Variational-Asymptotical Analysis of Initially Curved and Twisted Composite Beams

1993 ◽  
Vol 46 (11S) ◽  
pp. S211-S220 ◽  
Author(s):  
Carlos E. S. Cesnik ◽  
Dewey H. Hodges
Keyword(s):  
Wave Length ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Three Dimensional Representation ◽  
Beam Equations ◽  
Stiffness Model ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity ◽  
Asymptotical Analysis

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotripic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit first-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. Present numerical results show that it is insufficient to account for initial twist and curvature in the beam equations only. The corrections to the stiffness model derived herein are also necessary in general for proper representation of anisotropic beams.

Stiffness Constants for Composite Beams Including Large Initial Twist and Curvature Effects

1995 ◽  
Vol 48 (11S) ◽  
pp. S61-S67 ◽  
Author(s):  
Carlos E. S. Cesnik ◽  
Dewey H. Hodges
Keyword(s):  
Wave Length ◽  
Three Dimensional ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Curvature Effects ◽  
Three Dimensional Representation ◽  
Stiffness Model ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity ◽  
Coupling Phenomena

An asymptotically exact methodology, based on geometrically nonlinear, three-dimensional elasticity, is presented for cross-sectional analysis of initially curved and twisted, nonhomogeneous, anisotropic beams. Through accounting for all possible deformation in the three-dimensional representation, the analysis correctly accounts for the complex elastic coupling phenomena in anisotropic beams associated with shear deformation. The analysis is subject only to the restrictions that the strain is small relative to unity and that the maximum dimension of the cross section is small relative to the wave length of the deformation and to the minimum radius of curvature and/or twist. The resulting cross-sectional elastic constants exhibit second-order dependence on the initial curvature and twist. As is well known, the associated geometrically-exact, one-dimensional equilibrium and kinematical equations also depend on initial twist and curvature. The corrections to the stiffness model derived herein are also necessary in general for proper representation of initially curved and twisted beams.

Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams

2004 ◽  
Vol 71 (1) ◽  
pp. 15-23 ◽  
Author(s):  
Wenbin Yu ◽  
Dewey H. Hodges
Keyword(s):  
Classical Model ◽  
Computational Cost ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Cross Sectional ◽  
Variational Asymptotic ◽  
Dimensional Finite Element ◽  
Elasticity Solutions ◽  
Sectional Analysis ◽  
Three Dimensional Elasticity

The original three-dimensional elasticity problem of isotropic prismatic beams has been solved analytically by the variational asymptotic method (VAM). The resulting classical model (Euler-Bernoulli-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and pure bending in two orthogonal directions. The resulting refined model (Timoshenko-like) is the same as the superposition of elasticity solutions of extension, Saint-Venant torsion, and both bending and transverse shear in two orthogonal directions. The fact that the VAM can reproduce results from the theory of elasticity proves that two-dimensional finite-element-based cross-sectional analyses using the VAM, such as the variational asymptotic beam sectional analysis (VABS), have a solid mathematical foundation. One is thus able to reproduce numerically with VABS the same results for this problem as one obtains from three-dimensional elasticity, but with orders of magnitude less computational cost relative to three-dimensional finite elements.

A Variational-Asymptotic Theory of Smart Slender Structures

Aerospace ◽  
2005 ◽  
Author(s):  
Sitikantha Roy ◽  
Wenbin Yu
Keyword(s):  
Dimensional Analysis ◽  
Piezoelectric Materials ◽  
Three Dimensional ◽  
Reduction Process ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Variational Asymptotic ◽  
Small Parameters ◽  
Sectional Analysis ◽  
Slender Structures

The goal of the present work is to develop an efficient simulation tool with high-fidelity to help the engineers design and analyze smart slender structures with embedded piezoelectric materials. Actuation and sensing capabilities of piezoelectric material embedded in smart beam including geometric nonlinearity will be explored. The dimensional reduction process has been carried out using the powerful Variational Asymptotic Method. Starting from the exact three-dimensional electric-mechanically coupled enthalpy functional, the asymptotical analysis is done on the functional itself with respect to the naturally occurring small parameters. The original three-dimensional electric-mechanical problem of the slender structure is decomposed into two separate problems: a two-dimensional analysis over the cross section and a one-dimensional analysis over the beam reference line. The coupled cross-sectional analysis is being implemented in VABS, a versatile cross-sectional analysis code.

Increased Stiffness of Bioresorbable Plates Following Heating and Three-Dimensional Contouring

2004 ◽  
Author(s):  
Terence E. McIff ◽  
Richard Lark ◽  
Andrea Hilty ◽  
Andrew Cooper ◽  
E. Bruce Toby
Keyword(s):  
Three Dimensional ◽  
Torsional Stiffness ◽  
Radius Of Curvature ◽  
Structural Stiffness ◽  
Metacarpal Fracture ◽  
Cross Sectional ◽  
Fixation Methods ◽  
Metacarpal Bones ◽  
Standard Fixation ◽  
Bioresorbable Plate

A wide copolymer bioresorable plate offers increased structural stiffness following heated contouring of the plate to various diameters which increases its resisting moment of inertia. The increase in bending and torsional stiffness of this design is measured as a function of cross-sectional radius of curvature achieved. Its structural stiffness is compared to three other standard fixation methods used for metacarpal fracture. Substantial increases in stiffness are found after contouring of the wide bioresorbable plate to fit diameters similar to those found in metacarpal bones.

scholarly journals BIOFILM BACTERIA PLAYS A ROLE IN CSOM PATHOGENESIS AND HAS SIGNIFICANT CORRELATION WITH UNSAFE TYPE CSOM

2016 ◽  
Vol 51 (4) ◽  
pp. 208 ◽  
Author(s):  
Artono Artono ◽  
Nyilo Purnami ◽  
Rosydiah Rahmawati
Keyword(s):  
Amorphous Material ◽  
Three Dimensional ◽  
Bacterial Biofilm ◽  
P Value ◽  
Cross Sectional ◽  
Suppurative Otitis Media ◽  
Surface Attachment ◽  
Major Health Problem ◽  
Three Dimensional Representation ◽  
Biofilm Bacteria

Chronic suppurative otitis media (CSOM) may cause severe morbidity and mortality and remains a major health problem worldwide. The incidence of CSOM in Indonesia (1994-1996) is estimated at about 8.36 million people and CSOM general prevalence is 3.8% (Helmi 2005). This study aims to prove the existence of bacterial biofilm in patients with safe type and hazard type CSOM from mastoidectomy. The design was observational analytic with cross sectional approach. This study was conducted at the Teratai Wards, IBP Dr. Soetomo Hospital, and Electron Microscopy Unit, Faculty of Medicine, Airlangga University Surabaya, from November 2013 to June 2014. Samples of pathological tissues were taken by consecutive sampling and bacterial biofilms examination was done by SEM. SEM results categorized the biofilm bacteria as positive or negative. Biofilm bacteria tested positive when it shows three-dimensional representation of bacteria with clear shapes and sizes and clusters, the formation of amorphous material consisting of glycocalyx material surrounding the bacteria, and surface attachment. Biofilm bacteria was regarded as negative when there is no bacterial cluster, glycocalyx and surface attachment. This study was performed on 33 CSOM patients.  Samples were divided into unsafe type CSOM (17 patients) and safe type CSOM (16 patients). Positive biofilm bacteria was found in 12 patients with unsafe type (75%) and 6 patients with safe type (35.35%). Negative biofilm bacteria was found in 4 patients with the unsafe type (25%) and 11 patients with safe type (67.9%). Logistic regression analysis revealed p value = 0.027, indicating the biofilm bacteria have a significant correlation with unsafe type CSOM (p <0.05). In conclusion, biofilm bacteria plays a role in CSOM pathogenesis of biofilm bacteria has significant correlation with unsafe type CSOM.

Generalized Free-Edge Stress Analysis Using Mechanics of Structure Genome

2016 ◽  
Vol 83 (10) ◽  
Author(s):  
Bo Peng ◽  
Johnathan Goodsell ◽  
R. Byron Pipes ◽  
Wenbin Yu
Keyword(s):  
Stress Analysis ◽  
Composite Laminates ◽  
Three Dimensional ◽  
Free Edge ◽  
Stress Fields ◽  
Element Analysis ◽  
Cross Sectional ◽  
Edge Stress ◽  
Out Of Plane ◽  
Sectional Analysis

This work reveals the potential of mechanics of structure genome (MSG) for the free-edge stress analysis of composite laminates. First, the cross-sectional analysis specialized from MSG is formulated for solving a generalized free-edge problem of composite laminates. Then, MSG and the companion code SwiftComp™ are applied to the free-edge stress analysis of several composite laminates with arbitrary layups and general loads including extension, torsion, in-plane and out-of-plane bending, and their combinations. The results of MSG are compared with various existing solutions for symmetric angle-ply laminates. New results are presented for the free-edge stress fields in general laminates for combined mechanical loads and compared with three-dimensional (3D) finite element analysis (FEA) results, which agree very well.

Photon Emission Microscope as a Tool for 3-Dimensional Semiconductor Device Failure Analysis

2012 ◽  
Author(s):  
Steven J. Chun
Keyword(s):  
Failure Analysis ◽  
Semiconductor Device ◽  
Photon Emission ◽  
Three Dimensional ◽  
Analysis Method ◽  
Cross Sectional ◽  
3 Dimensional ◽  
Two Photon ◽  
Processing Times ◽  
Sectional Analysis

Abstract A three dimensional (3-D) photon emission failure analysis method has been developed to pinpoint failure sites or emission sites on the x, y, and z planes of a degraded diode. The 3-D analysis consists of a cross-sectioning step process on two adjacent sides of a diode utilizing two photon emission sites from respective sides of the die as a map. This process negates the uncertainty and long processing times during cross-sectional analysis to find minute defects in diodes.

Component-Based Modeling and Sensitivity Analysis of Composite Beam Cross-Sections

2019 ◽  
Author(s):  
Matteo Scapolan ◽  
Valentin Sonneville ◽  
Alfonso Callejo ◽  
Olivier A. Bauchau
Keyword(s):  
Sensitivity Analysis ◽  
Cross Sections ◽  
Three Dimensional ◽  
Real Life ◽  
Adjoint Sensitivity ◽  
Cross Sectional ◽  
Analysis And Design ◽  
Design And Manufacturing ◽  
Slender Bodies ◽  
Sectional Analysis

Abstract Flexible multibody systems often include slender bodies that can be modeled as beams. In contrast with their three-dimensional counterparts, beam formulations are much more efficient and produce models that are more intuitive from engineering and design standpoints. This paper presents a modular approach for the analysis and design of complex beam cross-sections made of heterogeneous and isotropic materials. This approach builds on previous research by the authors, namely research that dealt with cross-sectional analysis and adjoint sensitivity analysis. In addition to the theoretical and software developments, a number of practical examples are shown and verified. The results show that this parametric approach facilitates the definition, analysis and design of complex beam cross-sections, all of which are necessary components in real-life design and manufacturing.

Small apex-to-base heterogeneity in radius-to-thickness ratio by three-dimensional magnetic resonance imaging

1993 ◽  
Vol 264 (1) ◽  
pp. H133-H140 ◽  
Author(s):  
R. Beyar ◽  
J. L. Weiss ◽  
E. P. Shapiro ◽  
W. L. Graves ◽  
W. J. Rogers ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Ejection Fraction ◽  
Myocardial Function ◽  
Three Dimensional ◽  
Stress Index ◽  
Radius Of Curvature ◽  
Cross Sectional ◽  
Large Variability ◽  
Small Base ◽  
Image Planes

Reported large base-to-apex differences in endocardial area ejection fraction may suggest large variability in myocardial function and load. To test ventricular load heterogeneities, we measured the ratio of radius of curvature to wall thickness (R/T), as a stress index reflecting myocardial load. End-diastolic (ED) and end-systolic (ES) magnetic resonance cross-sectional images were obtained in 15 open-chest dogs at 5 levels from base to apex, from which 4 three-dimensional thick disks were generated from adjacent image planes. The average R/T for each disk was calculated by planar and three-dimensional methods, using both midwall and endocardial radii of curvature. R/T was normalized to the apical value to quantify the relative changes in myocardial load. Normalized R/T using the midwall three-dimensional approach was 1.08, 1.11, 1.06, and 1.0 for ED (P = NS) and 1.25, 1.013, 1.08, and 1.0 for ES (P < 0.02), base to apex, respectively, while the other methods yielded higher values. Therefore, R/T calculated by the three-dimensional midwall approach shows only small apex-to base variations at ED (< 11%) and ES (< 25%), which is substantially less than the variability in area ejection fraction (102%). This suggests only small base-to-apex load heterogeneities, in spite of large changes in the area ejection fraction, an index reflecting specific ventricular geometry rather than local myocardial function.

Determination of leg cross-sectional curvatures and application in pressure prediction for lower body compression garments

2018 ◽  
Vol 89 (10) ◽  
pp. 1835-1852 ◽  
Author(s):  
Rong Liu ◽  
Jundong Liu ◽  
Terence T Lao ◽  
Michael Ying ◽  
Xinbo Wu
Keyword(s):  
Three Dimensional ◽  
Compression Therapy ◽  
Lower Limbs ◽  
Radius Of Curvature ◽  
Compression Stockings ◽  
Cross Sectional ◽  
Compression Garments ◽  
Quantitative Evidence ◽  
Sectional Curvatures ◽  
Peak Pressures

It has been recognized that the cross-sectional curvatures of lower extremities directly influence pressure magnitudes and distributions exerted by compression garments. In the practice of compression therapy, higher peak pressures produced by compression shells occurred at anatomic sites with smaller radius of curvatures and led to side effects and discomfort perception. An effective and operational method to determine leg curvature properties in order to predict pressure performances is desirable to improve comfort and mechanical function of compression garment. By employing three-dimensional (3D) digital anthropometry and two-dimensional (2D) digital image simulation, the curvatures and radius of curvatures of a total of 300 cross-sectional slices involving 1200 anatomic sites along the lower limbs were determined onto the ten healthy female subjects when they were and were not wearing compression stockings. Based on the determined cross-sectional characteristics, the skin pressures were calculated using the circumference-based and the radius of curvature-based Laplace’s equations, respectively, which were further validated against the experimental skin pressures measured by a PicoPress transducer. This study provided quantitative evidence in the exploration of the working mechanisms of uneven pressures produced by compression garments, and established a standardized method to determine cross-section-related curvature characteristics for pressure assessment and prediction, which will contribute to improving user compliance of compression garments in long-term wear.

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