scholarly journals Natural Spring Cell Substitutes of Simplex Finite Elements

2020 ◽  
Vol 15 ◽  
Keyword(s):  
Finite Elements ◽  
Elastic Anisotropy ◽  
Triangular Element ◽  
Cell Models ◽  
Plane Case ◽  
Tetrahedral Element ◽  
Flexibility Matrix ◽  
The Subject ◽  
Natural Spring ◽  
Natural Description

Spring cell models are presented which derive from the natural description of simplex finite elements, that is in conformity with the geometry of the triangle in the plane and of the tetrahedron in space. Thereby, the spring cells are interpreted as part of the finite elements. The deduction of two spring cells as defective substitutes is demonstrated for the triangular element. One approximates the flexibility matrix of the element, the other approximates the stiffness matrix. The performance with respect to the finite element is analyzed, the issue of elastic anisotropy is discussed. In space, the spring cell substitute of the tetrahedral element is derived from the flexibility matrix, an inherent difference to the plane case is pointed out. Remarks on the implication of plasticity are added. The account gives a brief summary of recent work on the subject.

scholarly journals Spring Cell Equivalence of Simplex Finite Elements – Exploration of an Iterative Approach

2021 ◽  
Vol 15 ◽  
pp. 222-235
Author(s):  
Ioannis Doltsinis
Keyword(s):  
Finite Elements ◽  
Stiffness Matrix ◽  
Iterative Approach ◽  
Convergence Criteria ◽  
Element Level ◽  
Flexibility Matrix ◽  
Triangular Elements ◽  
Natural Spring ◽  
Set Up

Natural spring cell substitutes of triangular and tetrahedral finite elements at constant strain take advantage of a formalism oriented along the element sides/edges. Two different models in use account just for the diagonal entities of either the flexibility matrix of the element or of its stiffness matrix. Both are incomplete substitutes, and defective to a degree depending on the significance of the off-diagonal parts of the element matrices. The present work discusses an iterative completeness of the substitution accounting for the discarded parts by additives to the spring members of the cell. In this connection, the iteration schemes are set up for either model at the material and at the element level, and convergence criteria are defined in terms of the spectral radii of the iteration operators. The convergence regions are confined for triangular elements, and are demonstrated with reference to a case study.

scholarly journals The family of multilayered finite elements for the analysis of plates and shells of variable thickness

2019 ◽  
Vol 91 ◽  
pp. 02013
Author(s):  
Vladimir Agapov
Keyword(s):  
Finite Elements ◽  
Variable Thickness ◽  
Triangular Element ◽  
Building Structures ◽  
Natural Phenomena ◽  
The Family ◽  
Cubic Polynomial ◽  
Plates And Shells ◽  
Lateral Displacements ◽  
The One

Urban development requires careful attitude to environment on the one hand and protection of the population from the natural phenomena on the other. To solve these problems, various building structures are used, in which slabs and shells of variable thickness find the wide application. In this work, the family of multilayered finite elements for the analysis of plates and shells of variable thickness is described. The family is based on the simplest flat triangular element of the Kirchhoff type. The lateral displacements in this element are approximated by an incomplete cubic polynomial. Such an element is unsuitable for practical use, but on its basis, improved elements of triangular and quadrilateral shape are built. Particular attention is paid to taking into account the variability of the cross-section. The results of the developed elements testing are presented, and the advantages of their use in the practice of designing and calculating the structures are shown.

On the Construction of Well-Conditioned Hierarchical Bases for (div)-Conforming ℝn Simplicial Elements

2013 ◽  
Vol 14 (3) ◽  
pp. 621-638 ◽  
Author(s):  
Jianguo Xin ◽  
Wei Cai ◽  
Nailong Guo
Keyword(s):  
Triangular Element ◽  
Johannes Kepler ◽  
Tetrahedral Element ◽  
Hierarchical Bases ◽  
Tetrahedral Elements ◽  
Stiffness Matrices ◽  
Mass Matrices ◽  
The One ◽  
Order Four ◽  
Better Than

AbstractHierarchical bases of arbitrary order for (div)-conforming triangular and tetrahedral elements are constructed with the goal of improving the conditioning of the mass and stiffness matrices. For the basis with the triangular element, it is found numerically that the conditioning is acceptable up to the approximation of order four, and is better than a corresponding basis in the dissertation by Sabine Zaglmayr [High Order Finite Element Methods for Electromagnetic Field Computation, Johannes Kepler Universität, Linz, 2006]. The sparsity of the mass matrices from the newly constructed basis and from the one by Zaglmayr is similar for approximations up to order four. The stiffness matrix with the new basis is much sparser than that with the basis by Zaglmayr for approximations up to order four. For the tetrahedral element, it is identified numerically that the conditioning is acceptable only up to the approximation of order three. Compared with the newly constructed basis for the triangular element, the sparsity of the mass matrices from the basis for the tetrahedral element is relatively sparser.

scholarly journals A MATLAB-Based Symbolic Approach for the Quick Developing of Nonlinear Solid Mechanics Finite Elements

2020 ◽  
Author(s):  
Antonio Bilotta
Keyword(s):  
Finite Elements ◽  
Solid Mechanics ◽  
Mathematical Formulation ◽  
Object Oriented Programming ◽  
Theoretical Formulation ◽  
Tetrahedral Element ◽  
Plane Element ◽  
Deformation Kinematics ◽  
Nonlinear Solid Mechanics ◽  
Symbolic Approach

A symbolic mathematical approach for the rapid early phase developing of finite elements is proposed. The algebraic manipulator adopted is MATLAB® and the applicative context is the analysis of hyperelastic solids or structures under the hypothesis of finite deformation kinematics. The work has been finalized through the production, in an object-oriented programming style, of three MATLAB® classes implementing a truss element, a tetrahedral element and plane element. The approach proposed, starting from the mathematical formulation and finishing with the code implementation, is described and its effectiveness, in terms of minimization of the gap between the theoretical formulation and its actual implementation, is highlighted.

scholarly journals Development of a refinement algorithm for tetrahedral finite elements

2020 ◽  
Vol 36 ◽  
Author(s):  
A. Hermosillo-Arteaga ◽  
M. Romo-Organista ◽  
R. Magaña del Toro ◽  
J. Carrera-Bolaños
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Finite Element Mesh ◽  
Time Dependent ◽  
Triangular Element ◽  
Soil Consolidation ◽  
Element Mesh ◽  
Engineering Problems ◽  
Close Form ◽  
Refinement Algorithm

Many of the engineering problems are analyzed using numerical methods such as the finite element (FEM) whose results provide a basis to make basic decisions regarding the design of many important works. It is commonly accepted that FEM computations are reliable; however, the results may be affected by the configuration of the finite element mesh to simulate the medium to be analyzed, this is particularly true when the internal and external boundaries are time dependent, as is the case of soil consolidation. Accordingly, a thorough investigation was carried out with the main purpose of eliminating this shortcoming. The main steps to carried out the development of the innovative geometric procedure to automatically refine finite element tetrahedra-type (3D) are described. This geometric algorithm is based on the theory of fractals and is a generalization of the algorithm for triangular element finite element meshes (2D) [1,2]. This paper presents the fundaments of this new algorithm and shows its great approximation using 3D close form solutions, and its versatility to adapt the original Finite Element Mesh when the load boundary conditions are modified (Neumann conditions).

scholarly journals Ascending from the Abstract to the Concrete in School Teaching — the double Move between Theoretical Concepts and Children’s Concepts

2020 ◽  
Vol 25 (5) ◽  
pp. 44-57
Author(s):  
M. Hedegaard
Keyword(s):  
Germ Cell ◽  
Historical Change ◽  
Design Experiment ◽  
Cell Models ◽  
Theoretical Concepts ◽  
Abstract Knowledge ◽  
School Teaching ◽  
Subject Areas ◽  
The Subject ◽  
Double Move

Vasily V. Davydov’s solved the problem between situated and abstract knowledge and integrated these conceptions into a connected theory of knowledge and thinking. His use of germ-cell models as a methodological tool is the key to understand this integration of abstract knowledge with the concrete complex and situated knowledge of a domain. I will show how I built on these ideas in my research of children’s learning and development by presenting a design experiment I conducted. The aim in this article is to illustrate the importance but also the complexity of using germ-cell models in developmental teaching as a tool focusing on the students’ activity that orient children to formulate core models as their own tool to, reflect and analyse within the complexity of concrete life scenarios. The design experiment demonstrates that a primary-substantial abstraction may be a first step in formulating germ-cell models that can evolve so different subject areas can be connected when ascending to the concrete in developmental teaching. To accomplish this, it was important to take the children’s perspective in the teaching process as a ‘double move’ between children’s motive orientation and the subject matter area. The design experiment included the subject areas of biology, history and geography focusing on the evolution of animals, the origin of man and the historical change of societies.

scholarly journals Rotation-Free Based Numerical Model for Nonlinear Analysis of Thin Shells

Buildings ◽  
2021 ◽  
Vol 11 (12) ◽  
pp. 657
Author(s):  
Hrvoje Smoljanović ◽  
Ivan Balić ◽  
Ante Munjiza ◽  
Viktor Hristovski
Keyword(s):  
Numerical Model ◽  
Finite Elements ◽  
Yield Criterion ◽  
Geometrical Nonlinearity ◽  
Time Integration ◽  
Triangular Element ◽  
Integration Scheme ◽  
Flow Rule ◽  
Thin Shells ◽  
Time Step

This paper presents a computationally efficient numerical model for the analysis of thin shells based on rotation-free triangular finite elements. The geometry of the structure in the vicinity of the observed triangular element is approximated through a controlled domain consisting of nodes of the observed finite element and nodes of three adjacent finite elements between which a second-order spatial polynomial is defined. The model considers large displacements, large rotations, small strains, and material and geometrical nonlinearity. Material nonlinearity is implemented by considering the von Mises yield criterion and the Levi-Mises flow rule. The model uses an explicit time integration scheme to integrate motion equations but an implicit radial returning algorithm to compute the plastic strain at the end of each time step. The presented numerical model has been embedded in the program Y based on the finite–discrete element method and tested on simple examples. The advantage of the presented numerical model is displayed through a series of analyses where the obtained results are compared with other results presented in the literature.

A Plate Element With Second-Order Absolute Nodal Coordinate Slopes: Numerical Computation of Shape Functions

2014 ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Numerical Computation ◽  
Equations Of Motion ◽  
Second Order ◽  
Triangular Element ◽  
Shape Functions ◽  
Absolute Nodal Coordinate ◽  
Systematic Enumeration ◽  
New Type

In this paper, the procedure of construction of geometrical and structural matrices of plate finite elements employing absolute nodal coordinate formulation (ANCF) is studied. The kinematic and topological properties of an arbitrary plate finite element are described using universal digital code dncm that provides systematic enumeration of finite elements. This code is formed using the element’s dimension d, the number of nodes it possesses n, the number of scalar coordinates per node c, and a multiplier describing the process of transforming a conventional finite element to an ANCF element m. The detailed generation of a new type of triangular plate finite element 2343 using numerical computation of shape functions is discussed in the paper. The new triangular element employs position vectors and slope vectors up to second order mixed-derivative slope vector. A detailed derivation of the equations of motion of the element is provided; the examples of numerical simulation and validation are presented. The features of creating the models and numerical methods as well as results obtained by applying both approaches are discussed in the paper.

scholarly journals Textual Artifact of Advertising: A Thrust of Halliday’s Mood System Resources

2019 ◽  
Vol 19 (3) ◽  
pp. 407-454 ◽  
Author(s):  
Taofeek O. Dalamu
Keyword(s):  
Finite Elements ◽  
Cultural Norms ◽  
The Subject ◽  
System Resources

ABSTRACT This paper argued that advertising contains variegated texts that theoretical terminologies are capable of exemplifying. Thus, ten beverage advertisements, among other types were chosen for analysis. Halliday’s mood exchange resources decomposed the texts into meaningful components, which were further calculated with tables and graphs. The calibration indicated that Complement (official milk, Uncle Thomas), Adjunct (with *826#, of Akwa Ibom), and Predicator (Dial, Drink) were dominant grammatical forms of semiosis sometimes appearing without the Subject and Finite elements. Moreover, the examination revealed exchanges initiated in the “interactions” as operating in the spheres of half-constitutive and half-ancillary organs that are significantly associated with socio-cultural norms. Prominent in the text were features of products, personal benefits and textual exaltations. Theoretical mediums, as this study suggests, would serve to uncover communication details to influence the authorities on advertising regulations.

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