  
Author(s):  
Adil Yucel ◽  
Alaeddin Arpaci ◽  
Ekrem Tufekci
Keyword(s):  
Cross Sections ◽  
Torsional Vibration ◽  
Complex Modulus ◽  
Linear Equations ◽  
Frame Structure ◽  
Rotational Inertia ◽  
Bending Vibrations ◽  
Element Analysis ◽  
Out Of Plane ◽  
Simultaneous Linear Equations

In this study, free in-plane and out-of-plane bending vibrations of frame structures have been analyzed together with torsional vibration. Axial extension, rotational inertia and shear effects have also been considered. The frame structure has been constructed as having two beams with doubly symmetric cross-sections and connected at any angle to each other. These types of frames frequently appear on ships as bridge wings which are probably the most problematic members experiencing severe vibration. Internal damping has been incorporated into the analyses by using a complex modulus of elasticity. Natural frequencies have been obtained analytically by solving simultaneous linear equations of complex coefficients. A finite element analysis has also been conducted to verify the analytical results. Furthermore, an experimental modal analysis has been carried out and the results have been compared with theoretical ones in tables for various connection angles and damping factors. The agreement among results has been found to be good.

scholarly journals Robust Sample Preparation of Large-Area In- and Out-of-Plane Cross Sections of Layered Materials with Ultramicrotomy

2020 ◽  
Vol 12 (13) ◽  
pp. 15867-15874 ◽  
Author(s):  
Magdalena O. Cichocka ◽  
Maarten Bolhuis ◽  
Sabrya E. van Heijst ◽  
Sonia Conesa-Boj
Keyword(s):  
Sample Preparation ◽  
Cross Sections ◽  
Layered Materials ◽  
Large Area ◽  
Out Of Plane

scholarly journals Stress Resultants and Out-of-Plane Deformations in Stiff Rings Attached to Elastic Cylinders and Subject to Concentrated Loads

1971 ◽  
Vol 93 (3) ◽  
pp. 835-844 ◽  
Author(s):  
Bernard W. Shaffer ◽  
Eric E. Ungar
Keyword(s):  
Cross Sections ◽  
Bending Moment ◽  
Elastic Cylinder ◽  
Concentrated Force ◽  
Direction Parallel ◽  
Out Of Plane ◽  
Elastic Cylinders ◽  
Special Case ◽  
Radial Axis ◽  
Plane Deformations

Expressions are derived which give the internal loads and deformations of a relatively stiff ring which is mounted on an elastic cylinder. Three basic types of loads acting on the ring are considered: a concentrated force acting in the direction parallel to the axis of the cylinder, a bending moment acting about a radial axis, and a bending moment acting about a tangential axis. The entire problem is first analyzed for the general case in which the centers of twist of the ring cross sections do not coincide with the mid-surface of the cylinder, and then also developed for the special case where these do coincide. An illustrative example is presented which gives an indication of the effect of the lack of coincidence of the centers of twist of the ring and the cylinder mid-surface.

Automated RVE computations for evaluation of microdamage initiation in structural stitched non-crimp fabric composites

2020 ◽  
Vol 54 (30) ◽  
pp. 4751-4771
Author(s):  
Gerrit Pierreux ◽  
Danny Van Hemelrijck ◽  
Thierry J Massart
Keyword(s):  
Cross Sections ◽  
Fiber Volume Fraction ◽  
Volume Fraction ◽  
Fiber Direction ◽  
Fiber Volume ◽  
Damage Initiation ◽  
Processing Step ◽  
Fabric Composites ◽  
Out Of Plane ◽  
Generate Unit

This contribution presents an approach to generate unit-cell models of structural stitched non-crimp fabric composites. Resin-rich regions and out-of-plane undulations caused by the stitching yarn are represented by initially straight discretised lines, while the stitching yarn is represented initially by a single discretised line which can be transformed into a multi-line configuration to model stitch cross-section variations. The discretised lines are shaped by geometrical operations with a contact treatment and boundary conditions being used to account, respectively, for line interactions and to control the shape of the bottom and top surfaces of each lamina respectively. A fiber-reinforced distorted zone with local variations in fiber volume fraction and fiber direction is modelled in cross-sections of the lamina in a post-processing step. Models for different stacking sequences and stitching parameters are then automatically generated and subsequently being in the stiffness calculation and damage initiation assessment using finite element based mechanical simulations.

Preferential Site Precipitation and Subcell Stability in AA6061 Sandwich Cores

2006 ◽  
Vol 977 ◽  
Author(s):  
B. A. Bouwhuis ◽  
G. D. Hibbard
Keyword(s):  
Sheet Metal ◽  
Cross Sections ◽  
Mechanical Performance ◽  
Small Deformation ◽  
Collapse Mechanisms ◽  
Truss Core ◽  
Out Of Plane ◽  
Perforated Sheet ◽  
6061 Aluminium Alloy ◽  
Sandwich Core

AbstractPeriodic cellular metal (PCM) sandwich cores can be considered hybrids of the solid and gas type. These can be designed at both the architectural and microstructural levels. PCM cores with 95% open porosity have been constructed from perforated 6061 aluminium alloy (AA6061) sheets using a perforation-stretching method. This method places planar, periodically-perforated sheet metal in an alternating-pin jig. The pins apply force out-of-plane, plastically deforming the sheet metal into a truss-like array of struts (i.e. metal supports) and nodal peaks (i.e. strut intersections). The result is a non-uniform work-hardened profile exhibiting large deformation at the nodes and small deformation at the struts.For identical PCM architectures, this study looks at the interaction of microstructural strengthening mechanisms and the resultant performance of PCM truss cores. Beginning with fabrication, work-hardening induced a subcell network of dislocation tangles within the AA6061 matrix. Following this stage, a variety of microstructures were created through recovery, recrystallization and precipitation mechanisms. Microhardness measurements and electron back-scattered diffraction (EBSD) characterization were employed through truss core cross-sections in order to study the microstructural gradients of subcell size as well as interaction between subcells and precipitates in the truss cores. To determine the effect of microstructure on mechanical performance, PCM cores were compressed to study deformation and collapse mechanisms.The present data can be used to illustrate engineering at the architectural and microstructural levels to achieve a range of mechanical properties in a hybrid sandwich core.

Smooth Mixed Geometry Profiles of Nozzles and Transition Ducts

2005 ◽  
Vol 127 (6) ◽  
pp. 1211-1213 ◽  
Author(s):  
James F. Wilson
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Smooth Surface ◽  
Axial Flow ◽  
Plane Flow ◽  
Out Of Plane ◽  
Surface Profiles

Parametric equations are derived that characterize smooth surface profiles for two general classes of nozzles and nonbranching transition ducts: straight sections for axial flow and curved sections (elbows) for in-plane or out-of-plane flow. For each profile, the terminal cross sections are specified as rectangular, elliptical, circular, or a combination of those shapes. At each terminal and in line with the flow, the displacement, slope, and curvature with its respective intersecting uniform section is maintained. Included is a design example of a 90deg elbow duct whose cross section remains constant between terminals of elliptical and circular cross sections.

Design and Analysis of Symmetrical, Monolithic Tip-Tilt-Piston Flexure Stages

2017 ◽  
Author(s):  
Guangbo Hao
Keyword(s):  
High Precision ◽  
Cross Sections ◽  
Plane Motion ◽  
Cnc Milling ◽  
Compliance Matrix ◽  
Design Synthesis ◽  
Generic Structure ◽  
Symmetrical Structure ◽  
Out Of Plane ◽  
Physical Prototype

This paper mainly deals with the determinate design/synthesis of a class of symmetrical and monolithic flexure mechanisms. Each is composed of 6 identical in-plane wire beams with uniform square cross sections. These flexure stages can provide three out-of-plane tip-tilt-piston motions for applications in high-precision or miniaturisation environments. A generic symmetrical structure is proposed as first with a group of defined parameters considering constraint and non-interference conditions. Normalised static analytical compliance entries for the diagonal compliance matrix of a generic structure are derived and symbolically represented by the parameters. Comprehensive compliance analysis is then followed using the analytical results, and quick insights into effects of parameters on compliances in different directions are gained. Case studies without and with actuation consideration are finally discussed. As a second contribution, a physical prototype with three actuation legs is monolithically fabricated (using CNC milling machining), kinematically modelled and experimentally tested, which shows that the desired out-of-plane motion can be generated from the in-plane actuation.

ELASTIC PROPERTY PREDICTION OF THE STITCHED MULTI-AXIAL WARP KNIT FABRIC COMPOSITES

2006 ◽  
Vol 20 (25n27) ◽  
pp. 4022-4027 ◽  
Author(s):  
HEOUNG-JAE CHUN ◽  
HYUNG-WOO KIM ◽  
JOON-HYUNG BYUN
Keyword(s):  
Composite Materials ◽  
Elastic Properties ◽  
Cross Sections ◽  
Averaging Method ◽  
Geometric Parameters ◽  
Suggested Model ◽  
Fabric Composites ◽  
Out Of Plane ◽  
Experimental Values ◽  
Good Agreement

In order to improve the resistances to delamination, damage tolerance, some in-plane and out-of-plane properties of composite materials, a through-thickness reinforcement must be provided. This through-thickness reinforcement is achieved by stitching multi-axial warp knit (MWK) fabrics used as preforms for the fabrication of composite materials. The MWK fabrics are constructed with layers of insertion fiber bundles in the warp, weft and bias directions. In order to correlate the microstructure of a preform with the elastic properties of stitched MWK composite, the analytical model for stitched MKW composite is developed. The overall geometry and geometric parameters of a representative volume are determined from the photomicrographs of cross sections of the fabricated composite specimens. The various elastic properties of MWK fabric composites are predicted as functions of various geometric parameters using an averaging method. The experimental results are compared with the predicted results in order to validate the suggested model. It is found that the predicted elastic properties are in reasonably good agreement with the experimental values.

Theoretical study of the stereo-dynamics of the H + HeH+(v = 0, j = 0) → H2+ + He reaction

2010 ◽  
Vol 88 (12) ◽  
pp. 899-904 ◽  
Author(s):  
Juanjuan Lv ◽  
Xinguo Liu ◽  
Jingjuan Liang ◽  
Haizhu Sun
Keyword(s):  
Reaction Mechanism ◽  
Cross Sections ◽  
Collision Energy ◽  
Energy Surface ◽  
Theoretical Study ◽  
Classical Trajectory ◽  
Direct Reaction ◽  
Generalized Polarization ◽  
Product Molecule ◽  
Out Of Plane

Theoretical study of the stereo-dynamics of the reaction, H + HeH+ (v = 0,  j = 0) → H 2+  + He, have been performed with quasi-classical trajectory (QCT) method at different collision energies on a new ab initio potential energy surface. The distributions of P(θr), P(ϕr) and four generalized polarization-dependent differential cross-sections have been calculated. The results indicate that both the orientation and alignment of the rotational angular momentum are impacted by collision energies. With the collision energy increases, the rotation of the product molecule has a preference of changing from the “in-plane” reaction mechanism to the “out-of-plane” mechanism. Although the reaction is mainly dominated by the direct reaction mechanism, the indirect mechanism plays a role while the collision energy is very low.

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