A formulation of membrane finite elements with true drilling rotation

2019 ◽  
Vol 37 (1) ◽  
pp. 203-236 ◽  
Author(s):  
Djamel Boutagouga
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Polynomial Interpolation ◽  
Normal Displacement ◽  
Geometric Transformation ◽  
Rotational Degree ◽  
Content Type ◽  
Corner Node

Purpose This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF). Design/methodology/approach The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation. Findings New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs). Originality/value Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.

Truss and Beam Finite Elements Revisited: A Derivation Based on Displacement-Field Decomposition

1996 ◽  
Vol 11 (4) ◽  
pp. 371-380 ◽  
Author(s):  
Alphose Zingoni
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Symmetry Group ◽  
Displacement Field ◽  
Three Dimensional ◽  
Beam Elements ◽  
Symmetry Properties ◽  
Mass Matrices ◽  
General Displacement

Where a finite element possesses symmetry properties, derivation of fundamental element matrices can be achieved more efficiently by decomposing the general displacement field into subspaces of the symmetry group describing the configuration of the element. In this paper, the procedure is illustrated by reference to the simple truss and beam elements, whose well-known consistent-mass matrices are obtained via the proposed method. However, the procedure is applicable to all one-, two- and three-dimensional finite elements, as long as the shape and node configuration of the element can be described by a specific symmetry group.

Structural and Continuum Mechanics Approaches for a 3D Shear Deformable ANCF Beam Finite Element: Application to Buckling and Nonlinear Dynamic Examples

2013 ◽  
Vol 9 (1) ◽  
Author(s):  
Karin Nachbagauer ◽  
Johannes Gerstmayr
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Continuum Mechanics ◽  
Degrees Of Freedom ◽  
Mass Matrix ◽  
Finite Element Software ◽  
High Order Convergence ◽  
Dynamics Problems ◽  
Transverse Slope ◽  
Shear Deformable

For the modeling of large deformations in multibody dynamics problems, the absolute nodal coordinate formulation (ANCF) is advantageous since in general, the ANCF leads to a constant mass matrix. The proposed ANCF beam finite elements in this approach use the transverse slope vectors for the parameterization of the orientation of the cross section and do not employ an axial nodal slope vector. The geometric description, the degrees of freedom, and a continuum-mechanics-based and a structural-mechanics-based formulation for the elastic forces of the beam finite elements, as well as their usage in several static problems, have been presented in a previous work. A comparison to results provided in the literature to analytical solution and to the solution found by commercial finite element software shows accuracy and high order convergence in statics. The main subject of the present paper is to show the usability of the beam finite elements in dynamic and buckling applications.

A Local Refinement Technique for B-Spline Finite Element Shell Modeling

2013 ◽  
Author(s):  
Antonio Carminelli ◽  
Giuseppe Catania
Keyword(s):  
Finite Element ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Element Model ◽  
Complex Structures ◽  
Local Refinement ◽  
B Spline ◽  
Spline Finite Element ◽  
Shell Finite Element

This paper presents a refinement technique for a B2-spline degenerate isoparametric shell finite element model for the analysis of the vibrational behavior of thin and moderately thick-walled structures. Complex structures to be refined are modeled by means of FE B-spline patches assembled with C0 continuity as usual in FE technique. The model refinement was performed by adding, on the domain of the selected patch, a tensorial set of polynomial B-spline functions, defined on local clamped knot vectors, and normalizing all the functions so that the resulting displacement field remain polynomial and continuous overall the domain except on the boundaries of the refined subdomain. A degrees of freedom trasformation, based on the knot-insertion algorthim, is adopted in order to guarantee the C0 continuity of the displacement field on the boundaries of the refined subdomain. Two numerical examples are presented in order to test the proposed approach. The natural frequencies of two structures, computed by means of the proposed modelling technique, are compared with reference results available in the literature or computed by means of reference standard FE models. Strengths and limits of the approach are finally discussed.

The Application of Harmonic Finite Elements in the Seismic Response Spectrum Analysis of a Skirt Supported Vessel

2010 ◽  
Author(s):  
Bikramjit Singh Antaal ◽  
Yogeshwar Hari ◽  
Dennis K. Williams
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Seismic Response ◽  
Spectrum Analysis ◽  
Degrees Of Freedom ◽  
Response Spectrum ◽  
Response Spectrum Analysis ◽  
Element Analysis ◽  
Structure Interaction ◽  
Input Response

This paper describes the finite element considerations employed in a seismic response spectrum analysis of a skirt supported, liquid containing pressure vessel. Like many axisymmetric cylindrical vessels, the gross seismic response to an input response spectrum can be categorized by a simplified lump mass model that includes both the mass of the vessel proper in combination with the associated mass of multiple fluid levels. This simplified response may be utilized to determine the initial sizing of the supporting configuration, such as a skirt, but lacks the ability to properly address the fluid-structure interaction that creates sloshing loads on the vessel walls. The most obvious method to address the fluid-structure interaction when considering the finite element method is to build a three-dimensional model of the vessel proper, including, but not limited to the shell courses, the top and bottom heads (for a vertical vessel), and the support skirt. The inclusion of the fluid effects may now be incorporated with a “contained fluid” finite element, however, for vessels of any significant volume, the number of finite elements can easily exceed 100,000 and the number of degrees of freedom can sore from as few as 300,000 to as many as 500,000 or more. While these types of finite element analysis problems can be solved with today’s computer hardware and software, it is not desirable in any analysis to have that volume of information that has to be reviewed and approved in a highly regulated nuclear QA environment (if at all possible). With these items in mind, the methodology described in this paper seeks to minimize the number of degrees of freedom associated with a response spectrum analysis of a liquid filled, skirt supported vertical pressure vessel. The input response spectra are almost always provided in Cartesian coordinates, while many, if not most liquid containing pressure vessels are almost always axisymmetric in geometry without having benefit of being subjected to an axisymmetric load (acceleration in this case) due to the specified seismic event. The use of harmonic finite elements for both the vessel structure and the contained fluid medium permit the efficiencies associated with an axisymmetric geometry to be leveraged when the seismic response spectrum is formulated in terms of a Fourier series and combined to regain the effects of the two orthogonal, horizontally applied accelerations as a function of frequency. The end result as discussed and shown in this paper is a finite element model that permits a dense mesh of both the fluid and the structure, while economizing on the number of simultaneous equations required to be solved by the chosen finite element analysis.

Modeling of fast pre-joining processes optimization for skin-stringer panels

2014 ◽  
Vol 34 (4) ◽  
pp. 323-332 ◽  
Author(s):  
Gang Liu ◽  
Wei Tang ◽  
Ying-Lin Ke ◽  
Qing-Liang Chen ◽  
Yunbo Bi
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Traditional Approach ◽  
Element Model ◽  
Optimal Number ◽  
Neighborhood Search ◽  
Adaptive Genetic Algorithm ◽  
Time Saving ◽  
Content Type

Purpose – The purpose of this paper is to propose a new model for optimizing pre-joining processes quickly and accurately, guiding workers to standardized operations. For the automatic riveting in panel assemblies, the traditional approach of determination of pre-joining processes entirely rests on the experience of workers, which leads to the improper number, location and sequence of pre-joining, the low quality stability and the high repair rate in most cases. Design/methodology/approach – The clearances computation with the complete finite element model for every process combination is time-consuming. Therefore a fast pre-joining processes optimization model (FPPOM) is proposed. This model treats both the measured initial clearances and the stiffness matrices of key points of panels as an input; considers the permissive clearances as an evaluation criterion; regards the optimal number, location and sequence as an objective; and takes the neighborhood-search-based adaptive genetic algorithm as a solution. Findings – A comparison between the FPPOM and complete finite element model with clearances (CFEMC) was made in practice. Further, the results indicate that running the FPPOM is time-saving by >90 per cent compared with the CFEMC. Practical implications – This paper provides practical insights into realizing the pre-joining processes optimization quickly. Originality/value – This paper is the first to propose the FPPOM, which could simplify the processes, reduce the degrees of freedom of nodes and conduct the manufacturers to standardized manipulations.

Dynamic Analysis of a Mobile Mechanical System with Deformable Elements

2012 ◽  
Vol 463-464 ◽  
pp. 1242-1245 ◽  
Author(s):  
Nicolae Dumitru ◽  
Raluca Malciu ◽  
Madalina Calbureanu ◽  
Sorin Dumitru ◽  
Gabriel Cătălin Marinescu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
System Modeling ◽  
Rigid Motion ◽  
Elastic Solid ◽  
Constant Matrix ◽  
Lagrange Formulation

The paper presents a method for studying mechanisms with deformable elements, based on overlapping the solid rigid motion over the elastic solid one, in order to identify the dynamic response of the system. Modeling was based on finite element method, so the cinematic elements were meshed in bar type finite elements and the degrees of freedom per node were settled according to the motion character (planar or spatial). A Lagrange formulation of the finite element was adopted for the deformable elements connected in multibody systems. In order to define the joints constraints, the conditions for compatibility between elements were defined using a Boolean constant matrix. Computer processed results were verified by an experimental model.

Thermo-Mechanical Stress near Apex of a Bi-Material Wedge by a Novel Finite Element Analysis

2012 ◽  
Vol 525-526 ◽  
pp. 93-96
Author(s):  
Xue Cheng Ping ◽  
Lin Leng ◽  
Si Hai Wu
Keyword(s):  
Finite Element Method ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Finite Elements ◽  
Mechanical Stress ◽  
Displacement Field ◽  
Thermal Loading ◽  
Numerical Solutions ◽  
Asymptotic Solutions ◽  
Element Analysis

A super wedge tip element for application to a bi-material wedge is develop utilizing the thermo-mechanical stress and displacement field solutions in which the singular parts are numerical solutions. Singular stresses near apex of an arbitrary bi-material wedge under mechanical and thermal loading can be obtained from the coupling between the super wedge tip element and conventional finite elements. The validity of this novel finite element method is established through existing asymptotic solutions and conventional detailed finite element analysis.

scholarly journals On a bending problem of thick laminated composite plates

2002 ◽  
Vol 24 (1) ◽  
pp. 35-45
Author(s):  
Ngo Nhu Khoa ◽  
Ngo Ich Thinh
Keyword(s):  
Finite Element ◽  
Closed Form ◽  
Displacement Field ◽  
Degrees Of Freedom ◽  
Laminated Composite ◽  
Composite Plates ◽  
Layered Composite ◽  
Laminated Composite Plates ◽  
Quadrilateral Element ◽  
Transverse Loads

A high-order displacement field in quadrilateral element with nine nodes and twelve-degrees-of-freedom per node is developed for bending analysis of thick arbitrary layered composite plates under transverse loads. Results for plate deformations, internal stress-resultants and stresses for selected examples are shown to compare well with the closed-form and other finite element solutions.

Homogenization of multi-turn coil with elliptic cross-section using complex permeability

2019 ◽  
Vol 38 (3) ◽  
pp. 999-1008 ◽  
Author(s):  
Shogo Fujita ◽  
Hajime Igarashi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Finite Elements ◽  
Cross Section ◽  
Fe Analysis ◽  
Complex Permeability ◽  
Elliptic Cross Section ◽  
Content Type ◽  
Elliptic Cross ◽  
Good Agreement

Purpose The tensor complex permeability of a multi-turn coil with elliptic cross-section is analytically expressed. In field analysis, a multi-turn coil can be modeled by the uniform material that has the present tensor complex permeability. It is shown that the frequency characteristic of the present tensor complex permeability is in good agreement with that evaluated by finite element method applied to a unit cell of the multi-turn coil region. Design/methodology/approach The authors introduce a new method to evaluate the complex permeability of a multi-turn rectangular coil. To obtain the complex permeability of a rectangular coil in a closed form, it is approximated as an elliptic coil. Because the rectangular coil has different complex permeabilities in the vertical and horizontal directions, the complex permeability have to be defined in a tensor form. It suffices to discretize the coil region into rather coarse finite elements without considering the skin depth in contrast to the conventional finite element method. Findings The proposed method is shown to give the impedance of multi-turn coils which is in good agreement with results obtained by the conventional finite element (FE) analysis. By extending the proposed approach, the authors can easily perform 3D FE analysis without difficulty in discretization of the coil region with fairly fine finite elements. Moreover, they found that the approximation of rectangular coils as the elliptic coils is valid for analysis of quasi-static fields using this homogenization method. Originality/value The novelty of this study is in the approximation of the rectangular coils with elliptic coils, and the complex permeability for them is formulated here in a closed form. The proposed formula includes that for the round coils. Using the present method, the authors analyze the rectangular coils without fine discretization.

Couple stress-based unsymmetric 8-node planar membrane elements with good tolerances to mesh distortion

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Yan Shang ◽  
Huanpu Wu
Keyword(s):  
Finite Element ◽  
Couple Stress ◽  
Degrees Of Freedom ◽  
Virtual Work ◽  
A Priori ◽  
Element Model ◽  
Test Functions ◽  
Content Type ◽  
Size Dependent ◽  
C1 Continuity

PurposeThe paper aims to propose two new 8-node quadrilateral membrane elements with good distortion tolerance for the modified couple stress elasticity based on the unsymmetric finite element method (FEM).Design/methodology/approachThe nodal rotation degrees of freedom (DOFs) are introduced into the virtual work principle and constrained by the penalty function for approximating the test functions of the physical rotation and curvature. Therefore, only the C0 continuity instead of C1 continuity is required for the displacement during the element construction. The first unsymmetric element assumes the test functions of the displacement and strain using the standard 8-node isoparametric interpolations, while these test functions in the second model are further enhanced by the nodal rotation DOFs. Besides, the trial functions in these two elements are constructed based on the stress functions that can a priori satisfy related governing equations.FindingsThe benchmark tests show that both the two elements can efficiently simulate the size-dependent plane problems, exhibiting good numerical accuracies and high distortion tolerances. In particular, they can still exactly reproduce the constant couple stress state when the element shape deteriorates severely into the degenerated triangle. Moreover, it can also be observed that the second element model, in which the linked interpolation technique is used, has better performance than the first one, especially in capturing the steep gradients of the physical rotations.Originality/valueAs the proposed new elements use only three DOFs per node, they can be readily incorporated into the existing finite element (FE) programs. Thus, they are of great benefit to analysis of size-dependent membrane behaviors of micro/nano structures.

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