scholarly journals Prestress behaviour and ductility requirements in structures: solutions from a unified algebraic approach

2021 ◽  
Vol 8 (12) ◽  
Author(s):  
Jaime Cervera Bravo ◽  
Laura Navas-Sánchez
Keyword(s):  
Limit State ◽  
Algebraic Approach ◽  
Unified Framework ◽  
Structural Problems ◽  
Internal Forces ◽  
Deformed State ◽  
Nodal Displacements ◽  
Loaded Structure ◽  
Value Decomposition

This paper presents an algebraic approach that unifies both the elastic and limit theories of static structural analysis. This approach reveals several previously unpublished improvements, which are based on several dualities in the mathematical description. Firstly, we show a novel duality between the solutions to two different problems: the elastic solution to the internal forces of an externally loaded structure, and the nodal displacements induced by prestressing in one or several elements of the same structure. This duality is proven and discussed. The application of this solution to the limit state analysis is very productive, and includes the determination of the ductility requirements necessary to achieve full plastic behaviour, and the assessment of the prestress needed to limit or eliminate such requirements. The unified framework also allows to obtain the elasto-plastic deformed state at the beginning of the plastic structural collapse. We have also detailed the theoretical duality between two classes of structures—hyperstatic and hypostatic—which was derived from the linear algebra principles that define these solutions. Finally, we studied and exposed the dimensionality reduction of structural problems given by the singular value decomposition and the eigenvalues problem. An illustrative example that clearly illustrates all these points is provided.

Determination of Internal Forces in End Plates of Simple End Plate Joints

2009 ◽  
Vol 12 (-1) ◽  
pp. 83-94
Author(s):  
Stefan Dominikowski ◽  
Piotr Bogacz
Keyword(s):  
End Plate ◽  
Internal Forces

MANUFACTURE INVESTIGATION OF CARTRIDGE WITH BOTTOM-MOST PART FLANGE BY DIRECT EXTRUSION WITH COUNTERPUNCH. REPORT 13. DETERMINATION OF DEFORMED STATE UNDER STRAITENED EXTRUSION IN FOURTH CENTRAL AREA OF PLASTIC DEFORMATION

2020 ◽  
Vol 0 (4) ◽  
pp. 43-51
Author(s):  
A. L. Vorontsov ◽  
◽  
I. A. Nikiforov ◽  
Keyword(s):  
Plastic Deformation ◽  
Plastic Flow ◽  
Central Area ◽  
Direct Extrusion ◽  
Deformed State ◽  
Cumulative Deformation ◽  
The Given ◽  
General Method

Formulae have been obtained that are necessary to calculate cumulative deformation in the process of straitened extrusion in the central area closed to the working end of the counterpunch. The general method of plastic flow proposed by A. L. Vorontsov was used. The obtained formulae allow one to determine the deformed state of a billet in any point of the given area. The formulae should be used to take into account the strengthening of the extruded material.

Determination of Internal Forces in Human Hand

1978 ◽  
Vol 104 (1) ◽  
pp. 255-272
Author(s):  
E.Y. Chao ◽  
K.N. An
Keyword(s):  
Human Hand ◽  
Internal Forces

Research of stamping of unequal channel bars. Part 4. Deformed state of the workpiece when extruding channels. 2. Deformations under the punch end

2021 ◽  
pp. 53-57
Author(s):  
A.L. Vorontsov
Keyword(s):  
Plastic Deformation ◽  
Plane Strain ◽  
Deformation Zone ◽  
Plastic Deformation Zone ◽  
Die Forging ◽  
Deformed State

Determination of the deformed state of the workpiece at free extrusion of channels is considered. Formulas are obtained for determining the accumulated deformations at a given point of the plastic deformation zone and extruded walls of the product for any punch working stroke. Keywords: die forging, extrusion, misalignment, punch, matrix, plane strain, accumulated deformations, hardening. [email protected]

Influence of Human Error on Structural Reliability

2017 ◽  
Author(s):  
Eric Brehm ◽  
Robert Hertle ◽  
Markus Wetzel
Keyword(s):  
Human Error ◽  
Structural Reliability ◽  
Failure Modes ◽  
Structural Model ◽  
Limit State ◽  
Design Procedure ◽  
Material Strength ◽  
Limit States ◽  
The Impact

In common structural design, random variables, such as material strength or loads, are represented by fixed numbers defined in design codes. This is also referred to as deterministic design. Addressing the random character of these variables directly, the probabilistic design procedure allows the determination of the probability of exceeding a defined limit state. This probability is referred to as failure probability. From there, the structural reliability, representing the survival probability, can be determined. Structural reliability thus is a property of a structure or structural member, depending on the relevant limit states, failure modes and basic variables. This is the basis for the determination of partial safety factors which are, for sake of a simpler design, applied within deterministic design procedures. In addition to the basic variables in terms of material and loads, further basic variables representing the structural model have to be considered. These depend strongly on the experience of the design engineer and the level of detailing of the model. However, in the clear majority of cases [1] failure does not occur due to unexpectedly high or low values of loads or material strength. The most common reasons for failure are human errors in design and execution. This paper will provide practical examples of original designs affected by human error and will assess the impact on structural reliability.

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Calculation of thin isotropic shells beyond the elastic limit by the method of elastic solutions

2018 ◽  
Vol 196 ◽  
pp. 01014 ◽  
Author(s):  
Avgustina Astakhova
Keyword(s):  
Elastic Limit ◽  
Physical Nonlinearity ◽  
Elasticity Tensor ◽  
Thin Shells ◽  
Equilibrium Equations ◽  
Spherical Shells ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Internal Forces

The paper focuses on the model of calculation of thin isotropic shells beyond the elastic limit. The determination of the stress-strain state of thin shells is based on the small elastic-plastic deformations theory and the elastic solutions method. In the present work the building of the solution based on the equilibrium equations and geometric relations of linear theory of thin shells in curved coordinate system α and β, and the relations between deformations and forces based on the Hirchhoff-Lave hypothesis and the small elastic-plastic deformations theory are presented. Internal forces tensor is presented in the form of its expansion to the elasticity tensor and the additional terms tensor expressed the physical nonlinearity of the problem. The functions expressed the physical nonlinearity of the material are determined. The relations that allow to determine the range of elastic-plastic deformations on the surface of the present shell and their changing in shell thickness are presented. The examples of the calculation demonstrate the convergence of elastic-plastic deformations method and the range of elastic-plastic deformations in thickness in the spherical shell. Spherical shells with the angle of half-life regarding 90 degree vertical symmetry axis under the action of equally distributed ring loads are observed.

EVALUATION OF THE STRESSED DEFORMED STATE OF MAIN GAS PIPELINES RUNNING IN PERMANENTLY FROZEN GROUNDS

2020 ◽  
pp. 58-63
Author(s):  
M. M. Sidorov ◽  
N. I. Golikov ◽  
R. P. Tihonov
Keyword(s):  
Experimental Data ◽  
Calculated Data ◽  
Gas Pipeline ◽  
Loss Of Stability ◽  
Portable Equipment ◽  
Ray Method ◽  
X Ray ◽  
Deformed State ◽  
Pipeline Monitoring

The work evaluates the stress deformed state of the section of the interfield gas collecting main, running in permanently frozen grounds. The object of research is a section of a pipeline with an arched discharge formed as a result of loss of stability as a result of thermal erosion of permanently frozen grounds to disturbance of the vegetation cover. The determination of stresses was carried out by the X-ray method using portable equipment. The experimental data were analyzed with the calculated. The calculated data were obtained by measuring the spatial position of the gas pipeline section. The obtained values of the acting stresses and the estimates of the critical indicators of the gas pipeline monitoring section made it possible to reasonably estimate the stress state. The methodology for determining the acting stresses of pipelines using portable X-ray equipment can be successfully applied to estimate the stressed-deformed state of pipeline systems running in the zone of permafrost.

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