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

2006 ◽  
Vol 2 (2) ◽  
pp. 146-154 ◽  
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.

Absolute Nodal Coordinate Formulation Coupled Deformation Modes

2006 ◽  
Author(s):  
Bassam A. Hussein ◽  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Structures ◽  
Mindlin Plate ◽  
Elastic Line ◽  
Absolute Nodal Coordinate ◽  
Geometric Stiffening ◽  
General Continuum ◽  
Deformation Modes

The finite element absolute nodal coordinate formulation (ANCF) leads to beam and plate models that relax the assumption of the classical Euler-bernoulli and Timoshenko beam and Mindlin plate theories. In these more general models, the cross section is allowed to deform and it is no longer treated as a rigid surface. The coupling between the bending and cross section deformations leads to the new ANCF-coupled deformation modes that are examined in this study. While these coupled deformation can be source of numerical and convergence problems when thin and stiff beam models are considered, the inclusion of the effect of these modes in the dynamic model is necessary in the case of very flexible structures. In order to examine the effect of these coupled deformation modes in this investigation, three different large deformation dynamic beam models are discussed. Two of these models, which differ in the way the beam elastic forces are calculated in the absolute nodal coordinate formulation, allow for systematically eliminating the coupled deformation modes, while the third allows for including these modes. The first of these models is based on a general continuum mechanics approach that leads to a model that includes the ANCF-coupled deformation modes; while the second and third methods that can be used to eliminate the coupled deformation modes are based on the elastic line approach and the Hellinger-Reissner principle. It is shown in this study that the inclusion of the ANCF-coupled deformation modes introduces geometric stiffening effects that can not be captured using other finite element models.

scholarly journals Validation of Welding Simulations Using Thermal Strains Measured with DIC

2011 ◽  
Vol 70 ◽  
pp. 129-134 ◽  
Author(s):  
Maarten De Strycker ◽  
Pascal Lava ◽  
Wim Van Paepegem ◽  
Luc Schueremans ◽  
Dimitri Debruyne
Keyword(s):  
Residual Stresses ◽  
Cross Section ◽  
Circular Cross Section ◽  
Welding Process ◽  
Weld Bead ◽  
Image Correlation ◽  
Steel Tubes ◽  
Element Analysis ◽  
Strain Evolution ◽  
The Cross

Residual stresses can affect the performance of steel tubes in many ways and as a result their magnitude and distribution is of particular interest to many applications. Residual stresses in cold-rolled steel tubes mainly originate from the rolling of a flat plate into a circular cross section (involving plastic deformations) and the weld bead that closes the cross section (involving non-uniform heating and cooling). Focus in this contribution is on the longitudinal weld bead that closes the cross section. To reveal the residual stresses in the tubes under consideration, a finite element analysis (FEA) of the welding step in the production process is made. The FEA of the welding process is validated with the temperature evolution of the thermal simulation and the strain evolution for the mechanical part of the analysis. Several methods for measuring the strain evolution are available and in this contribution it is investigated if the Digital Image Correlation (DIC) technique can record the strain evolution during welding. It is shown that the strain evolution obtained with DIC is in agreement with that found by electrical resistance strain gauges. The results of these experimental measuring methods are compared with numerical results from a FEA of the welding process.

Development of a Nonlinear, C1-Beam Finite-Element Code for Actuator Design of Slender Flexible Robots

2017 ◽  
Author(s):  
Hidenori Murakami ◽  
Oscar Rios ◽  
Takeyuki Ono
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Cross Section ◽  
Beam Model ◽  
Finite Element Code ◽  
Shape Functions ◽  
Lagrange Equations ◽  
Element Discretization ◽  
Flexible Robots ◽  
Actuator Design

For actuator design and motion simulations of slender flexible robots, planar C1-beam elements are developed for Reissner’s large deformation, shear-deformable, curbed-beam model. Internal actuation is mechanically modeled by a rate-form of beam constitutive relation, where actuation curvature is prescribed at each time. Geometrically, a curbed beam is modeled as a frame bundle, whereby at each point on beam’s curve of centroids a moving orthonormal frame is attached to a cross section. After a finite element discretization, a curve of centroids is modeled as a C1-curve, employing cubic shape functions for both planar coordinates with an arc-parameter. The cubic shape functions have already been utilized in linear Euler-Bernoulli beams for the interpolation of transverse displacement. To define the rotation angle of each cross section or the attitude of the moving frame, quadratic shape functions are used introducing a middle node, resulting in three angular nodal displacements. As a result, each beam element has total eleven nodal coordinates. The implementation of a nonlinear finite element code is facilitated by the principle of virtual work, which yields Reissner’s large deformation curbed beam model as the Euler-Lagrange equations. For time integration, the Newmark method is utilized. Finally, as applications of the code, a few inchworm motions induced by different actuation curvature fields are presented.

Revisiting the Basis for Hip Fracture Prediction Through Bone Mineral Density Scans: Large Potential Errors and Improved Methods

2020 ◽  
Vol 3 (3) ◽  
Author(s):  
W. P. Munsell, Jr.
Keyword(s):  
Bone Mineral Density ◽  
Hip Fracture ◽  
Cross Section ◽  
Bone Mineral ◽  
Moment Of Inertia ◽  
Mineral Density ◽  
Element Analysis ◽  
Cross Sectional ◽  
Complex Cross ◽  
The Cross

Abstract Researchers have attempted to evaluate the likelihood of hip fracture as a function of an engineering concept called the moment of inertia, as applied to the cross-sectional area of hip bones. While the premise is sound, the results have been disappointing. Although several authors have acknowledged that errors may arise in the current methods investigators employ to determine the cross section moment of inertia (CSMI), none have looked critically at the sources, or even the magnitude, of those errors. This paper evaluates the nature of the error that can be introduced by the use of one-dimensional bone mineral density scans to estimate the CSMI and quantifies its impact on predictive calculations. In addition, this paper presents an improved method for approximating the mechanical section properties of highly complex cross sections. The factors affecting the accuracy of the proposed method are tested, and its error rate is also quantified. The method employs a two-dimensional analysis of digital images of the subject cross section and does not require extensive user expertise or investment in expensive finite element analysis programs to implement. The limited file space necessary to install the required code means that standard smart phones could be used to directly evaluate the most complex cross section in the field.

scholarly journals Analytical Model of a Multi-Step Straightening Process for Linear Guideways Considering Neutral Axis Deviation

Symmetry ◽  
2018 ◽  
Vol 10 (8) ◽  
pp. 316 ◽  
Author(s):  
Yongquan Zhang ◽  
Hong Lu ◽  
He Ling ◽  
Yang Lian ◽  
Mingtian Ma
Keyword(s):  
Analytical Model ◽  
Cross Section ◽  
Predictive Accuracy ◽  
Neutral Axis ◽  
Longitudinal Stress ◽  
Linear Superposition ◽  
Element Analysis ◽  
Cross Sectional ◽  
The Cross ◽  
Sectional Shape

The cross-sectional shape of a linear guideway has been processed before the straightening process. The cross-section features influence not only the position of the neutral axis, but also the applied and residual stresses along the longitudinal direction, especially in a multi-step straightening process. This paper aims to present an analytical model based on elasto-plastic theory and three-point reverse bending theory to predict straightening stroke and longitudinal stress distribution during the multi-step straightening process of linear guideways. The deviation of the neutral axis is first analyzed considering the asymmetrical features of the cross-section. Owing to the cyclic loading during the multi-step straightening process, the longitudinal stress curves are then calculated using the linear superposition of stresses. Based on the cross-section features and the superposition of stresses, the bending moment is corrected to improve the predictive accuracy of the multi-step straightening process. Finite element analysis, as well as straightening experiments, have been performed to verify the applicability of the analytical model. The proposed approach can be implemented in the multi-step straightening process of linear guideways with similar cross-sectional shape to improve the straightening accuracy.

Effects of Cross-Section Ovalization of Subsea Thin-Walled Bends Under In-Plane Bending

2010 ◽  
Author(s):  
Ranil Banneyake ◽  
Ayman Eltaher ◽  
Paul Jukes
Keyword(s):  
Cross Section ◽  
Computational Cost ◽  
Straight Pipe ◽  
Limit States ◽  
Element Analysis ◽  
High Tendency ◽  
Thin Walled ◽  
Plane Bending ◽  
The Cross ◽  
The Impact

Ovalization of the cross-section of bends under in-plane bending (a.k.a. Brazier effect) is a known phenomenon caused by the longitudinal stress acting on the cross-section as the pipe bends. Besides its tendency to induce stresses in the bend above what is predicted using simple beam theory, excessive cross-section ovalization is particularly critical to subsea pipes, as it can lead to collapse of the pipe under external pressure. Also, being in a plastic regime may cause the bend material to ratchet and undergo excessive strains under cyclic operational loads, especially under high-pressure high-temperature (HPHT) conditions. Ovalization normally results in local increase of stresses and could lead to failure of the bend before the bend globally reaches its limiting capacity. The offshore industry standards and design codes address the impact of initial ovality in straight pipes, but their applicability to bends is not clear. Therefore, this paper presents an investigation into the increased tendency of thin-walled bends to ovalize, and the effect of bend cross-section ovalization on their stiffness and yielding and collapse limit states, with emphasis on offshore applications. Due to the lack of analytical solutions for the bend response taking into account cross-section ovalization, finite element analysis (FEA) is used in this study. Predictions of the bend models are compared with those of straight pipe models and predictions of models of the bend made of beam elements (with pipe section) are compared with those of models made of brick /shell elements. The increased tendency of thin-walled bends to ovalize compared to straight pipes is investigated (e.g. 100 times in the linear range), and the impact and significance of ovalization in bends are assessed (e.g., stress increase of the order of 35% has been observed in some example situations). Also discussed in the paper is the selection of proper element specifications in order to accurately capture the ovalization response while keeping the computational cost manageable. Recommendations as to how to account for ovalization effects are presented. This paper helps to gain a better understanding of the response of subsea thin-walled bends under in-plane bending and their comparatively high tendency to ovalize compared to straight pipe, and emphasizes the significance of local effects such as cross-section ovalization, the overlooking of which may result in a significant underestimation of involved stresses and strains.

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 Dynamic Analysis of Single-Layered Graphene Nano-Ribbons (SLGNRs) with Variable Cross-Section Resting on Elastic Foundation

2019 ◽  
Vol 6 (1) ◽  
pp. 132-145 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Elastic Foundation ◽  
Cross Section ◽  
Differential Quadrature Method ◽  
Beam Theory ◽  
Nonlocal Elasticity Theory ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Winkler Elastic Foundation ◽  
The Cross ◽  
Euler Bernoulli Beam

AbstractThis article deals with free vibration of the variable cross-section (non-uniform) single-layered graphene nano-ribbons (SLGNRs) resting on Winkler elastic foundation using the Differential Quadrature Method (DQM). Here characteristic width of the cross-section is varied exponentially along the length of the nano-ribbon while the thickness of the cross section is kept constant. Euler–Bernoulli beam theory in conjunction with Eringen nonlocal elasticity theory is considered in this study. The numerical as well as graphical results are reported by using MATLAB codes developed by authors. Convergence of present method is explored and our results are compared with known results available in literature showing excellent agreement. Further, effects various parameters on frequency parameters are studied comprehensively.

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