scholarly journals Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150790 ◽  
Author(s):  
F. dell’Isola ◽  
I. Giorgio ◽  
M. Pawlikowski ◽  
N. L. Rizzi
Keyword(s):  
Large Deformations ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Computationally Efficient ◽  
Nonlinear Beam ◽  
Pantographic Structures ◽  
Diffusion Of Technology ◽  
Second Gradient

The aim of this paper is to find a computationally efficient and predictive model for the class of systems that we call ‘pantographic structures’. The interest in these materials was increased by the possibilities opened by the diffusion of technology of three-dimensional printing. They can be regarded, once choosing a suitable length scale, as families of beams (also called fibres) interconnected to each other by pivots and undergoing large displacements and large deformations. There are, however, relatively few ‘ready-to-use’ results in the literature of nonlinear beam theory. In this paper, we consider a discrete spring model for extensible beams and propose a heuristic homogenization technique of the kind first used by Piola to formulate a continuum fully nonlinear beam model. The homogenized energy which we obtain has some peculiar and interesting features which we start to describe by solving numerically some exemplary deformation problems. Furthermore, we consider pantographic structures, find the corresponding homogenized second gradient deformation energies and study some planar problems. Numerical solutions for these two-dimensional problems are obtained via minimization of energy and are compared with some experimental measurements, in which elongation phenomena cannot be neglected.

Modeling and Experimentation of a Ribbed Caudal Fin for Aquatic Robots

2017 ◽  
Author(s):  
Oscar Rios ◽  
Ardavan Amini ◽  
Hidenori Murakami
Keyword(s):  
Large Deformation ◽  
Beam Theory ◽  
Fe Model ◽  
Beam Model ◽  
Caudal Fin ◽  
Nonlinear Beam ◽  
Beam Elements ◽  
Side Walls ◽  
Thin Beams ◽  
Shear Deformable

Presented in this study is a mathematical model and preliminary experimental results of a ribbed caudal fin to be used in an aquatic robot. The ribbed caudal fin is comprised of two thin beams separated by ribbed sectionals as it tapers towards the fin. By oscillating the ribbed caudal fin, the aquatic robot can achieve forward propulsion and maneuver around its environment. The fully enclosed system allows for the aquatic robot to have very little effect on marine life and fully blend into its respective environment. Because of these advantages, there are many applications including surveillance, sensing, and detection. Because the caudal fin actuator has very thin side walls, Kirchhoff-Love’s large deformation beam theory is applicable for the large deformation of the fish-fin actuator. In the model, it is critical to accurately model the curvature of beams. To this end, C1 beam elements for thin beams are developed by specializing the shear-deformable beam elements, developed by the authors, based upon Reissner’s shear-deformable nonlinear beam model. Furthermore, preliminary experiments on the ribbed fin are presented to supplement the FE model.

scholarly journals Thermally Induced Deformations in Nuclear Fuel Elements

2021 ◽  
Author(s):  
Haihui (Stella) Yang
Keyword(s):  
Fuel Element ◽  
Transfer Factor ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Beam Theory ◽  
Operating Conditions ◽  
Operational Parameters ◽  
Thermally Induced ◽  
Sensitivity Studies ◽  
Fuel Elements

Nonlinear three-dimensional multibody surface-surface contacts, thermally induced deformations, and the curvature transfer factor in CANDU fuel elements are investigated using the finite element method in this thesis. ANSYS is selected to obtain numerical solutions for CANDU fuel elements under several operating conditions. In the ANSYS models, the 20-node structural elements (SOLID186) are employed to mesch individual solids; the surface-to surface contact pairs (TARGE170 and CONTA174) are used to handle contacts between solids. Sensitivity studies on the curvature transfer factor are conducted for several key operational parameters. If there is full radial contact between the pellets and the sheath, a CANDU fuel element may be considered as a composite beam because of the large length-to-diameter ratio. The Timoshenko beam theory is used in conjunction with a three-node mean element to explore the thermal deformation behaviours of a fuel element. A program written in MATLAB is much more efficient compared with the ANSYS solutions.

Integrability Conditions in Nonlinear Beam Kinematics

2016 ◽  
Author(s):  
Hidenori Murakami
Keyword(s):  
Virtual Work ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Moving Frame ◽  
Beam Model ◽  
Mathematical Tool ◽  
Nonlinear Beam ◽  
Differentiable Manifolds ◽  
Beam Equations ◽  
Integrability Conditions

In order to develop an active nonlinear beam model, the beam’s kinematics is examined by employing the kinematic assumption of a rigid cross section during deformation. As a mathematical tool, the moving frame method, developed by Élie Cartan (1869–1951) on differentiable manifolds, is utilized by treating a beam as a frame bundle on a deforming centroidal curve. As a result, three new integrability conditions are obtained, which play critical roles in the derivation of beam equations of motion. They also serve a role in a geometrically-exact finite-element implementation of beam models. These integrability conditions enable the derivation of beam models starting from the three-dimensional Hamilton’s principle and the d’Alembert principle of virtual work. Finally, the reconstruction scheme for rotation matrices for given angular velocity at each time is presented.

scholarly journals Bending and free vibrational analysis of bi-directional functionally graded beams with circular cross-section

2020 ◽  
Vol 41 (10) ◽  
pp. 1497-1516 ◽  
Author(s):  
Yong Huang
Keyword(s):  
Three Dimensional ◽  
Circular Cross Section ◽  
Vibrational Analysis ◽  
Beam Theory ◽  
Single Equation ◽  
Auxiliary Function ◽  
Functionally Graded ◽  
Beam Model ◽  
Various Boundary Conditions ◽  
Differential Motion

Abstract The bending and free vibrational behaviors of functionally graded (FG) cylindrical beams with radially and axially varying material inhomogeneities are investigated. Based on a high-order cylindrical beam model, where the shear deformation and rotary inertia are both considered, the two coupled governing differential motion equations for the deflection and rotation are established. The analytical bending solutions for various boundary conditions are derived. In the vibrational analysis of FG cylindrical beams, the two governing equations are firstly changed to a single equation by means of an auxiliary function, and then the vibration mode is expanded into shifted Chebyshev polynomials. Numerical examples are given to investigate the effects of the material gradient indices on the deflections, the stress distributions, and the eigenfrequencies of the cylindrical beams, respectively. By comparing the obtained numerical results with those obtained by the three-dimensional (3D) elasticity theory and the Timoshenko beam theory, the effectiveness of the present approach is verified.

On the dynamics of a massless beam with end mass rotating in the three-dimensional space

2012 ◽  
Vol 227 (3) ◽  
pp. 434-448 ◽  
Author(s):  
Giancarlo Genta
Keyword(s):  
Rotation Axis ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Inertial Reference Frame ◽  
Centrifugal Stiffening ◽  
Constant Rate ◽  
Fixed Axis ◽  
Three Dimensional Space

Many elements of machines, like shafts, blades, connecting rods, etc., are often modeled using the so-called beam theory and, when these elements rotate with respect to an inertial reference frame, this rotation can deeply affect their dynamic behavior. The position of the beam with respect to the rotation axis and the possibility that the rotation is more complicated than a simple constant-rate rotation about a fixed axis influence this effect, and different models are usually employed. As a result, different phenomena, like gyroscopic effect, centrifugal stiffening or softening, and instability due to rotation are often mentioned in reference to the different cases. The aim of this article is that of building a much simplified beam model, and to subject it to a compound, nonconstant rate rotation. Since the model can be solved in closed form, at least in several cases, a general discussion of the revant phenomena can be done to shed some light on some aspects, like the instability ranges due to rotation and to the damping of the system.

scholarly journals Thermally Induced Deformations in Nuclear Fuel Elements

2021 ◽  
Author(s):  
Haihui (Stella) Yang
Keyword(s):  
Fuel Element ◽  
Transfer Factor ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Beam Theory ◽  
Operating Conditions ◽  
Operational Parameters ◽  
Thermally Induced ◽  
Sensitivity Studies ◽  
Fuel Elements

Nonlinear three-dimensional multibody surface-surface contacts, thermally induced deformations, and the curvature transfer factor in CANDU fuel elements are investigated using the finite element method in this thesis. ANSYS is selected to obtain numerical solutions for CANDU fuel elements under several operating conditions. In the ANSYS models, the 20-node structural elements (SOLID186) are employed to mesch individual solids; the surface-to surface contact pairs (TARGE170 and CONTA174) are used to handle contacts between solids. Sensitivity studies on the curvature transfer factor are conducted for several key operational parameters. If there is full radial contact between the pellets and the sheath, a CANDU fuel element may be considered as a composite beam because of the large length-to-diameter ratio. The Timoshenko beam theory is used in conjunction with a three-node mean element to explore the thermal deformation behaviours of a fuel element. A program written in MATLAB is much more efficient compared with the ANSYS solutions.

scholarly journals Effects of geometric nonlinearity in an adhered microbeam for measuring the work of adhesion

2018 ◽  
Vol 474 (2211) ◽  
pp. 20170594
Author(s):  
Wenqiang Fang ◽  
Joyce Mok ◽  
Haneesh Kesari
Keyword(s):  
Three Dimensional ◽  
Beam Theory ◽  
Work Of Adhesion ◽  
Element Analysis ◽  
Nonlinear Beam ◽  
Force Microscopy ◽  
Atomic Force ◽  
Microelectromechanical Devices ◽  
The One ◽  
Good Agreement

Design against adhesion in microelectromechanical devices is predicated on the ability to quantify this phenomenon in microsystems. Previous research related the work of adhesion for an adhered microbeam to the beam's unadhered length, and as such, interferometric techniques were developed to measure that length. We propose a new vibration-based technique that can be easily implemented with existing atomic force microscopy tools or similar metrology systems. To make such a technique feasible, we analysed a model of the adhered microbeam using the nonlinear beam theory put forth by Woinowsky–Krieger. We found a new relation between the work of adhesion and the unadhered length; this relation is more accurate than the one by Mastrangelo & Hsu (Mastrangelo & Hsu 1993 J. Microelectromech. S. , 2 , 44–55. ( doi:10.1109/84.232594 )) which is commonly used. Then, we derived a closed-form approximate relationship between the microbeam's natural frequency and its unadhered length. Results obtained from this analytical formulation are in good agreement with numerical results from three-dimensional nonlinear finite-element analysis.

Two and Three Dimensional Image Registration Based on B-Spline Composition and Level Sets

2017 ◽  
Vol 21 (2) ◽  
pp. 600-622 ◽  
Author(s):  
Chiu Ling Chan ◽  
Cosmin Anitescu ◽  
Yongjie Zhang ◽  
Timon Rabczuk
Keyword(s):  
Signal Processing ◽  
Image Registration ◽  
Level Sets ◽  
Large Deformations ◽  
Three Dimensional ◽  
Computationally Efficient ◽  
3D Images ◽  
B Spline ◽  
Different Types ◽  
2D And 3D

AbstractAmethod for non-rigid image registration that is suitable for large deformations is presented. Conventional registration methods embed the image in a B-spline object, and the image is evolved by deforming the B-spline object. In this work, we represent the image using B-spline and deform the image using a composition approach. We also derive a computationally efficient algorithm for calculating the B-spline coefficients and gradients of the image by adopting ideas from signal processing using image filters. We demonstrate the application of our method on several different types of 2D and 3D images and compare it with existing methods.

Aeroelastic Modelling of Three-Dimensional Lifting Bodies With an Accelerated Boundary Element Method

2020 ◽  
Author(s):  
Ludwig Könnecke ◽  
Joseph Saverin
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Analytical Model ◽  
Lift Force ◽  
Structural Model ◽  
Three Dimensional ◽  
Beam Theory ◽  
Beam Model ◽  
Set Up ◽  
Element Method

Abstract Investigated was the aeroelastic treatment of a three-dimensional NACA0006 wing by coupling the boundary element method (panel method) for the aerodynamic solution with a beam model (Chrono) for the structural-elastic solution to obtain an aeroelastic solution. Aerodynamic information is interpolated to the structural model by using radial basis functions. As a validation case an analytical model was set up by calculating the lift force from the lifting-line theory and the resulting deflection and torsion predicted with a linear beam theory. This analytical model considers a purely torsional aeroelastic case which is comparable with the simulation results. The distribution of the lift force over the span position of the simulation and the analytical model agrees well, particularly in comparison to the purely torsional case.

Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

2009 ◽  
Vol 37 (2) ◽  
pp. 62-102 ◽  
Author(s):  
C. Lecomte ◽  
W. R. Graham ◽  
D. J. O’Boy
Keyword(s):  
Internal Pressure ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Prediction Method ◽  
Analytical Models ◽  
Beam Model ◽  
Impedance Boundary ◽  
Bending Waves ◽  
Tire Rotation ◽  
Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

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