Three-Dimensional Beam Element Based on a Cross-Sectional Coordinate System Approach

2006 ◽  
Vol 43 (4) ◽  
pp. 311-327 ◽  
Author(s):  
Kari E. Dufva ◽  
Jussi T. Sopanen ◽  
Aki M. Mikkola
Keyword(s):  
Coordinate System ◽  
System Approach ◽  
Three Dimensional ◽  
Beam Element ◽  
Cross Sectional

A New Three-Dimensional Moving Timoshenko Beam Element for Moving Load Problem Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yan Xu ◽  
Weidong Zhu ◽  
Wei Fan ◽  
Caijing Yang ◽  
Weihua Zhang
Keyword(s):  
Dynamic Analysis ◽  
Coordinate System ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Three Dimensional ◽  
Beam Element ◽  
Superposition Method ◽  
Reference Coordinate System ◽  
Current Formulation ◽  
Timoshenko Beam Element

Abstract A new three-dimensional moving Timoshenko beam element is developed for dynamic analysis of a moving load problem with a very long beam structure. The beam has small deformations and rotations, and bending, shear, and torsional deformations of the beam are considered. Since the dynamic responses of the beam are concentrated on a small region around the moving load and most of the long beam is at rest, owing to the damping effect, the beam is truncated with a finite length. A control volume that is attached to the moving load is introduced, which encloses the truncated beam, and a reference coordinate system is established on the left end of the truncated beam. The arbitrary Lagrangian–Euler method is used to describe the relationship of the position of a particle on the beam between the reference coordinate system and the global coordinate system. The truncated beam is spatially discretized using the current beam elements. Governing equations of a moving element are derived using Lagrange’s equations. While the whole beam needs to be discretized in the finite element method or modeled in the modal superposition method (MSM), only the truncated beam is discretized in the current formulation, which greatly reduces degrees-of-freedom and increases the efficiency. Furthermore, the efficiency of the present beam element is independent of the moving load speed, and the critical or supercritical speed range of the moving load can be analyzed through the present method. After the validation of the current formulation, a dynamic analysis of three-dimensional train–track interaction with a non-ballasted track is conducted. Results are in excellent agreement with those from the commercial software simpack where the MSM is used, and the calculation time of the current formulation is one-third of that of simpack. The current beam element is accurate and more efficient than the MSM for moving load problems of long three-dimensional beams. The derivation of the current beam element is straightforward, and the beam element can be easily extended for various other moving load problems.

A super-convergent thin-walled 3D beam element for analysis of laminated composite structures with arbitrary cross-section

2021 ◽  
pp. 1-23
Author(s):  
M. Talele ◽  
M. van Tooren ◽  
A. Elham
Keyword(s):  
Cross Sections ◽  
Composite Structures ◽  
Three Dimensional ◽  
Laminated Composite ◽  
Beam Element ◽  
Arbitrary Cross Section ◽  
Beam Model ◽  
Cross Sectional ◽  
Thin Walled ◽  
The Cross

Abstract An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

scholarly journals An Analytical Formulation for the Lateral Support Stiffness of a Spatial Flexure Strip

2015 ◽  
Author(s):  
Marijn Nijenhuis ◽  
J. P. Meijaard ◽  
Just L. Herder ◽  
Shorya Awtar ◽  
Dannis M. Brouwer
Keyword(s):  
Three Dimensional ◽  
Beam Element ◽  
Element Analysis ◽  
Cross Sectional ◽  
Flexure Mechanism ◽  
Stiffness Properties ◽  
Spatial Beam ◽  
Discrete Nature ◽  
Stiffness Characteristics

A flexure strip has constraint characteristics, such as stiffness properties and error motions, that limit its performance as a basic constituent of flexure mechanisms. This paper presents a framework for modeling the deformation and stiffness characteristics of general three-dimensional flexure strips that exhibit bending, shear and torsion deformation. The formulation is based on a finite strain discrete spatial beam element with refinements to account for plate-like behavior due to constrained cross-sectional warping. This framework is suited for analytical calculations thanks to the accuracy of the beam element, while its discrete nature allows for easy implementation in numeric software to serve as calculation aid. As case study, a closed-form parametric analytical expression is derived for the lateral support stiffness of a parallel flexure mechanism. This captures the deteriorating support stiffness when the mechanism moves in the intended degree of freedom. By incorporating relevant geometric nonlinearities and a warping constraint stiffening factor, an accurate load-displacement and stiffness expression for the lateral support direction is obtained. This result is verified by nonlinear finite element analysis.

Automatic 6-D.O.F. Kinematic Trajectory Acquisition and Analysis

1989 ◽  
Vol 111 (1) ◽  
pp. 31-39 ◽  
Author(s):  
E. K. Antonsson ◽  
R. W. Mann
Keyword(s):  
Coordinate System ◽  
Detailed Analysis ◽  
Camera Calibration ◽  
System Approach ◽  
Three Dimensional ◽  
Spatial Accuracy ◽  
Independent Verification ◽  
Position And Orientation

An optoelectronic photogrammetric system to measure the spatial kinematic histories of linkages is presented. A Body Coordinate System approach produces both three-dimensional position and orientation trajectories with no singularities for any rotation. Bandwidth is in excess of 300 Hz for each of 10 link elements. A detailed analysis and measurement of the intrinsic camera calibration corrections has been performed using 12,000 calibration points per camera. An independent verification of spatial accuracy has been performed.

Computer Analysis of Three-Dimensional Turbulent Flows around Ships' Hulls

1980 ◽  
Vol 194 (1) ◽  
pp. 239-248 ◽  
Author(s):  
N. C. Markatos ◽  
M. R. Malin ◽  
D. G. Tatchell
Keyword(s):  
Differential Equations ◽  
Coordinate System ◽  
Turbulent Flows ◽  
Solution Method ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Grid Method ◽  
Solution Procedure ◽  
The Body ◽  
Cross Sectional

This paper describes a general solution method for three-dimensional, steady, turbulent flows around long, smoothly-shaped bodies, of arbitrary and varying cross-sectional shape. The particular example considered here concerns the flow around the hull of a ship, but the method can equally well be applied to other, similarly shaped bodies such as an aircraft fuselage, or a submarine. Moreover, the basic non-orthogonal grid method described can also be applied to internal flows in irregular shaped passages, or to the prediction of flows around bodies in ducts. The mathematical model consists of the partial differential equations for continuity and three components of momentum, along with a two-equation model of turbulence, and proper modelling of the ship's hull. The solution method utilizes a non-orthogonal coordinate system in the plane normal to the axis of the body, which has one coordinate surface coinciding with the hull surface. This coordinate system is flexible and is easily modified to enable the calculation procedure to handle bulbous ships' hulls, which are of great importance in modern ship design. The differential equations involved are solved numerically after provision of the proper boundary and initial conditions. The solution procedure is a unique one, called ‘partially-parabolic’, as first used by Pratap and Spalding (1). Solutions are presented for flow around ships' hulls, which demonstrate the physical realism of the achieved results and the potential of the present method.

scholarly journals Accuracy and Reproducibility of Facial Measurements of Digital Photographs and Wrapped Cone Beam Computed Tomography (CBCT) Photographs

Diagnostics ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 757
Author(s):  
Maged Sultan Alhammadi ◽  
Abeer Abdulkareem Al-mashraqi ◽  
Rayid Hussain Alnami ◽  
Nawaf Mohammad Ashqar ◽  
Omar Hassan Alamir ◽  
...  
Keyword(s):  
Computed Tomography ◽  
Soft Tissue ◽  
Cone Beam Computed Tomography ◽  
High Reliability ◽  
Three Dimensional ◽  
Cone Beam ◽  
Cross Sectional ◽  
Facial Profile ◽  
Digital Photographs ◽  
Gonial Angle

The study sought to assess whether the soft tissue facial profile measurements of direct Cone Beam Computed Tomography (CBCT) and wrapped CBCT images of non-standardized facial photographs are accurate compared to the standardized digital photographs. In this cross-sectional study, 60 patients with an age range of 18–30 years, who were indicated for CBCT, were enrolled. Two facial photographs were taken per patient: standardized and random (non-standardized). The non-standardized ones were wrapped with the CBCT images. The most used soft tissue facial profile landmarks/parameters (linear and angular) were measured on direct soft tissue three-dimensional (3D) images and on the photographs wrapped over the 3D-CBCT images, and then compared to the standardized photographs. The reliability analysis was performed using concordance correlation coefficients (CCC) and depicted graphically using Bland–Altman plots. Most of the linear and angular measurements showed high reliability (0.91 to 0.998). Nevertheless, four soft tissue measurements were unreliable; namely, posterior gonial angle (0.085 and 0.11 for wrapped and direct CBCT soft tissue, respectively), mandibular plane angle (0.006 and 0.0016 for wrapped and direct CBCT soft tissue, respectively), posterior facial height (0.63 and 0.62 for wrapped and direct CBCT soft tissue, respectively) and total soft tissue facial convexity (0.52 for both wrapped and direct CBCT soft tissue, respectively). The soft tissue facial profile measurements from either the direct 3D-CBCT images or the wrapped CBCT images of non-standardized frontal photographs were accurate, and can be used to analyze most of the soft tissue facial profile measurements.

scholarly journals A Numerical Study of Sub-Millisecond Integrated Mix-and-Inject Microfluidic Devices for Sample Delivery at Synchrotron and XFELs

2021 ◽  
Vol 11 (8) ◽  
pp. 3404
Author(s):  
Majid Hejazian ◽  
Eugeniu Balaur ◽  
Brian Abbey
Keyword(s):  
Molecular Dynamics ◽  
Flow Rate ◽  
Numerical Study ◽  
Three Dimensional ◽  
Microfluidic Devices ◽  
Liquid Jets ◽  
Mixing Efficiency ◽  
X Ray Diffraction ◽  
Cross Sectional ◽  
Time Required

Microfluidic devices which integrate both rapid mixing and liquid jetting for sample delivery are an emerging solution for studying molecular dynamics via X-ray diffraction. Here we use finite element modelling to investigate the efficiency and time-resolution achievable using microfluidic mixers within the parameter range required for producing stable liquid jets. Three-dimensional simulations, validated by experimental data, are used to determine the velocity and concentration distribution within these devices. The results show that by adopting a serpentine geometry, it is possible to induce chaotic mixing, which effectively reduces the time required to achieve a homogeneous mixture for sample delivery. Further, we investigate the effect of flow rate and the mixer microchannel size on the mixing efficiency and minimum time required for complete mixing of the two solutions whilst maintaining a stable jet. In general, we find that the smaller the cross-sectional area of the mixer microchannel, the shorter the time needed to achieve homogeneous mixing for a given flow rate. The results of these simulations will form the basis for optimised designs enabling the study of molecular dynamics occurring on millisecond timescales using integrated mix-and-inject microfluidic devices.

scholarly journals The patellofemoral morphology and the normal predicted value of tibial tuberosity-trochlear groove distance in the Chinese population

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Zhe Li ◽  
Guanzhi Liu ◽  
Run Tian ◽  
Ning Kong ◽  
Yue Li ◽  
...  
Keyword(s):  
Individual Differences ◽  
Chinese Population ◽  
Pearson Correlation ◽  
Three Dimensional ◽  
Correlation Coefficients ◽  
Tibial Tuberosity ◽  
Trochlear Groove ◽  
Lasso Regression ◽  
Cross Sectional ◽  
Anterior Posterior

Abstract Background Our objective was to obtain normal patellofemoral measurements to analyse sex and individual differences. In addition, the absolute values and indices of tibial tuberosity-trochlear groove (TT-TG) distances are still controversial in clinical application. A better method to enable precise prediction is still needed. Methods Seventy-eight knees of 78 participants without knee pathologies were included in this cross-sectional study. A CT scan was conducted for all participants and three-dimensional knee models were constructed using Mimics and SolidWorks software. We measured and analysed 19 parameters including the TT-TG distance and dimensions and shapes of the patella, femur, tibia, and trochlea. LASSO regression was used to predict the normal TT-TG distances. Results The dimensional parameters, TT-TG distance, and femoral aspect ratio of the men were significantly larger than those of women (all p values < 0.05). However, after controlling for the bias from age, height, and weight, there were no significant differences in TT-TG distances and anterior-posterior dimensions between the sexes (all p values > 0.05). The Pearson correlation coefficients between the anterior femoral offset and other indexes were consistently below 0.3, indicating no relationship or a weak relationship. Similar results were observed for the sulcus angle and the Wiberg index. Using LASSO regression, we obtained four parameters to predict the TT-TG distance (R2 = 0.5612, p < 0.01) to achieve the optimal accuracy and convenience. Conclusions Normative data of patellofemoral morphology were provided for the Chinese population. The anterior-posterior dimensions of the women were thicker than those of men for the same medial-lateral dimensions. More attention should be paid to not only sex differences but also individual differences, especially the anterior condyle and trochlea. In addition, this study provided a new method to predict TT-TG distances accurately.

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