Modeling and Experimentation of a Ribbed Caudal Fin for Aquatic Robots

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2017-71235 ◽

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.

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Development of an Adjustable Frequency Device for a Test Vehicle Based on Curved Beam Theory

WSEAS TRANSACTIONS ON ACOUSTICS AND MUSIC ◽

10.37394/232019.2021.8.2 ◽

2021 ◽

Vol 8 ◽

pp. 5-8

Author(s):

J. D. Yau ◽

S. Urushadze

Keyword(s):

Experimental Studies ◽

Beam Theory ◽

Frequency Measurement ◽

Curved Beam ◽

Beam Model ◽

Lumped Mass ◽

Test Beam ◽

Test Vehicle ◽

Instrumented Vehicle ◽

Thin Beams

In this article, an adjustable frequency device based on curved beam theory is designed to control vertical stiffness of an instrumented vehicle that it can detect dynamic data when moving on a test beam for frequency measurement. The adjustable frequency device consists of a set of two-layer cantilever semi-circular thin-beams to support a lumped mass for vibrations, in which a rotatable U-frame is used to change its subtended angle for adjustment of the supporting stiffness and corresponding vertical frequencies of the vehicle. Based on curved beam theory, an analytical frequency equation of the single-degree-of-freedom test vehicle was derived and applied to mobile frequency measurement of a simple beam. To determine the sectional rigidity of the semi-circular thin-beams, both theoretical and experimental studies were be carried out in the ITAM laboratory of the Academy of Science in Czech. The analytical and experimental results indicated that the present semi-circular beam model with guided ends is applicable to prediction of natural frequencies of the test vehicle considering different supporting stiffness

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

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0790 ◽

2016 ◽

Vol 472 (2185) ◽

pp. 20150790 ◽

Cited By ~ 177

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.

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BEAM ELEMENT UNDER FINITE ROTATIONS

Acta Polytechnica CTU Proceedings ◽

10.14311/app.2021.30.0087 ◽

2021 ◽

Vol 30 ◽

pp. 87-92

Author(s):

Emma La Malfa Ribolla ◽

Milan Jirásek ◽

Martin Horák

Keyword(s):

Cross Sections ◽

Shooting Method ◽

Small Strain ◽

Beam Model ◽

Equilibrium Equations ◽

Finite Rotations ◽

Nonlinear Beam ◽

Linear Elastic ◽

Beam Elements ◽

Large Rotations

The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law.The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

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Static analysis of wind turbine blade using 1D FE model

International Journal of Engineering Science and Technology ◽

10.4314/ijest.v13i1.19s ◽

2021 ◽

Vol 13 (1) ◽

pp. 125-130

Author(s):

Tushar Sharma ◽

V. Murari ◽

K.K. Shukla

Keyword(s):

Wind Turbine ◽

Beam Theory ◽

Fe Model ◽

Beam Model ◽

Static Response ◽

Order Polynomial ◽

1D Model ◽

Twisting Angle ◽

Blade Model ◽

Fourth Order Polynomial

The study presents a unique technique to determine the static response of wind turbine (WT) blade. A 1D Finite element (FE) beam model of WT blade is developed using thin-walled beam theory coupled with PreComp tool used to compute crosssectional stiffness with elastic coupling effects. A realistic 9.2 m long, WT blade is developed using different aerofoils with fourth order polynomial variation for twisting angle of blade span. Three different aerfoil sections NREL S818, NREL S825, and NACA 2412 are employed in the current study. For validation, the results of 1D model developed using MATLAB are compared with that of 3D WT blade model which is analyzed in ANSYS using NuMAD..

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Mechanics of Bimaterial Interface: Shear Deformable Split Bilayer Beam Theory and Fracture

Journal of Applied Mechanics ◽

10.1115/1.1978920 ◽

2005 ◽

Vol 72 (5) ◽

pp. 674-682 ◽

Cited By ~ 12

Author(s):

Jialai Wang ◽

Pizhong Qiao

Keyword(s):

Finite Element Analysis ◽

Composite Beam ◽

Present Model ◽

Local Buckling ◽

Crack Tip ◽

Beam Theory ◽

Local Deformation ◽

Beam Model ◽

Element Analysis ◽

Shear Deformable

A novel split beam model is introduced to account for the local effects at the crack tip of bi-material interface by modeling a bi-layer composite beam as two separate shear deformable beams bonded perfectly along their interface. In comparisons with analytical two-dimensional continuum solutions and finite element analysis, better agreements are achieved for the present model, which is capable of capturing the local deformation at the crack tip in contrast to the conventional composite beam theory. New solutions of two important issues of cracked beams, i.e., local buckling and interface fracture, are then presented based on the proposed split bi-layer shear deformable beam model. Local buckling load of a delaminated beam considering the root rotation at the delamination tip is first obtained. By considering the root rotation at the crack tip, the buckling load is lower than the existing solution neglecting the local deformation at the delamination tip. New expressions of energy release rate and stress intensity factor considering the transverse shear effect are obtained by the solution of local deformation based on the novel split beam model, of which several new terms associated with the transverse shear force are present, and they represent an improved solution compared to the one from the classical beam model. Two specimens are analyzed with the present model, and the corresponding refined fracture parameters are provided, which are in better agreement with finite element analysis compared to the available classical solutions.

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Coupled Deformation Modes in the Large Deformation Finite-Element Analysis: Problem Definition

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.2447353 ◽

2006 ◽

Vol 2 (2) ◽

pp. 146-154 ◽

Cited By ~ 22

Author(s):

Bassam A. Hussein ◽

Hiroyuki Sugiyama ◽

Ahmed A. Shabana

Keyword(s):

Large Deformation ◽

Cross Section ◽

Flexible Structures ◽

Beam Theory ◽

Problem Definition ◽

Beam Model ◽

Element Analysis ◽

Elastic Line ◽

The Cross ◽

Deformation Modes

In the classical formulations of beam problems, the beam cross section is assumed to remain rigid when the beam deforms. In Euler–Bernoulli beam theory, the rigid cross section remains perpendicular to the beam centerline; while in the more general Timoshenko beam theory the rigid cross section is permitted to rotate due to the shear deformation, and as a result, the cross section can have an arbitrary rotation with respect to the beam centerline. In more general beam models as the ones based on the absolute nodal coordinate formulation (ANCF), the cross section is allowed to deform and it is no longer treated as a rigid surface. These more general models lead to new geometric terms that do not appear in the classical formulations of beams. Some of these geometric terms are the result of the coupling between the deformation of the cross section and other modes of deformations such as bending and they lead to a new set of modes referred to in this paper as the ANCF-coupled deformation modes. The effect of the ANCF-coupled deformation modes can be significant in the case of very flexible structures. In this investigation, three different large deformation dynamic beam models are discussed and compared in order to investigate the effect of the ANCF-coupled deformation modes. The three methods differ in the way the beam elastic forces are calculated. The first method is based on a general continuum mechanics approach that leads to a model that includes the ANCF-coupled deformation modes; while the second method is based on the elastic line approach that systematically eliminates these modes. The ANCF-coupled deformation modes eliminated in the elastic line approach are identified and the effect of such deformation modes on the efficiency and accuracy of the numerical solution is discussed. The third large deformation beam model discussed in this investigation is based on the Hellinger–Reissner principle that can be used to eliminate the shear locking encountered in some beam models. Numerical examples are presented in order to demonstrate the use and compare the results of the three different beam formulations. It is shown that while the effect of the ANCF-coupled deformation modes is not significant in very stiff and moderately stiff structures, the effect of these modes can not be neglected in the case of very flexible structures.

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Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽

10.3390/nano11040923 ◽

2021 ◽

Vol 11 (4) ◽

pp. 923

Author(s):

Kun Huang ◽

Ji Yao

Keyword(s):

Mechanical Properties ◽

Carbon Nanotubes ◽

Beam Theory ◽

Bending Stiffness ◽

Single Wall Carbon Nanotubes ◽

Beam Model ◽

Euler Beam ◽

New Model ◽

Mechanical Coupling ◽

Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

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INHOMOGENEOUS LARGE DEFORMATION KINETICS OF POLYMERIC GELS

International Journal of Applied Mechanics ◽

10.1142/s1758825113500014 ◽

2013 ◽

Vol 05 (01) ◽

pp. 1350001 ◽

Cited By ~ 45

Author(s):

WILLIAM TOH ◽

ZISHUN LIU ◽

TENG YONG NG ◽

WEI HONG

Keyword(s):

Large Deformation ◽

Soft Matter ◽

Inner Core ◽

Kinetic Studies ◽

Fe Model ◽

One Dimensional ◽

Simplified Approach ◽

Deformation Kinetics ◽

Polymeric Gels ◽

Kinetics Of

This work examines the dynamics of nonlinear large deformation of polymeric gels, and the kinetics of gel deformation is carried out through the coupling of existing hyperelastic theory for gels with kinetic laws for diffusion of small molecules. As finite element (FE) models for the transient swelling process is not available in commercial FE software, we develop a customized FE model/methodology which can be used to simulate the transient swelling process of hydrogels. The method is based on the similarity between diffusion and heat transfer laws by determining the equivalent thermal properties for gel kinetics. Several numerical examples are investigated to explore the capabilities of the present FE model, namely: a cube to study free swelling; one-dimensional constrained swelling; a rectangular block fixed to a rigid substrate to study swelling under external constraints; and a thin annulus fixed at the inner core to study buckling phenomena. The simulation results for the constrained block and one-dimensional constrained swelling are compared with available experimental data, and these comparisons show a good degree of similarity. In addition to this work providing a valuable tool to researchers for the study of gel kinetic deformation in the various applications of soft matter, we also hope to inspire works to adopt this simplified approach, in particular to kinetic studies of diffusion-driven mechanisms.

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