scholarly journals Contravariant tensor algebra for anisotropic hyperelasticity

2021 ◽  
Vol 2070 (1) ◽  
pp. 012161
Author(s):  
Arthesh Basak ◽  
Amirtham Rajagopal ◽  
Umesh Basappa
Keyword(s):  
Coordinate System ◽  
Damage Model ◽  
Tensor Algebra ◽  
Element Analysis ◽  
Damage Models ◽  
Simple Geometry ◽  
Anisotropic Hyperelasticity ◽  
Novel Method ◽  
Cartesian Coordinate ◽  
Definition Of

Abstract Analysis of tensors in oblique Cartesian coordinate systems always requires the definition of a set of orthogonal covariant basis vectors called the Reciprocal basis. This increases the complexity of the analysis and hence makes the method cumbersome. In this work a novel method is presented to effectively carry out the various transformations of tensors to and between oblique coordinate system/s without the need to create the covariant reciprocal basis. This will simplify the procedure of transformations involving problems where tensors are required to be defined in the oblique coordinate system. This work also demonstrates how the analysis of contravariant tensors can be applied to hyperelasticity. Continuum material and damage models can integrate this approach to model anisotropy and non linearity using a much simpler approach. The accuracy of the models was illustrated by matching the predictions to experimental results. A finite element analysis of material and damage model based on contravariant tensors was also carried out on a simple geometry with a re-entrant corner.

Textual Topography

2020 ◽  
pp. 83-101
Author(s):  
Ciaran McMorran
Keyword(s):  
Coordinate System ◽  
James Joyce ◽  
Fourth Dimension ◽  
Structural Level ◽  
Cartesian Coordinate System ◽  
Nonlinear Form ◽  
Cartesian Coordinate ◽  
Definition Of ◽  
Narrative Framework

This chapter examines how the branching narrative framework of “Wandering Rocks” reflects the structure of the manneristic maze and emulates the nonlinear visual structures which are traced by the characters of Ulysses as they wander through Dublin’s streets. In light of Henri Poincaré’s definition of geometry as “the summary of the laws by which images succeed each other,” it explores how James Joyce presents time presented as the fourth dimension of space in his construction of a textual “picture of Dublin” which follows the movement of wandering bodies. This chapter provides a schema of the narrative network in “Wandering Rocks,” illustrating how Joyce’s textual remapping of Dublin involves the structural emulation of fundamental geometric constructs and related topographical concepts which involve the coincident meeting of lines (as in triangulation, parallax, and the Cartesian coordinate system). In light of the parallactic perspectives which are facilitated by the episode’s branching structure, this chapter demonstrates how the labyrinthine “Wandering Rocks” narrative epitomizes Joyce’s Brunonian perversion of unidirectional rectilinearity on a structural level, disrupting “wider manifestations […] of ‘conceptual and behavioral rectilinearity’” in its nonlinear form.

scholarly journals Semiotic Insights into Aristotle’s Theory of Being: Definition and Model of Sign

2012 ◽  
Vol 61 ◽  
pp. 113-135
Author(s):  
Algirdas Budrevičius
Keyword(s):  
Coordinate System ◽  
Initial Part ◽  
Cartesian Coordinate System ◽  
Fundamental Theory ◽  
Cartesian Coordinates ◽  
Surface Maps ◽  
Proposed Model ◽  
Cartesian Coordinate ◽  
Definition Of

This paper is aimed to develop a model of the sign as homomorphism (i.e. similarity of form) as the initial part of a strict and fundamental theory of sign. Many various signs—photographs, pictures, sculptures, diagrams, surface maps, etc.—might be viewed in terms of homomorphism. The proposed model of sign as a homomorphism is derived using Aristotle’s theory of being. Two principles of Aristotle’s theory—form and matter—are used as elementary ideas in the model of sign. The main peculiarity of the undertaken approach to semiotics is treating a sign and a signified object as derivative ideas; they are constructed as compounds of form and matter. To achieve more strictness, the model of sign is treated in terms of the system of Cartesian coordinates modified for the articulation of being. Intentionality is viewed as the key idea in the model of sign. The approach to the definition of sign presented in this paper can be viewed as an ontological alternative to Peirce’s one.Keywords: sign as homomorphism, Aristotle, hylomorphism, Cartesian coordinate system, ontology.Aristotelio esaties teorijos semiotinės įžvalgosAlgirdas BudrevičiusSantraukaPagrindinis šio straipsnio tyrimo dalykas yra ženklas kaip žymimojo objekto homomorfizmas – tai yra ženklas kaip formos panašumas. Pagrindinis tikslas – sukurti ženklo kaip homomorfizmo modelį, kuris būtų griežtos, pamatinės ženklo teorijos pradinė dalis. Daug įvairių ženklų gali būti nagrinėjami kaip homomorfizmai: fotografijos, paveikslai, skulptūros, diagramos, žemėlapiai ir kt. Pasiūlytas homomorfinio ženklo modelis išvestas naudojant Aristotelio esaties teoriją. Kaip elementariosios sąvokos jame naudojami du Aristotelio esaties teorijos principai – forma ir materija (medžiaga). Dėstomo požiūrio ypatumas semiotikos atžvilgiu yra tas, kad ženklas ir žymimasis objektas traktuojami kaip išvestinės sąvokos; jos konstruojamos kaip formos ir materijos junginiai. Siekiant, kad modelis būtų griežtesnis, jam sudaryti naudojama Dekarto koordinačių sistema, pritaikyta esaties artikuliavimui. Homomorfinio ženklo apibrėžimo kertine laikoma intencionalumo sąvoka. Straipsnyje pateiktas požiūris į ženklo apibrėžimą gali būti laikomas ontologine alternatyva Peirce’o požiūriui.

Assessment of Residual Ultimate Hull Girder Strength of Damaged Ships

2014 ◽  
Author(s):  
Xiaoli Jiang ◽  
Haiyang Yu ◽  
Miroslaw Lech Kaminski
Keyword(s):  
Ultimate Strength ◽  
Oil Spills ◽  
Damage Model ◽  
Ship Hull ◽  
Element Analysis ◽  
Detailed Measurement ◽  
Hull Girder ◽  
Damage Models ◽  
Actual Damage ◽  
Damaged Ship

The risk of ship collision and grounding has increased significantly in recent years as a result of the growing size and number of ships at sea. The potentially costly consequences of collision and grounding in the form of fatalities, property, and cargo, as well as environmental pollution in the form of oil spills, etc., are the main motivations for research on collision and grounding. From a structural evaluation standpoint, there is a great deal of uncertainty related to the residual strength of damaged ships considering various influential parameters, such as damage size, geometry and location, internal structural arrangement, material property, loading case, and sea weather. Therefore, it is important to clarify the residual hull girder strength of damaged ships by collision or grounding in order to ensure their safety. The present study undertook a deliberate finite element analysis to investigate the residual ultimate strength of damaged ship hull, where two damage models were assumed and compared. One model simulated actual damage resulting from an accident in the form of hole with adjacent plastic deformation, while the other applied simplified damage, considering unavailable measurement of the damage by removing the damaged part from the original ship hull. The comparison showed that the assessment of residual ultimate strength of a damaged ship based on the simplified damage model could produce a sufficiently accurate result and stay slightly safer, provided that a reasonable criterion of simplification was defined first. The studies showed that it is possible to accurately estimate the residual ultimate strength of a damaged ship without detailed measurement of the damage, and consequently facilitate decision-making regarding the ship salvage under emergency.

Introduction

2017 ◽  
Author(s):  
Valentin Jeutner
Keyword(s):  
Coordinate System ◽  
Nuclear Weapons ◽  
Legal Order ◽  
Cartesian Coordinate System ◽  
Military Alliances ◽  
International Legal Order ◽  
Research Questions ◽  
Cartesian Coordinate ◽  
Definition Of ◽  
The Way

This part introduces and illustrates the idea of a legal dilemma by means of a hypothetical Cartesian coordinate system. The introduction alsosets out the objectives of the book. It does so with reference to three research questions concerning, first, the definition of a legal dilemma, second, the possibility of the existence of a legal dilemma, and, finally, the way in which the international legal order should address legal dilemmas. Subsequently, the introduction outlines five examples to which the book keeps referring. The examples concern the regulation of nuclear weapons, submarine warfare, military alliances, conflicting infrastructure treaties, and the rescue of persons in distress at sea.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

scholarly journals Shape Sensing of a Complex Aeronautical Structure with Inverse Finite Element Method

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Strain Field ◽  
Element Analysis ◽  
Inverse Finite Element Method ◽  
Shape Sensing ◽  
Definition Of ◽  
High Level ◽  
Element Method

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.

scholarly journals LiDAR-Based Glass Detection for Improved Occupancy Grid Mapping

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2263
Author(s):  
Haileleol Tibebu ◽  
Jamie Roche ◽  
Varuna De Silva ◽  
Ahmet Kondoz
Keyword(s):  
Laser Scanner ◽  
Point Clouds ◽  
Light Detection And Ranging ◽  
Test Results ◽  
New Approach ◽  
Occupancy Grid ◽  
Laser Scanners ◽  
Novel Method ◽  
Occupancy Grid Mapping ◽  
Cartesian Coordinate

Creating an accurate awareness of the environment using laser scanners is a major challenge in robotics and auto industries. LiDAR (light detection and ranging) is a powerful laser scanner that provides a detailed map of the environment. However, efficient and accurate mapping of the environment is yet to be obtained, as most modern environments contain glass, which is invisible to LiDAR. In this paper, a method to effectively detect and localise glass using LiDAR sensors is proposed. This new approach is based on the variation of range measurements between neighbouring point clouds, using a two-step filter. The first filter examines the change in the standard deviation of neighbouring clouds. The second filter uses a change in distance and intensity between neighbouring pules to refine the results from the first filter and estimate the glass profile width before updating the cartesian coordinate and range measurement by the instrument. Test results demonstrate the detection and localisation of glass and the elimination of errors caused by glass in occupancy grid maps. This novel method detects frameless glass from a long range and does not depend on intensity peak with an accuracy of 96.2%.

scholarly journals Vector Arithmetic in the Triangular Grid

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 373
Author(s):  
Khaled Abuhmaidan ◽  
Monther Aldwairi ◽  
Benedek Nagy
Keyword(s):  
Coordinate System ◽  
Triangular Grid ◽  
Vector Addition ◽  
Plane Space ◽  
Physical Simulations ◽  
Rectangular Grids ◽  
Cartesian Coordinate ◽  
Zero Sum ◽  
Coordinate Geometry ◽  
Point Lattice

Vector arithmetic is a base of (coordinate) geometry, physics and various other disciplines. The usual method is based on Cartesian coordinate-system which fits both to continuous plane/space and digital rectangular-grids. The triangular grid is also regular, but it is not a point lattice: it is not closed under vector-addition, which gives a challenge. The points of the triangular grid are represented by zero-sum and one-sum coordinate-triplets keeping the symmetry of the grid and reflecting the orientations of the triangles. This system is expanded to the plane using restrictions like, at least one of the coordinates is an integer and the sum of the three coordinates is in the interval [−1,1]. However, the vector arithmetic is still not straightforward; by purely adding two such vectors the result may not fulfill the above conditions. On the other hand, for various applications of digital grids, e.g., in image processing, cartography and physical simulations, one needs to do vector arithmetic. In this paper, we provide formulae that give the sum, difference and scalar product of vectors of the continuous coordinate system. Our work is essential for applications, e.g., to compute discrete rotations or interpolations of images on the triangular grid.

Sign in / Sign up

Export Citation Format

Share Document