Geometric Modeling of Objects’ Thermal Characteristics by the Functional-Voxel Method

2020 ◽  
Vol 8 (1) ◽  
pp. 25-32 ◽  
Author(s):  
A. Plaksin ◽  
S. Pushkarev
Keyword(s):  
Thermal Expansion ◽  
Heat Source ◽  
Temperature Stress ◽  
Geometric Modeling ◽  
Thermal Loading ◽  
Geometric Model ◽  
The Body ◽  
Heat Conducting ◽  
Voxel Representation ◽  
Traditional Approaches

In this paper the influence of objects’ thermal processes on their correspondence to a given geometry has been considered, and an alternative apparatus for geometric modeling of bodies’ temperature stress and thermal expansion after effect of a heat source, based on a functional-voxel approach, has been proposed as well. A discrete geometric model of temperature stress at a point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, allowing simulate a single action of a heat source to obtain local geometric characteristics of thermal stress in the body. This approach, unlike traditional approaches based on the FEM, allows apply the temperature load at the object’s point taken by itself. A discrete geometric model for expansion at the point of thermal loading in an isotropic heat-conducting body for a functional-voxel representation has been developed, which allows simulate the change of an object’s local geometric characteristics during the process of material expansion from a single effect of a heat source to obtain a value upon the body volume changing. This approach, unlike traditional approaches based on the FEM, allows simulate a change in the body’s surface geometry from thermal expansion at a point taken by itself without errors arising from calculations using a mesh. Have been proposed algorithms for functional-voxel modeling of temperature stress and expansion under distributed thermal loading. These algorithms allow construct a loading region of complex configuration based on the spatial distribution and scaling of the temperature stress’s geometric model for a single point of thermal loading, uniformly form a contour (surface) after material expansion, and obtain information about the change in products’ length (volume) based on information about each point of functional space. Has been presented an example of using the proposed approach for solving a processing tool’s correction problem based on the temperature in the cutting zone and material thermal reaction. The geometric model can be used to the automated design of a processing tool path for parts cutting on CNC machines.

scholarly journals Functional-Voxel Method in Problems of Geometric Modeling of Thermal Characteristics of Objects

2020 ◽  
pp. paper53-1-paper53-11
Author(s):  
Aleksandr Plaksin ◽  
Alexey Tolok
Keyword(s):  
Thermal Expansion ◽  
Heat Source ◽  
Temperature Stress ◽  
Geometric Modeling ◽  
Thermal Loading ◽  
Thermal Characteristics ◽  
Heat Conducting ◽  
Temperature Stresses ◽  
Single Temperature ◽  
Contour Surface

The paper presents an approach developed on the basis of the functional voxel method to the geometric representation of the thermal expansion of objects and temperature stresses in a material when exposed to a surface of a heat source. A discrete geometric law of a single temperature stress in an isotropic heat-conducting body is derived, applicable in the concept of functional voxel modeling. Based on this law, functional-voxel models of thermal stress are developed for a single and distributed application of a heat source. Algorithms of functional-voxel modeling of temperature stress and expansion in the case of distributed thermal loading are presented, which make it possible to construct a loading region of a complex configuration, uniformly form a contour (surface) after material expansion and obtain information about changes in the length (volume) of products. The advantages of the proposed functional-voxel approach to modeling thermal expansion and stress over approaches based on the FEM are substantiated.

Assessing Model Uncertainty for the Scaling Function Inversion of Potential Fields

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Mahak Singh Chauhan ◽  
Ivano Pierri ◽  
Mrinal K. Sen ◽  
Maurizio FEDI
Keyword(s):  
Simulated Annealing Algorithm ◽  
Scaling Function ◽  
Vertical Section ◽  
Gravity Data ◽  
Geometric Model ◽  
Salt Dome ◽  
The Body ◽  
Gravity Inversion ◽  
Geometrical Parameters ◽  
The Scaling Function

We use the very fast simulated annealing algorithm to invert the scaling function along selected ridges, lying in a vertical section formed by upward continuing gravity data to a set of altitudes. The scaling function is formed by the ratio of the field derivative by the field itself and it is evaluated along the lines formed by the zeroes of the horizontal field derivative at a set of altitudes. We also use the same algorithm to invert gravity anomalies only at the measurement altitude. Our goal is analyzing the different models obtained through the two different inversions and evaluating the relative uncertainties. One main difference is that the scaling function inversion is independent on density and the unknowns are the geometrical parameters of the source. The gravity data are instead inverted for the source geometry and the density simultaneously. A priori information used for both the inversions is that the source has a known depth to the top. We examine the results over the synthetic examples of a salt dome structure generated by Talwani’s approach and real gravity datasets over the Mors salt dome and the Decorah (USA) basin. For all these cases, the scaling function inversion yielded models with a better sensitivity to specific features of the sources, such as the tilt of the body, and reduced uncertainty. We finally analyzed the density, which is one of the unknowns for the gravity inversion and it is estimated from the geometric model for the scaling function inversion. The histograms over the density estimated at many iterations show a very concentrated distribution for the scaling function, while the density contrast retrieved by the gravity inversion, according to the fundamental ambiguity density/volume, is widely dispersed, this making difficult to assess its best estimate.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

2007 ◽  
Vol 129 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Heat Source ◽  
Oscillation Amplitude ◽  
The Body ◽  
Transient Temperature ◽  
Dimensionless Frequency ◽  
Heat Sources ◽  
Infinite Body ◽  
Fitting Method ◽  
Wide Range ◽  
Analytical Expressions

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

Role of Out-of-Plane Coefficient of Thermal Expansion in Electronic Packaging Modeling

1999 ◽  
Vol 122 (2) ◽  
pp. 121-127 ◽  
Author(s):  
Manjula N. Variyam ◽  
Weidong Xie ◽  
Suresh K. Sitaraman
Keyword(s):  
Thermal Expansion ◽  
Electronic Packaging ◽  
Thermal Loading ◽  
Coefficient Of Thermal Expansion ◽  
Plane Deformation ◽  
Three Dimensional ◽  
Dissimilar Materials ◽  
3D Models ◽  
Material Behavior ◽  
Element Analysis

Components in electronic packaging structures are of different dimensions and are made of dissimilar materials that typically have time, temperature, and direction-dependent thermo-mechanical properties. Due to the complexity in geometry, material behavior, and thermal loading patterns, finite-element analysis (FEA) is often used to study the thermo-mechanical behavior of electronic packaging structures. For computational reasons, researchers often use two-dimensional (2D) models instead of three-dimensional (3D) models. Although 2D models are computationally efficient, they could provide misleading results, particularly under thermal loading. The focus of this paper is to compare the results from various 2D, 3D, and generalized plane-deformation strip models and recommend a suitable modeling procedure. Particular emphasis is placed to understand how the third-direction coefficient of thermal expansion (CTE) influences the warpage and the stress results predicted by 2D models under thermal loading. It is seen that the generalized plane-deformation strip models are the best compromise between the 2D and 3D models. Suitable analytical formulations have also been developed to corroborate the findings from the study. [S1043-7398(00)01402-X]

scholarly journals The Method of High Accuracy Calculation of Robot Trajectory for the Complex Curves

2020 ◽  
Vol 28 (4) ◽  
pp. 247-252
Author(s):  
Alexander Lozhkin ◽  
Pavol Bozek ◽  
Konstantin Maiorov
Keyword(s):  
Calculation Method ◽  
Geometric Modeling ◽  
Classical Method ◽  
Geometric Model ◽  
New Method ◽  
Approximation Methods ◽  
Linear Transformations ◽  
Design Quality ◽  
Complex Curves ◽  
Internal Properties

AbstractThe geometric model accuracy is crucial for product design. More complex surfaces are represented by the approximation methods. On the contrary, the approximation methods reduce the design quality. A new alternative calculation method is proposed. The new method can calculate both conical sections and more complex curves. The researcher is able to get an analytical solution and not a sequence of points with the destruction of the object semantics. The new method is based on permutation and other symmetries and should have an origin in the internal properties of the space. The classical method consists of finding transformation parameters for symmetrical conic profiles, however a new procedure for parameters of linear transformations determination was acquired by another method. The main steps of the new method are theoretically presented in the paper. Since a double result is obtained in most stages, the new calculation method is easy to verify. Geometric modeling in the AutoCAD environment is shown briefly. The new calculation method can be used for most complex curves and linear transformations. Theoretical and practical researches are required additionally.

scholarly journals MODELING ARCHITECTURAL FORM SURFACE DEPENDENT SECTIONS

2021 ◽  
pp. 53-58
Author(s):  
A. A. Chekalin ◽  
M. K. Reshetnikov ◽  
V. V. Shpilev ◽  
S. V. Borodulina ◽  
S. A. Ryazanov
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Residential Building ◽  
Cubic Splines ◽  
Piecewise Smooth ◽  
Additional Parameter ◽  
Mathematical Apparatus ◽  
Surface Design ◽  
Fourth Degree ◽  
Architectural Form

For the design of surfaces in architecture, as a rule, universal techniques developed for other technical industries are used. First of all, these are general kinematic surfaces and interpolation cubic splines for modeling complex piecewise smooth surfaces. The authors propose to use the fourth degree inerodifferential spline developed by them for problems of geometric modeling of architectural forms. For calculations and constructions on a computer, the proposed spline is not much more complicated than traditional cubic splines, since it has one additional parameter - a coefficient. However, this allows you to locally control the shape of a curve or surface during design, that is, to change the shape in individual areas without affecting other areas. The article proposes a method for constructing a geometric model of the kinematic surface of dependent sections with a fourth degree parabola as a generator. When using cubic splines as a guide, the surface is a 3 × 4 non-uniform (heterogeneous) spline. The article shows that the surface on the basis of the proposed mathematical apparatus can be composite piecewise-smooth. A particular case of surface design is considered on the example of creating a model of the surface of the facade of a residential building according to the existing concept. The algorithm can be easily programmed and added as a tool to existing CAD systems.

BIOMECHANICAL MODEL PREDICTING VALUES OF MUSCLE FORCES IN THE SHOULDER GIRDLE DURING ARM ELEVATION

2010 ◽  
Vol 10 (04) ◽  
pp. 643-666 ◽  
Author(s):  
ERIC BERTHONNAUD ◽  
MELISSA MORROW ◽  
GUILLAUME HERZBERG ◽  
KAI-NAN AN ◽  
JOANNES DIMNET
Keyword(s):  
Geometric Modeling ◽  
Geometric Model ◽  
Contractile Element ◽  
Muscle Forces ◽  
Active Muscle ◽  
Cross Sectional ◽  
Shoulder Complex ◽  
Arm Elevation

A three-dimensional (3D) geometric model for predicting muscle forces in the shoulder complex is proposed. The model was applied throughout the range of arm elevation in the scapular plan. In vitro testing has been performed on 13 cadaveric shoulders. The objectives were to determine homogeneous values of physiological parameters of shoulder muscles and to locate sites of muscular attachment to any bone of the shoulder complex. Muscular fiber lengths, lengths of contractile element (CE), and muscle volumes were measured, corresponding physiological cross-sectional area (PCSA) were calculated, and force/length muscle relations were found. An in vivo biplanar radiography was performed on five volunteers. The photogrammetric reconstruction of bone axes and landmarks were coupled with a geometric modeling of bones and muscle sites of attachment. Muscular paths were drawn and changes in lengths during movement have been estimated. Directions of muscle forces are the same as that of muscular path at the point of attachment to bone. Magnitudes of muscular forces were found from muscle lengths coupled with force/length relations. Passive forces were directly determined contrary to active muscle forces. A resulting active muscle force is calculated from balancing weight and passive forces at each articular center. Active muscle forces were calculated by distributing the resulting force among active muscles based on the muscular PCSA values.

scholarly journals Geometric modeling of surfaces dependent cross sections in the tasks of spinning and laying

2019 ◽  
Vol 110 ◽  
pp. 01057
Author(s):  
Yuri Deniskin ◽  
Pavel Miroshnichenko ◽  
Andrew Smolyaninov
Keyword(s):  
Composite Materials ◽  
Cross Sections ◽  
Geometric Modeling ◽  
Geometric Model ◽  
Solid Modeling ◽  
Uniform Method ◽  
Calculation Methods ◽  
Related Process

The article is devoted to the development of a geometric model of surfaces of dependent sections to solve the problems of winding by continuous fibers in the direction of the force and its related process of automated winding of composite materials. A uniform method for specifying the surfaces of dependent sections with a curvilinear generator and a method for solid modeling of the shell obtained by winding or calculation methods are described.

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