Empirical Equations for the Direct Definition of Stress–Strain Laws for Fiber-Section-Based Macromodeling of Infilled Frames

2018 ◽  
Vol 144 (11) ◽  
pp. 04018101 ◽  
Author(s):  
Fabio Di Trapani ◽  
Gabriele Bertagnoli ◽  
Marco Filippo Ferrotto ◽  
Diego Gino
Keyword(s):  
Empirical Equations ◽  
Stress Strain ◽  
Infilled Frames ◽  
Direct Definition ◽  
Definition Of

Cubical Agda: A dependently typed programming language with univalence and higher inductive types

2021 ◽  
Vol 31 ◽  
Author(s):  
ANDREA VEZZOSI ◽  
ANDERS MÖRTBERG ◽  
ANDREAS ABEL
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Type Checking ◽  
Dependent Type Theory ◽  
Wide Range ◽  
General Schema ◽  
Direct Definition ◽  
Inductive Types ◽  
Definition Of ◽  
Cubical Type Theory

Abstract Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to Homotopy Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types (HITs). This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of HITs. These new primitives allow the direct definition of function and propositional extensionality as well as quotient types, all with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. The adoption of cubical type theory extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

Definition of the yield point in plasticity and its effect on the shape of the yield locus

1966 ◽  
Vol 1 (4) ◽  
pp. 331-338 ◽  
Author(s):  
T C Hsu
Keyword(s):  
Yield Point ◽  
Experimental Work ◽  
Strain Curve ◽  
Yield Locus ◽  
Experimental Results ◽  
Stress Strain Curve ◽  
Proportional Limit ◽  
Stress Strain ◽  
Small Section ◽  
Definition Of

Three different definitions of the yield point have been used in experimental work on the yield locus: proportional limit, proof strain and the ‘yield point’ by backward extrapolation. The theoretical implications of the ‘yield point’ by backward extrapolation are examined in an analysis of the loading and re-loading stress paths. It is shown, in connection with experimental results by Miastkowski and Szczepinski, that the proportional limit found by inspection is in fact a point located by backward extrapolation based on a small section of the stress-strain curve, near the elastic portion of the curve. The effect of different definitions of the yield point on the shape of the yield locus and some considerations for the choice between them are discussed.

Tarski

Truth ◽  
2011 ◽  
Author(s):  
Alexis G. Burgess ◽  
John P. Burgess
Keyword(s):  
Mathematical Logic ◽  
Model Theory ◽  
The State ◽  
Truth Predicate ◽  
Object Language ◽  
French And English ◽  
Direct Definition ◽  
Definition Of ◽  
Basic Features ◽  
Self Reference

This chapter offers a simplified account of the most basic features of Alfred Tarski's model theory. Tarski foresaw important applications for a notion of truth in mathematics, but also saw that mathematicians were suspicious of that notion, and rightly so given the state of understanding of it circa 1930. In a series of papers in Polish, German, French, and English from the 1930s onward, Tarski attempted to rehabilitate the notion for use in mathematics, and his efforts had by the 1950s resulted in the creation of a branch of mathematical logic known as model theory. The chapter first considers Tarski's notion of truth, which he calls “semantic” truth, before discussing his views on object language and metalanguage, recursive versus direct definition of the truth predicate, and self-reference.

scholarly journals Calculation of composite elements of slabs in buildings, structures and fragments of spans of bridges

2018 ◽  
Vol 230 ◽  
pp. 02007 ◽  
Author(s):  
Stanislav Fomin ◽  
Yuriy Izbash ◽  
Serhii Butenko ◽  
Maryna Iakymenko ◽  
Karina Spirande
Keyword(s):  
Bearing Capacity ◽  
High Temperatures ◽  
Composite Structures ◽  
Strain Ratio ◽  
Strain Diagram ◽  
Stress Strain ◽  
Maximum Deformation ◽  
Definition Of ◽  
Two Stages ◽  
The Mathematical Model

The calculation consists of two stages. The first one begins with the definition of their class, bearing capacity at temperature of 20 °C, according to EN 1992-1-1. At the second stage, the calculation at high temperatures shall be carried out in accordance with Eurocode 4 part 1-2. Comparison of the “stress-strain” diagram of concrete of class 30 under compression and temperature of 20 °C in two formulas showed their difference. That is, the designers do not have the opportunity to continue the calculation of diagrams at different heating temperatures. There was a need to improve the mathematical model of the “stress-strain” ratio of concrete high temperatures, clarification of the criteria of the bearing capacity of concrete in calculation of the fire resistance of composite structures in EN 1994-1-2:2005. In this paper, the method of determination of εcu1,θ developed has allowed, based on the energy approach, to formulate the corrected dependence of the limit deformation on temperature, dependence of the maximum deformation on temperature, and the value of the parameters of the “stress-strain” diagram. According to these data, using the formulas of the first stage, the “stress-strain” diagrams of the concrete of class 30 are calculated at the compression and heating according to EN 1992-1-2:2004.

Stress-Based Forming Limits in Sheet-Metal Forming

2000 ◽  
Vol 123 (4) ◽  
pp. 417-422 ◽  
Author(s):  
Thomas B. Stoughton
Keyword(s):  
Sheet Metal ◽  
Sheet Metal Forming ◽  
Metal Forming ◽  
Strain Path ◽  
Forming Limit ◽  
Stress Strain ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
The Stability ◽  
Definition Of

A strain-based forming limit criterion is widely used throughout the sheet-metal forming industry to gauge the stability of the deformed material with respect to the development of a localized neck prior to fracture. This criterion is strictly valid only when the strain path is linear throughout the deformation process. There is significant data that shows a strong and complex dependence of the limit criterion on the strain path. Unfortunately, the strain path is never linear in secondary forming and hydro-forming processes. Furthermore, the path is often found to be nonlinear in localized critical areas in the first draw die. Therefore, the conventional practice of using a path-independent strain-based forming limit criterion often leads to erroneous assessments of forming severity. Recently it has been reported that a stress-based forming limit criterion appears to exhibit no strain-path dependencies. Subsequently, it has been suggested that this effect is not real, but is due to the saturation of the stress-strain relation. This paper will review and compare the strain-based and stress-based forming limit criteria, looking at a number of factors that are involved in the definition of the stress-based forming limit, including the role of the stress-strain relation.

Realisability semantics of parametric polymorphism, general references and recursive types

2010 ◽  
Vol 20 (4) ◽  
pp. 655-703 ◽  
Author(s):  
LARS BIRKEDAL ◽  
KRISTIAN STØVRING ◽  
JACOB THAMSBORG
Keyword(s):  
Metric Spaces ◽  
Logical Relation ◽  
Data Types ◽  
General Reference ◽  
New Approach ◽  
Parametric Polymorphism ◽  
Abstract Data ◽  
Direct Definition ◽  
Semantic Types ◽  
Definition Of

We present a realisability model for a call-by-value, higher-order programming language with parametric polymorphism, general first-class references, and recursive types. The main novelty is a relational interpretation of open types that include general reference types. The interpretation uses a new approach to modelling references.The universe of semantic types consists of world-indexed families of logical relations over a universal predomain. In order to model general reference types, worlds are finite maps from locations to semantic types: this introduces a circularity between semantic types and worlds that precludes a direct definition of either. Our solution is to solve a recursive equation in an appropriate category of metric spaces. In effect, types are interpreted using a Kripke logical relation over a recursively defined set of worlds.We illustrate how the model can be used to prove simple equivalences between different implementations of imperative abstract data types.

scholarly journals ESSENCE OF THE SERVICE CATEGORY IN FORENSIC MERCHANDISING

2020 ◽  
Vol 2 ◽  
pp. 69-76
Author(s):  
I. Petrova ◽  
O. Dontsova
Keyword(s):  
Economic Value ◽  
Service Work ◽  
Structural Elements ◽  
Commercial Activity ◽  
Service Category ◽  
Direct Definition ◽  
Definition Of ◽  
Different Sources ◽  
Essential Service

The article states that market of services, as a field of economic activity, plays the role of a leading sector of the national economy is not without certain problems, among which was the possibility of evaluating the service within the forensic merchandising. It is noted that researchers of the concept of service paid attention to its direct definition, description of the characteristics inherent in services and identify differences between the concepts: Goods, service, work. It is established the essence of the concept of service remains debatable and insufficiently researched regarding its application in forensic merchandising. In view of this, various structural elements of the concept of service were systematized into a single holistic definition by studying scientific approaches, terminological analysis and refining the definitions of this concept from different sources. It is established that uncertainty of services is that they are processes, not material objects and do not fall under the traditional definition of goods; identified a number of properties that distinguish services from tangible goods, and identified specific features of intangible services. It is emphasized that researching on category essence of service in forensic merchandising, one cannot ignore the interpretation of this term by legislators and scholars. Analysis of the service definition in regulations has established that the generalizing concept of service for these acts is a service as an action that has a certain beneficial effect, i.e. has benefits for consumer. Scientists argue that the service usually is an intangible product, process, and ownership of it for its sale to the consumer does not arise; ownership may arise as a result of the provision of the service. The essential service characteristic is defined by scientists as economic value, which makes it an object of commercial activity, a subject of trade and an object of purchase and sale; it turns it into an economic good. It is established that service concept is most often associated with the action or activity of the service provider aimed at meeting the needs of the consumer and is realized at the time of its provision.

On the analysis of stress-strain curves by means of empirical equations

1975 ◽  
Vol 9 (11) ◽  
pp. 1147-1148 ◽  
Author(s):  
J.R.C. Guimaraes ◽  
D.L. Valeriano Alves
Keyword(s):  
Empirical Equations ◽  
Stress Strain
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