Stresses in Curved Beams of Noncircular Center Line

1960 ◽  
Vol 27 (3) ◽  
pp. 445-454
Author(s):  
M. M. Abbassi
Keyword(s):  
Cross Sections ◽  
Plane Curve ◽  
The Body ◽  
Curved Beam ◽  
Center Line ◽  
Curved Beams ◽  
Concentrated Load ◽  
Initial Curvature

The paper deals with the general case of a curved beam whose center line is a plane curve not necessarily circular. The body-stress equations and the compatibility equations for stresses in their general form are found for the chosen system of co-ordinates and put in their simplest form. Solutions for the equations with the aim of finding the stresses when the beam is subjected to a torque and to a bending out of its plane of initial curvature are obtained for both elliptic and circular cross sections of the beam. The case of a concentrated load at one end perpendicular to the plane of initial curvature is also considered.

Modeling Large Deflections of Initially Curved Beams in Compliant Mechanisms Using Chained Beam-Constraint-Model

2018 ◽  
Author(s):  
Guimin Chen ◽  
Fulei Ma ◽  
Guangbo Hao ◽  
Weidong Zhu
Keyword(s):  
Cross Sections ◽  
Compliant Mechanisms ◽  
Accurate Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Nonlinear Load ◽  
Circular Arc ◽  
Analysis And Design ◽  
Discretization Schemes ◽  
Constraint Model

Understanding and analyzing large and nonlinear deflections is one of the major challenges of designing compliant mechanisms. Initially curved beams can offer potential advantages to designers of compliant mechanisms and provide useful alternatives to initially straight beams. However, the literature on analysis and design using such beams is rather limited. This paper presents a general and accurate method for modeling large planar deflections of initially curved beams of uniform cross-sections, which can be easily adapted to curved beams of various shapes. This method discretizes a curved beam into a few elements and models each element as a circular-arc beam using the beam constraint model (BCM). Two different discretization schemes are provided for the method, among which the equal discretization is suitable for circular-arc beams and the unequal discretization is for curved beams of other shapes. Compliant mechanisms utilizing initially curved beams of circular-arc, cosine and parabola shapes are modeled to demonstrate the effectiveness of CBCM for initially curved beams of various shapes. The method is also accurate enough to capture the relevant nonlinear load-deflection characteristics.

Gender determination of caucasoid hair using image analysis

1993 ◽  
Vol 51 ◽  
pp. 216-217
Author(s):  
T.B. Ball ◽  
W.M. Hess
Keyword(s):  
Image Analysis ◽  
Cross Sections ◽  
Scalp Hair ◽  
The Body ◽  
Equivalent Diameter ◽  
Cross Sectional ◽  
Hair Samples ◽  
Length Width ◽  
Morphological Differences

It has been demonstrated that cross sections of bundles of hair can be effectively studied using image analysis. These studies can help to elucidate morphological differences of hair from one region of the body to another. The purpose of the present investigation was to use image analysis to determine whether morphological differences could be demonstrated between male and female human Caucasian terminal scalp hair.Hair samples were taken from the back of the head from 18 caucasoid males and 13 caucasoid females (Figs. 1-2). Bundles of 50 hairs were processed for cross-sectional examination and then analyzed using Prism Image Analysis software on a Macintosh llci computer. Twenty morphological parameters of size and shape were evaluated for each hair cross-section. The size parameters evaluated were area, convex area, perimeter, convex perimeter, length, breadth, fiber length, width, equivalent diameter, and inscribed radius. The shape parameters considered were formfactor, roundness, convexity, solidity, compactness, aspect ratio, elongation, curl, and fractal dimension.

Measurements of turbulent crossflow separation created by a curved body of revolution

2007 ◽  
Vol 589 ◽  
pp. 353-374 ◽  
Author(s):  
P. A. GREGORY ◽  
P. N. JOUBERT ◽  
M. S. CHONG
Keyword(s):  
Flow Visualization ◽  
Skin Friction ◽  
Cross Sections ◽  
Separated Flow ◽  
Surface Flow ◽  
The Body ◽  
Body Of Revolution ◽  
Outer Flow ◽  
Friction Measurements ◽  
Surface Flow Visualization

Using the method pioneered by Gurzhienko (1934), the crossflow separation produced by a body of revolution in a steady turn is examined using a stationary deformed body placed in a wind tunnel. The body of revolution was deformed about a radius equal to three times the body's length. Surface pressure and skin-friction measurements revealed regions of separated flow occurring over the rear of the model. Extensive surface flow visualization showed the presence of separated flow bounded by a separation and reattachment line. This region of separated flow began just beyond the midpoint of the length of the body, which was consistent with the skin-friction data. Extensive turbulence measurements were performed at four cross-sections through the wake including two stations located beyond the length of the model. These measurements revealed the location of the off-body vortex, the levels of turbulent kinetic energy within the shear layer producing the off-body vorticity and the large values of 〈uw〉 stress within the wake. Velocity spectra measurements taken at several points in the wake show evidence of the inertial sublayer. Finally, surface flow topologies and outer-flow topologies are suggested based on the results of the surface flow visualization.

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.

Earthquake response of linear-elastic arch-frames using exact curved beam formulations

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Baran Bozyigit
Keyword(s):  
Dynamic Stiffness ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Opening Angle ◽  
Earthquake Response ◽  
Response Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Base Shear ◽  
Content Type

PurposeThis study aims to obtain earthquake responses of linear-elastic multi-span arch-frames by using exact curved beam formulations. For this purpose, the dynamic stiffness method (DSM) which uses exact mode shapes is applied to a three-span arch-frame considering axial extensibility, shear deformation and rotational inertia for both columns and curved beams. Using exact free vibration properties obtained from the DSM approach, the arch-frame model is simplified into an equivalent single degree of freedom (SDOF) system to perform earthquake response analysis.Design/methodology/approachThe dynamic stiffness formulations of curved beams for free vibrations are validated by using the experimental data in the literature. The free vibrations of the arch-frame model are investigated for various span lengths, opening angle and column dimensions to observe their effects on the dynamic behaviour. The calculated natural frequencies via the DSM are presented in comparison with the results of the finite element method (FEM). The mode shapes are presented. The earthquake responses are calculated from the modal equation by using Runge-Kutta algorithm.FindingsThe displacement, base shear, acceleration and internal force time-histories that are obtained from the proposed approach are compared to the results of the finite element approach where a very good agreement is observed. For various span length, opening angle and column dimension values, the displacement and base shear time-histories of the arch-frame are presented. The results show that the proposed approach can be used as an effective tool to calculate earthquake responses of frame structures having curved beam elements.Originality/valueThe earthquake response of arch-frames consisting of curved beams and straight columns using exact formulations is obtained for the first time according to the best of the author’s knowledge. The DSM, which uses exact mode shapes and provides accurate free vibration analysis results considering each structural members as one element, is applied. The complicated structural system is simplified into an equivalent SDOF system using exact mode shapes obtained from the DSM and earthquake responses are calculated by solving the modal equation. The proposed approach is an important alternative to classical FEM for earthquake response analysis of frame structures having curved members.

Long bone cross-sectional geometry

2020 ◽  
pp. 307-320
Author(s):  
Christopher B. Ruff ◽  
Ryan W. Higgins ◽  
Kristian J. Carlson
Keyword(s):  
Mechanical Properties ◽  
Cross Sections ◽  
Lateral Displacement ◽  
Center Of Mass ◽  
Gait Pattern ◽  
Locomotor Behavior ◽  
The Body ◽  
Long Bone ◽  
Cross Sectional ◽  
Body Center

Long bone diaphyseal cross-sectional geometries reflect the mechanical properties of the bones, and can be used to aid in inferences of locomotor behavior in extinct hominins. This chapter considers all available long bone diaphyseal and femoral neck cross-sections of specimens from Sterkfontein Member 4, and presents comparisons of these section properties and other cross-sectional dimensions with those of other early hominins as well as modern samples. The cross-sectional geometry of the Sterkfontein Member 4 long bone specimens suggests some similarities to, but also interesting differences in, mechanical loading of these elements relative to modern humans. The less asymmetric cortical bone distribution in the Sterkfontein femoral necks is consistent with other evidence above indicating an altered gait pattern involving lateral displacement of the body center of mass over the stance limb. The relatively very strong upper limb of StW 431 implies that arboreal behavior formed a significant component of its locomotor repertoire. Bipedal gait may have been less efficient and arboreal climbing more prevalent in the Sterkfontein hominins.

Exact Solutions of Dynamic Characteristics for Curved Beams with Pinned-Pinned Ends

2013 ◽  
Vol 405-408 ◽  
pp. 702-705
Author(s):  
Xiao Fei Li ◽  
Wei Ming Yan ◽  
Hao Xiang He
Keyword(s):  
Exact Solutions ◽  
Dynamic Characteristics ◽  
Analytical Solutions ◽  
Stiffness Matrix ◽  
Virtual Work ◽  
Analytic Method ◽  
Curved Beam ◽  
Curved Beams ◽  
Curved Bridges ◽  
Scientific Base

Based on the theory of virtual work and principle of thermal elasticity, exact solutions for in-plane displacements of curved beams with pinned-pinned ends are derived explicitly. In the case of infinite limit of radius, these equations coincide with that of the straight beams. Compared with the results of FEM, the analytical solutions by the proposed formulae are accurate. Basing on the stiffness matrix of statically indeterminate curved beams at three freedom direction, the dynamic characteristics are derived explicitly. The analytic method of dynamic characteristics for curved beam performed in this paper would provide a scientific base for further study and design of the curved bridges.

Isogeometric Free Vibration Analysis of Curved Euler–Bernoulli Beams With Particular Emphasis on Accuracy Study

2020 ◽  
pp. 2150011
Author(s):  
Zhuangjing Sun ◽  
Dongdong Wang ◽  
Xiwei Li
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Convergence Rates ◽  
Harmonic Wave ◽  
Free Vibration Analysis ◽  
Curved Beam ◽  
Curved Beams ◽  
Stiffness Matrices ◽  
Accuracy Measure ◽  
Accuracy Study

An isogeometric free vibration analysis is presented for curved Euler–Bernoulli beams, where the theoretical study of frequency accuracy is particularly emphasized. Firstly, the isogeometric formulation for general curved Euler–Bernoulli beams is elaborated, which fully takes the advantages of geometry exactness and basis function smoothness provided by isogeometric analysis. Subsequently, in order to enable an analytical frequency accuracy study, the general curved beam formulation is particularized to the circular arch problem with constant radius. Under this circumstance, explicit mass and stiffness matrices are derived for quadratic and cubic isogeometric formulations. Accordingly, the coupled stencil equations associated with the axial and deflectional displacements of circular arches are established. By further invoking the harmonic wave assumption, a frequency accuracy measure is rationally attained for isogeometric free analysis of curved Euler–Bernoulli beams, which theoretically reveals that the isogeometric curved beam formulation with [Formula: see text]th degree basis functions is [Formula: see text]th order accurate regarding the frequency computation. Numerical results well confirm the proposed theoretical convergence rates for both circular arches and general curved beams.

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