Predicted Response of the Die-Carrier Assembly in Flexible Electronics to the Combined Action of Tension and Bending Applied to the Carrier

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
E. Suhir
Keyword(s):  
Mathematical Model ◽  
Normal Stress ◽  
Cross Sections ◽  
Flexible Electronics ◽  
Bending Moments ◽  
Analysis And Design ◽  
Tensile Forces ◽  
Combined Action ◽  
The Cross

A die-carrier assembly, subjected to the external tensile forces and bending moments applied to the flexible carrier is considered. The objective of the analysis is to develop a simple, easy-to-use, and physically meaningful predictive analytical (“mathematical”) model aimed at understanding the physics of the combined action of tension and bending experienced by the carrier and transmitted to the die through the more-or-less compliant bond. The addressed stresses include the interfacial shearing and peeling stresses, as well as the normal stress acting in the cross sections of the die. The obtained formulae can be used in the analysis and design of assemblies of the type in question.

scholarly journals TO QUESTION OF COMBINED SYSTEMS RATIONALIZATION

2019 ◽  
pp. 97-103
Author(s):  
S. D. SINCHUK
Keyword(s):  
Cross Sections ◽  
Bending Moment ◽  
Variable Number ◽  
Bending Moments ◽  
New Approach ◽  
Present Solution ◽  
Combined Structure ◽  
Optimal Values ◽  
The Cross ◽  
Effective Design

Purpose. Developing a new approach to the rationalization of the combined structure, taking into account constructive, technological, operational and economic requirements. Methodology. The bending moment adjustment method representations to achieve the goal, based on the properties of the thrust-systems, namely: in the combination beam construction cost material defining elements are experiencing stress state of compression with a bend; in cells operating at the bending compression, reducing the size of the cross section largely determined by the decrease of the bending moment; bending moments increase from the support to the middle of the span. Originality. On the basis of calculations using the methodology set forth above, the algorithm of optimal design of truss beams under the influence of permanent and temporary load. The present solution allows to obtain an effective design combined with a variable number of racks, depending on the required span length, corresponding to the received optimality criterion. Practical value. The use of this approach and the optimization algorithm based on the use of the design features of truss beams and requires minimization of bending moments, will significantly reduce the complexity of the calculation, as well as to find the optimal values of the cross sections for each case.

Reinforced earth retaining wall analysis and design

1986 ◽  
Vol 23 (3) ◽  
pp. 317-326 ◽  
Author(s):  
J. T. Laba ◽  
J. B. Kennedy
Keyword(s):  
Design Method ◽  
Retaining Wall ◽  
Tensile Force ◽  
Stress Transfer ◽  
Maximum Magnitude ◽  
Analysis And Design ◽  
Strength Capacity ◽  
Reinforced Earth ◽  
Tensile Forces ◽  
Combined Action

An experimental and theoretical study was conducted to assess the maximum tensile forces mobilized in a reinforced earth retaining wall, subjected to a vertical surcharge strip load or the combined action of vertical and horizontal surcharge strip loads. A simple design method for determining the maximum magnitude of the tensile force and its distribution with depth of the reinforced earth backfill was developed. The design method takes into consideration the ability of the reinforced earth wall system to retain its internl equilibrium by stress transfer from overstressed regions to those regions where the reinforcing elements have not yet reached their full frictional or strength capacity. The effect of the magnitude and location of the strip load on this phenomenon of stress transfer is shown. Favourable comparisons were obtained between the results given by the proposed design method and those from model tests. Key words: reinforced earth, vertical and horizontal surcharge strip load, reinforcing elements, internal stability, stress transfer.

Mathematical Modeling of the Circulation in the Liver Lobule

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Andrea Bonfiglio ◽  
Kritsada Leungchavaphongse ◽  
Rodolfo Repetto ◽  
Jennifer H. Siggers
Keyword(s):  
Mathematical Model ◽  
Porous Medium ◽  
Cross Section ◽  
Cross Sections ◽  
Total Blood ◽  
Liver Lobule ◽  
Tissue Compliance ◽  
Two Dimensional Flow ◽  
Qualitative Effect ◽  
The Cross

In this paper, we develop a mathematical model of blood circulation in the liver lobule. We aim to find the pressure and flux distributions within a liver lobule. We also investigate the effects of changes in pressure that occur following a resection of part of the liver, which often leads to high pressure in the portal vein. The liver can be divided into functional units called lobules. Each lobule has a hexagonal cross-section, and we assume that its longitudinal extent is large compared with its width. We consider an infinite lattice of identical lobules and study the two-dimensional flow in the hexagonal cross-sections. We model the sinusoidal space as a porous medium, with blood entering from the portal tracts (located at each of the vertices of the cross-section of the lobule) and exiting via the centrilobular vein (located in the center of the cross-section). We first develop and solve an idealized mathematical model, treating the porous medium as rigid and isotropic and blood as a Newtonian fluid. The pressure drop across the lobule and the flux of blood through the lobule are proportional to one another. In spite of its simplicity, the model gives insight into the real pressure and velocity distribution in the lobule. We then consider three modifications of the model that are designed to make it more realistic. In the first modification, we account for the fact that the sinusoids tend to be preferentially aligned in the direction of the centrilobular vein by considering an anisotropic porous medium. In the second, we account more accurately for the true behavior of the blood by using a shear-thinning model. We show that both these modifications have a small quantitative effect on the behavior but no qualitative effect. The motivation for the final modification is to understand what happens either after a partial resection of the liver or after an implantation of a liver of small size. In these cases, the pressure is observed to rise significantly, which could cause deformation of the tissue. We show that including the effects of tissue compliance in the model means that the total blood flow increases more than linearly as the pressure rises.

scholarly journals OPTIMIZATION OF TRUSS HEIGHT

2010 ◽  
Vol 2 (6) ◽  
pp. 56-60 ◽  
Author(s):  
Tomas Ulitinas ◽  
Stanislovas Kalanta
Keyword(s):  
Mathematical Model ◽  
Mathematical Programming ◽  
Programming Problem ◽  
Cross Sections ◽  
Software Package ◽  
Iterative Process ◽  
Mathematical Programming Problem ◽  
Mathematical Software ◽  
Nonlinear Mathematical Programming ◽  
The Cross

The article analyzes the task in truss height and in the optimization of the cross-sections of their elements. Element cross-sections are designed of steel profiles considering requirements for strength, stability and rigidity. A mathematical model is formulated as a nonlinear mathematical programming problem. It is solved as an iterative process, using mathematical software package “MATLAB” routine “fmincon”. The ratio of buckling is corrected in the each iteration. Optimization results are compared with those obtained applying software package “Robot Millennium”.

scholarly journals Cross-Sectional Performance of Hollow Square Prisms with Rounded Edges

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 996
Author(s):  
Hiroyuki Shima ◽  
Nao Furukawa ◽  
Yuhei Kameyama ◽  
Akio Inoue ◽  
Motohiro Sato
Keyword(s):  
Mechanical Properties ◽  
Mathematical Model ◽  
Cross Sections ◽  
Cross Sectional ◽  
Hollow Section ◽  
Buckling Resistance ◽  
The Cross ◽  
The Stability ◽  
External Forces ◽  
Sectional Shape

Hollow-section columns are one of the mechanically superior structures with high buckling resistance and high bending stiffness. The mechanical properties of the column are strongly influenced by the cross-sectional shape. Therefore, when evaluating the stability of a column against external forces, it is necessary to reproduce the cross-sectional shape accurately. In this study, we propose a mathematical method to describe a polygonal section with rounded edges and vertices. This mathematical model would be quite useful for analyzing the mechanical properties of plants and designing plant-mimicking functional structures, since the cross-sections of the actual plant culms and stems often show rounded polygons.

The cross sections for different channels in heavy ion nuclear reactions

1971 ◽  
Vol 32 (1) ◽  
pp. 7-9 ◽  
Author(s):  
J. Galin ◽  
D. Guerreau ◽  
M. Lefort ◽  
X. Tarrago
Keyword(s):  
Cross Sections ◽  
Nuclear Reactions ◽  
Heavy Ion ◽  
The Cross

Experimental Studies Of Multilayer Glass Structures On Compression, Compression With Bending And Simple Bending

2019 ◽  
pp. 22-30
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Applied Load ◽  
Experimental Studies ◽  
Strength Properties ◽  
Research Topic ◽  
Normative Values ◽  
Laminated Glass ◽  
The Cross ◽  
Experimental Values

The work of multilayer glass structures for central and eccentric compression and bending are considered. The substantiation of the chosen research topic is made. The description and features of laminated glass for the structures investigated, their characteristics are presented. The analysis of the results obtained when testing for compression, compression with bending, simple bending of models of columns, beams, samples of laminated glass was made. Overview of the types and nature of destruction of the models are presented, diagrams of material operation are constructed, average values of the resistance of the cross-sections of samples are obtained, the table of destructive loads is generated. The need for development of a set of rules and guidelines for the design of glass structures, including laminated glass, for bearing elements, as well as standards for testing, rules for assessing the strength, stiffness, crack resistance and methods for determining the strength of control samples is emphasized. It is established that the strength properties of glass depend on the type of applied load and vary widely, and significantly lower than the corresponding normative values of the strength of heat-strengthened glass. The effect of the connecting polymeric material and manufacturing technology of laminated glass on the strength of the structure is also shown. The experimental values of the elastic modulus are different in different directions of the cross section and in the direction perpendicular to the glass layers are two times less than along the glass layers.

scholarly journals Total cross sections of eγ → $$ eX\overline{X} $$ processes with X = μ, γ, e via multiloop methods

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Roman N. Lee ◽  
Alexey A. Lyubyakin ◽  
Vyacheslav A. Stotsky
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Elliptic Integral ◽  
High Energy ◽  
Calculation Methods ◽  
Complete Elliptic Integral ◽  
Total Cross Sections ◽  
Multiloop Calculation ◽  
The Cross ◽  
Analytical Expressions

Abstract Using modern multiloop calculation methods, we derive the analytical expressions for the total cross sections of the processes e−γ →$$ {e}^{-}X\overline{X} $$ e − X X ¯ with X = μ, γ or e at arbitrary energies. For the first two processes our results are expressed via classical polylogarithms. The cross section of e−γ → e−e−e+ is represented as a one-fold integral of complete elliptic integral K and logarithms. Using our results, we calculate the threshold and high-energy asymptotics and compare them with available results.

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