scholarly journals A Critical Review on the Complex Potentials in Linear Elastic Fracture Mechanics

2022 ◽  
Author(s):  
Johannes Scheel ◽  
Daniel Wallenta ◽  
Andreas Ricoeur
Keyword(s):  
Critical Review ◽  
Applied Mathematics ◽  
Crack Opening ◽  
Point Of View ◽  
Complex Potentials ◽  
Mathematical Treatment ◽  
Crack Plane ◽  
Essential Information ◽  
Full Field ◽  
Linear Elastic

AbstractIntroducing a crack in an elastic plate is challenging from the mathematical point of view and relevant within an engineering context of evaluating strength and reliability of structures. Accordingly, a multitude of associated works is available to date, emanating from both applied mathematics and mechanics communities. Although considering the same problem, the given complex potentials prove to be different, revealing various inconsistencies in terms of resulting stresses and displacements. Essential information on crack near-tip fields and crack opening displacements is nonetheless available, while intuitive adaption is required to obtain the full-field solutions. Investigating the cause of prevailing deficiencies inevitably leads to a critical review of classical works by Muskhelishvili or Westergaard. Complex potentials of the mixed-mode loaded Griffith crack, sparing restrictive assumptions or limitations of validity, are finally provided, allowing for rigorous mathematical treatment. The entity of stresses and displacements in the whole plate is finally illustrated and the distributions in the crack plane are given explicitly.

Translation and interpretation in Abhidharmakośa

Diogenes ◽  
2021 ◽  
Vol 29 (2) ◽  
Author(s):  
Mitko Momov
Keyword(s):  
Critical Review ◽  
Point Of View ◽  
Literal Meaning ◽  
The Other ◽  
Young Scholar ◽  
Other Hand ◽  
The One

Rosemberg (1991) has made a critical review of a long-standing discussion between Eastern philologists and Buddhist philosophers. The discussion is centered around the translation of the doctrine on the one hand, and its philosophical systematization on the other hand. When scientific-philological translation prevails, the literal meaning of Buddhist terminology is declared to be its basis. The young scholar, who had specialized in Japan, studied Buddhism from Japanese and Chinese sources and collected lexicographic material from non-Hindu sources. After comparing them, he encountered inaccuracies in the translation. In an attempt to overcome them, he preferred the point of view of the philosophy of Buddhism. The conclusion that he has drawn in the preface of this edition is that the study should begin with a systematization of antiquity.

Fully Plastic Solutions and Large Scale Yielding Estimates for Plane Stress Crack Problems

1976 ◽  
Vol 98 (4) ◽  
pp. 289-295 ◽  
Author(s):  
C. F. Shih ◽  
J. W. Hutchinson
Keyword(s):  
Plane Stress ◽  
Large Scale ◽  
Crack Opening ◽  
Opening Displacement ◽  
Stress Strain ◽  
Linear Elastic ◽  
Strain Relation ◽  
Stress Strain Relation ◽  
Crack Problems ◽  
Scale Yielding

Fully plastic plane stress solutions are given for a center-cracked strip in tension and an edge-cracked strip in pure bending. In the fully plastic formulation the material is characterized by a pure power hardening stress-strain relation which reduces at one limit to linear elasticity and at the other to rigid/perfect plasticity. Simple formulas are given for estimating the J-integral, the load-point displacement and the crack opening displacement in terms of the applied load for strain hardening materials characterized by the Ramberg-Osgood stress-strain relation in tension. The formulas make use of the linear elastic solution and the fully plastic solution to interpolate over the entire range of small and large scale yielding. The accuracy of the formulas is assessed using finite element calculations for some specific configurations.

Peranan Strategi Pemasaran Dalam Upaya Meningkatkan Penjualan Jasa Asuransi pada PT Asuransi Umum Bumiputera Muda 1967 Medan

2021 ◽  
Vol 1 (1) ◽  
pp. 29-45
Author(s):  
Sakinah Sakinah ◽  
Nur Aslami
Keyword(s):  
Side Effect ◽  
Market Competition ◽  
Point Of View ◽  
Essential Information ◽  
General Insurance ◽  
Individual Point ◽  
Job Vacancy ◽  
Tangible Evidence ◽  
The Individual

This review is expected to be ableto dissect the procedure of promotion work through the combination of 7Ps implemented by PT. General Insurance Bumiputera Muda 1967 Medan is now ready to compete in the field, this exam uses a fascinating exploration technique. This inspection was led by an organization engaged in the protection sector, namely PT. Bumiputera Muda General Insurance 1967 Medan. The methods of collecting information from this examination are (perception), documentation and meetings. Information obtained from the consequences of essential information and optional information. The information checking strategy used is an enlightening investigation that clarifies the actual conditions that occur substantially and significantly and explains exploratory information. The side effect of this expressive review is that the agreement is shaky and will often diminish with each passing year at PT. Bumiputera Muda 1967 General Insurance Medan was caused by the absence of the largest 7P advertising mix job vacancy applied by PT. Bumiputera Muda General Insurance 1967 Medan. The job of assisting the promotion procedure through the 7P advertising blend carried out by PT. Bumiputera Muda 1967 General Insurance Medan from the part (goods) offered to be competitive in search and very good, in terms of value it can compete in search, part of the circulation channel (place) is still not ideal and there are still weaknesses, part of progress (forward) ) is still not ideal and still uses the old strategy, the individual point of view is very large, the cycle perspective is sufficient, the point of view of tangible evidence is still poor in times of serious market competition.

Object-Oriented Cognitive Complexity Measures

2017 ◽  
pp. 917-940
Author(s):  
Sanjay Misra ◽  
Adewole Adewumi
Keyword(s):  
Software Development ◽  
Comparative Study ◽  
Critical Review ◽  
Cognitive Complexity ◽  
Object Oriented ◽  
Point Of View ◽  
Complexity Measures ◽  
Cognitive Informatics ◽  
Validation Criteria ◽  
Object Oriented Metrics

This chapter presents the analysis of ten recently proposed object-oriented metrics based on cognitive informatics. The metrics based on cognitive informatics use cognitive weight. Cognitive weight is the representation of the understandability of the piece of software that evaluates the difficulty experienced in comprehending and/or performing the piece of software. Development of metrics based on Cognitive Informatics (CI) is a new area of research, and from this point of view, for the analysis of these metrics, it is important to know their acceptability from other existing evaluation and validation criteria. This chapter presents a critical review on existing object-oriented cognitive complexity measures. In addition, a comparative study based on some selected attributes is presented.

Characterization of Cracks From Ultrasonic Scattering Data

1987 ◽  
Vol 54 (4) ◽  
pp. 754-760 ◽  
Author(s):  
J. D. Achenbach ◽  
D. A. Sotiropoulos ◽  
H. Zhu
Keyword(s):  
Scattered Field ◽  
Inverse Method ◽  
Crack Opening ◽  
Elastic Solid ◽  
Scattering Data ◽  
Crack Plane ◽  
Ultrasonic Scattering ◽  
Low Frequencies ◽  
Planar Crack

An inverse method for ultrasonic scattering data is proposed, to characterize a planar crack of general shape contained in an elastic solid. The method is based on an integral representation for the scattered field in the frequency domain. For a given scattered field the inverse problem has been formulated as a nonlinear optimization problem. At low frequencies its solution gives the location of the crack, the orientation of the crack-plane, and the crack-opening volumes. In addition the Mode I stress-intensity factor is obtained for a related static stress state corresponding to service loads.

scholarly journals Fractional Derivatives and Integrals: What Are They Needed For?

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 164 ◽  
Author(s):  
Vasily E. Tarasov ◽  
Svetlana S. Tarasova
Keyword(s):  
Power Law ◽  
Applied Mathematics ◽  
Mathematical Problem ◽  
Frequency Dispersion ◽  
Point Of View ◽  
Fading Memory ◽  
Fractional Operator ◽  
Distributed Lag ◽  
Pure Mathematics ◽  
New Research

The question raised in the title of the article is not philosophical. We do not expect general answers of the form “to describe the reality surrounding us”. The question should actually be formulated as a mathematical problem of applied mathematics, a task for new research. This question should be answered in mathematically rigorous statements about the interrelations between the properties of the operator’s kernels and the types of phenomena. This article is devoted to a discussion of the question of what is fractional operator from the point of view of not pure mathematics, but applied mathematics. The imposed restrictions on the kernel of the fractional operator should actually be divided by types of phenomena, in addition to the principles of self-consistency of mathematical theory. In applications of fractional calculus, we have a fundamental question about conditions of kernels of fractional operator of non-integer orders that allow us to describe a particular type of phenomenon. It is necessary to obtain exact correspondences between sets of properties of kernel and type of phenomena. In this paper, we discuss the properties of kernels of fractional operators to distinguish the following types of phenomena: fading memory (forgetting) and power-law frequency dispersion, spatial non-locality and power-law spatial dispersion, distributed lag (time delay), distributed scaling (dilation), depreciation, and aging.

Part-Elliptical Cracks Emanating From Open and Loaded Holes in Plates

1979 ◽  
Vol 101 (1) ◽  
pp. 12-17 ◽  
Author(s):  
T. E. Kullgren ◽  
F. W. Smith
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Crack Opening ◽  
Plate Thickness ◽  
Hole Diameter ◽  
Elastic Analysis ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Elliptical Cracks

A linear elastic analysis using the finite element-alternating method is conducted for problems of single semi-elliptical and double quarter-elliptical cracks near fastener holes. Mode-one stress intensity factors are presented along the crack periphery for cases of open and loaded holes and crack opening displacements are calculated. Results are shown for a variety of crack geometries and loading conditions and for two ratios of hole diameter to plate thickness.

The Aiming Problem in Aerial Gunnery

1957 ◽  
Vol 8 (1) ◽  
pp. 31-48
Author(s):  
M. Hancock
Keyword(s):  
Sufficient Accuracy ◽  
Point Of View ◽  
Complete Analysis ◽  
Mathematical Treatment ◽  
Approximate Methods ◽  
Simplified Analysis ◽  
Points Of View ◽  
Comparison Of The Results

SummaryThe aiming problem in aerial gunnery has formerly been analysed by approximate methods which allow results of sufficient accuracy for practical requirements to be obtained from a very simple mathematical treatment. There has therefore been no practical demand for any more elaborate analysis, although the development of a more exact treatment of the problem is not without interest from the academic point of view. In this paper a more complete analysis is developed in a form which is generally applicable to a broader class of aiming problems. The relevant parts of the standard external ballistic analysis for projectiles fired from guns are also included for the sake of completeness, and the earlier simplified analysis of the aiming problem is also presented to allow comparison of the results with those of the more complete analysis. Finally, a section on the gunner's view of the aiming problem is included, to provide an explanation of certain difficulties which frequently arise through neglect of the important differences between the points of view of an observer moving with the gun and an observer at rest in the air.

scholarly journals Failure Conditions from Push Out Tests of a Steel-Concrete Joint: Fracture Mechanics Approach

2011 ◽  
Vol 488-489 ◽  
pp. 710-713 ◽  
Author(s):  
Jan Klusák ◽  
Stanislav Seitl ◽  
Wouter de Corte ◽  
Peter Helincks ◽  
Veerle Boel ◽  
...  
Keyword(s):  
Fracture Mechanics ◽  
Epoxy Adhesive ◽  
Point Of View ◽  
Steel Plates ◽  
Concrete Core ◽  
Failure Initiation ◽  
Linear Elastic ◽  
Joint Fracture ◽  
Failure Conditions ◽  
Push Out

In order to evaluate the shear bond strength of a steel-concrete joint using an epoxy adhesive interlayer, push-out tests were carried out. The test samples consisted of two sandblasted steel plates and a self-compacting concrete sample, with the epoxy layer applied on the steel plates and gritted with granulates. During testing, an external force was applied to the concrete core and continuously recorded. To investigate the failure mechanism in detail, a fracture mechanics approach is required. In this paper theoretical-numerical assessment of the push-out test is performed. Regarding the finite element calculations, the locations suitable for failure initiation match bi-material (steel-concrete) notches. The most dangerous locations are evaluated from a generalized linear elastic fracture mechanics point of view. The critical load corresponding to the conditions of failure initiation is estimated and compared with the experimental results.

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