Smooth 3D manifolds based on thin plates

2016 ◽  
Vol 22 (3) ◽  
pp. 477-490
Author(s):  
VA Grachev ◽  
YS Neustadt
Keyword(s):  
Degrees Of Freedom ◽  
3D Structure ◽  
Three Dimensional ◽  
Small Diameter ◽  
Thin Plates ◽  
Mechanics Of Solids ◽  
Dimensional Manifold ◽  
Initial State ◽  
Rigid Plastic ◽  
Definition Of

This paper demonstrates a fractal system of thin plates connected with hinges. The system can be studied using the methods of the mechanics of solids with internal degrees of freedom. The structure is deployable, and initially, it is similar to a small-diameter one-dimensional manifold, which occupies significant volume after deployment. The geometry of solids is studied using the method of the moving hedron. The relationships enabling the definition of the geometry of the introduced manifolds are derived based on the Cartan structure equations. The proof substantially makes use of the fact that the fractal consists of thin plates that are not long compared to the sizes of the system. The mechanics are described for solids with rigid plastic hinges between the plates, and the hinges are made of shape memory material. Based on the ultimate load theorems, estimates are performed to specify the internal pressure that is required to deploy the package into a three-dimensional (3D) structure and the heat input needed to return the system into its initial state. Some possible applications of the smooth 3D manifolds are demonstrated.

A Three-Dimensional Dynamic Model for Determining the Equilibrium Configurations of Buoyantly Unstable Icebergs

1990 ◽  
Vol 112 (3) ◽  
pp. 253-262
Author(s):  
R. G. Jessup ◽  
S. Venkatesh
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Static Potential ◽  
Initial State ◽  
Model Simulations ◽  
Six Degrees Of Freedom ◽  
Equilibrium Configurations ◽  
Variation Range

This paper describes a dynamic model developed for the purpose of determining the final equilibrium configurations of buoyantly unstable icebergs. The model places no restrictions on the size, shape, or dimensionality of the iceberg, or on the variation range of the configuration coordinates. Furthermore, it includes all six degrees of freedom and is based on a Lagrangian formulation of the dynamic equations of motion. It can be used to advantage in those situations in which the iceberg has a complicated potential function and can acquire enough momentum and kinetic energy in the initial phase of its motion to make its final configuration uncertain on the basis of a static potential analysis. The behavior of the model is examined through several model simulations. The sensitivity of the final equilibrium position to the initial orientation and shape of the iceberg is clearly evident in the model simulations. Model simulations also show that when an iceberg is released from a nonequilibrium initial state, the time taken for it to settle down varies from about 40 s for a growler to nearly 400 s for a large iceberg. While these absolute times may change with better parameterization of the forces, the relative variations with iceberg size are likely to be preserved.

Three-dimensional relative reachable domain with initial state uncertainty in Gaussian distribution

2018 ◽  
Vol 233 (5) ◽  
pp. 1555-1570 ◽  
Author(s):  
Changxuan Wen ◽  
Yang Gao ◽  
Hao Shi
Keyword(s):  
Relative Motion ◽  
Gaussian Distribution ◽  
Three Dimensional ◽  
Rare Event ◽  
Random Variable ◽  
Initial State ◽  
State Uncertainty ◽  
Probability Threshold ◽  
Definition Of ◽  
Error Ellipsoid

A probability threshold is a confidence level defining a bound outside which the occurrence of a random variable is considered as a rare event. Upon providing such a probability threshold on the initial state uncertainty, relative reachable domain is defined as the minimum positional volume enclosing all the possible relative trajectories resulting from the initial state uncertainty. In this study, the conventional coplanar relative reachable domain with initial state uncertainty in isotropic Gaussian distribution is extended to the three-dimensional case with uncertainty in arbitrary Gaussian distribution. Positional errors in Gaussian distribution are thought to be confined within an error ellipsoid depending on the given probability threshold. Such an error ellipsoid will evolve with time and consequently sweep out a volume, which is the relative reachable domain to be determined. This paper proposed an algorithm of solving the envelope surface of the relative reachable domain for close range relative motion based on the linearized dynamical model and the mathematical definition of an envelope. Moreover, the algorithm is modified to improve the accuracy for long range relative motion. Comparisons between the solved relative reachable domain and the result of 10,000 Monte Carlo runs, which can be regarded as the true result, for different scenarios on circular reference orbits demonstrated the feasibility of the proposed method.

scholarly journals Researches on the Generation of Three-Dimensional Manifold Element under FEM Mesh Cover

2014 ◽  
Vol 2014 ◽  
pp. 1-17
Author(s):  
Li HaiFeng ◽  
Zhang Guoxing
Keyword(s):  
Three Dimensional ◽  
Detection Algorithm ◽  
Dimensional Manifold ◽  
Hexahedral Mesh ◽  
Element Mesh ◽  
Dimensional Finite Element ◽  
Definition Of ◽  
Three Dimensional Finite Element ◽  
Numerical Manifold ◽  
Contact Detection Algorithm

Three-dimensional manifold element generation and contact detection algorithm between blocks are the bottleneck for the development of three-dimensional numerical manifold method (NMM). For building mathematics cover, the technology of three-dimensional finite element mesh generation is utilized in the paper. Aiming at the characteristics of complex formation and difficult identification of three-dimensional manifold block, three-dimensional manifold cutting technology is developed. It is important to achieve the coding of mathematical cover (MC) and physical cover (PC) for NMM, which directly determines the correctness of three-dimensional manifold element generation. Based on the character that the coding of three-dimensional manifold is the same as two-dimensional field essentially, coding algorithm of PC system proposed by Dr. Shi is extended to be three-dimensional. A three-dimensional manifold cutting program 3D MC.f90 is developed in this paper, which can generate an arbitrary three-dimensional manifold element under tetrahedral and hexahedral mesh cover. Several examples are made, and results show that three-dimensional manifold block shape and the coding of manifold node and element generated by three-dimensional manifold cutting program all agree well with the definition of three-dimensional manifold element.

scholarly journals Strength analysis of an off-road lorry frame

2021 ◽  
Vol 110 ◽  
pp. 23-33
Author(s):  
Ján DIŽO ◽  
Miroslav BLATNICKÝ ◽  
Paweł DROŹDZIEL ◽  
Stanislav SEMENOV ◽  
Evgeny MIKHAILOV ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Degrees Of Freedom ◽  
Structural Unit ◽  
Three Dimensional ◽  
Strength Analysis ◽  
The Finite Element Method ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Definition Of ◽  
Distribution Of Stresses

The lorry frame is the main carrying part of a lorry, composed of several components. These components are connected by joints into one structural unit and it forms the lorry chassis. The contribution of this article is focused on the strength analyses of a backbone frame, which is used on an off-road lorry chassis. Strength analyses are carried out utilising the finite element method. This article presents a created three-dimensional model of the frame and definition of boundary conditions (loads, the definition of degrees of freedom) needed for simulation computations. Results of the numerical calculations are the main parts of this article. Attention is mainly centred on the distribution of stresses of the frame under defined loads and its deformations.

NONLINEAR MODEL OF A FABRIC WARP AND WEFT

2006 ◽  
Vol 09 (01n02) ◽  
pp. 99-120 ◽  
Author(s):  
PASCAL BRUNIAUX ◽  
CYRIL NGO NGOC
Keyword(s):  
Dynamic Behavior ◽  
3D Structure ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Nonlinear Phenomena ◽  
Initial State ◽  
Numerical Resolution ◽  
3D Space ◽  
Proposed Model ◽  
Nodal Model

This study aims to develop a realistic mathematical model of fabric. In contrast to other studies on fabric modeling as a deformable surface, the model described in this article takes into account the geometry of the object. Moreover, it integrates the nonlinear phenomena of the dynamic behavior of material. As input parameters, the weaving data that define the 3D structure of the object and the mechanical properties of the yarn that express its dynamics are used. Thus, the fabric model is composed of a geometrical model of fabric (structure) on which a model of yarn (material characterization) is added. This hypothesis may be reasonable since a fabric shows the result of a three-dimensional assembly of yarns judiciously disposed. Since these yarns interact dynamically: the main difficulty consists of defining the yarn model. In our case, it is composed of various nonlinear functions representing the dynamic behavior of yarn. In order to characterize the flexibility of material, the weight, the elasticity and any other mechanical characteristics defining the relation between the strain and the stretching out of the shape should be taken into account. Firstly, several works dealing with realistic mathematical models of fabric are described. A taxonomic classification is achieved in order to position our study (in comparison to the scientific community). Secondly, the model of the fabric is described. A geometrical model of the object is presented. It allows one to dimension the object in a 3D space and then to position it at its initial state. Subsequently, a nodal model of yarns is described, step by step, in order to demonstrate the separability of the various dynamic behaviors. These nodal links make it simple to integrate the proposed model in the global geometrical model. Thus, the methods of numerical resolution used to simulate the complete model of the fabric are exposed. One method is selected and used in order to improve the performances of the fabric simulator and to obtain better stability. Several simulations illustrate the quality of the results obtained.

scholarly journals Identification of Three-Dimensional Equivalent Material Properties for Laminated Disks Pack of Electric Machine Stators: Application in Reciprocal Compressors

2019 ◽  
Vol 2019 ◽  
pp. 1-18
Author(s):  
Jean C. Marcon ◽  
Olavo M. Silva ◽  
Thiago A. Fiorentin ◽  
Arcanjo Lenzi
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Magnetic Core ◽  
Synthesis Methods ◽  
Equivalent Material ◽  
The Difference ◽  
Three Dimensional Models ◽  
Orthotropic Properties ◽  
Definition Of ◽  
Laminated Structures

Laminated structures can be represented computationally by the finite element method (FEM) using the homogenization procedure, which consists of the adjustment of equivalent orthotropic properties to a homogeneous structure. The application occurs in stators of electric machines composed of stacked laminated disks connected to each other through windings and other fastening components. This paper describes a method to the dynamic characterization of a typical laminated stator through the application of the homogenization technique to the magnetic core and consideration of the effect of winding contour conditions and screw joints. Two simplified three-dimensional models for the stator were compared. The first considers the application of a typical tightening of the fastening screws and the presence of a homogeneous isotropic volume representing the winding. The second considers the effect of the boundary condition of the winding on the region of the teeth of the nucleus in order to reduce the degrees of freedom of the complete model. The coupling between the components is accomplished through the application of modal synthesis methods, which require the definition of the surfaces and the type of connection between the components. The obtainment of the set of equivalent orthotropic properties is based on the minimization of residues related to the difference between the natural and experimental frequencies in the range of 0 to 10 kHz. This was carried out using the multiobjective genetic algorithm (MOGA) method used in conjunction with commercial Ansys® software. Both models presented satisfactory experimental correlation. The simplified model demonstrated limitations of representativeness emphasized in specific frequency bands.

A SCHEME FOR SPATIAL WAVE FUNCTION TELEPORTATION IN THREE DIMENSIONS

2006 ◽  
Vol 04 (05) ◽  
pp. 781-790
Author(s):  
O. AKHAVAN ◽  
A. T. REZAKHANI ◽  
M. GOLSHANI
Keyword(s):  
Wave Function ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Quantum Object ◽  
Initial State ◽  
N Level ◽  
Spatial Wave Function ◽  
Three Dimensional Space

We propose a theoretical scheme for teleportation of a general wave function of a quantum object. In principle, this protocol provides teleportation of discrete N-level spatial states of an object with various degrees of freedom, e.g. spin, in ordinary three-dimensional space. All necessary Bell states and their corresponding operators to measure and reconstruct the initial state are represented.

scholarly journals Mixed Position and Twist Space Synthesis of 3R Chains

Robotics ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 13
Author(s):  
Neda Hassanzadeh ◽  
Alba Perez-Gracia
Keyword(s):  
Degrees Of Freedom ◽  
Traditional Approach ◽  
Three Dimensional ◽  
Dimensional Subspace ◽  
End Effector ◽  
Serial Chain ◽  
Higher Dimensional ◽  
Different Types ◽  
A Chain ◽  
Definition Of

Mixed-position kinematic synthesis is used to not only reach a certain number of precision positions, but also impose certain instantaneous motion conditions at those positions. In the traditional approach, one end-effector twist is defined at each precision position in order to achieve better guidance of the end-effector along a desired trajectory. For one-degree-of-freedom linkages, that suffices to fully specify the trajectory locally. However, for systems with a higher number of degrees of freedom, such as robotic systems, it is possible to specify a complete higher-dimensional subspace of potential twists at particular positions. In this work, we focus on the 3R serial chain. We study the three-dimensional subspaces of twists that can be defined and set the mixed-position equations to synthesize the chain. The number and type of twist systems that a chain can generate depend on the topology of the chain; we find that the spatial 3R chain can generate seven different fully defined twist systems. Finally, examples of synthesis with several fully defined and partially defined twist spaces are presented. We show that it is possible to synthesize 3R chains for feasible subspaces of different types. This allows a complete definition of potential motions at particular positions, which could be used for the design of precise interaction with contact surfaces.

6-DOF Loading System with the Simulated Border

2012 ◽  
Vol 549 ◽  
pp. 894-898
Author(s):  
Bing Li ◽  
Yu Lan Wei ◽  
Yue Zhan Wang ◽  
Qi Bo Yan
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Direction Cosine ◽  
Dimensional Structure ◽  
Structure Model ◽  
Technical Performance ◽  
Loading System ◽  
The Matrix ◽  
Definition Of ◽  
6 Degrees Of Freedom

There is a set of 6 degrees of freedom (6-DOF) loading system with the simulated border for the application of material structural strength and reliability tests. This is a novel equipment for the tests of structural mechanical properties and reliability in different materials. This study showed a three-dimensional structure model, introduced the definition of the test of the 6-DOF loading system with the simulated border, and discussed the primary theory of the system and technical performance. Based on the matrix of direction cosine of the system, the solutions of inverse kinematics of 6-DOF loading system were given. The system of control was introduced as well.

Methods for three-dimensional reconstruction of cellular components within a thick section

1986 ◽  
Vol 44 ◽  
pp. 18-21
Author(s):  
J. Frank ◽  
B. F. McEwen ◽  
M. Radermacher ◽  
C. L. Rieder
Keyword(s):  
Tilt Angle ◽  
Tomographic Reconstruction ◽  
3D Structure ◽  
Three Dimensional ◽  
Thick Section ◽  
Three Dimensional Reconstruction ◽  
Axis Ratio ◽  
Dimensional Reconstruction ◽  
Cellular Components

The tomographic reconstruction from multiple projections of cellular components, within a thick section, offers a way of visualizing and quantifying their three-dimensional (3D) structure. However, asymmetric objects require as many views from the widest tilt range as possible; otherwise the reconstruction may be uninterpretable. Even if not for geometric obstructions, the increasing pathway of electrons, as the tilt angle is increased, poses the ultimate upper limitation to the projection range. With the maximum tilt angle being fixed, the only way to improve the faithfulness of the reconstruction is by changing the mode of the tilting from single-axis to conical; a point within the object projected with a tilt angle of 60° and a full 360° azimuthal range is then reconstructed as a slightly elliptic (axis ratio 1.2 : 1) sphere.

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