A necessary modification for the finite element analysis of cracked members detection, construction, and justification

Ranjbaran, Abdolrasoul; Rousta, Hamid; Ranjbaran, Mohammad; Hashemi, Mohammad R.; Moravej, M. T.

doi:10.1007/s00419-013-0736-7

Cited by 10 publications

(3 citation statements)

References 10 publications

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“…The equivalent mass method was only applicable to free vibration analysis. The investigation on the analysis of cracked problems was continued and led to the derivation of the innovative weak form equations for the finite element analysis of cracked beams in Ranjbaran and Rousta [20], a necessary modification for the finite element analysis of cracked members in Ranjbaran et al [21], the square of the Dirac's delta for use in structural mechanics by Ranjbaran [22], new finite element formulation for buckling analysis of cracked structures in Ranjbaran and Ranjbaran [23], and free vibration analysis of stiffened frames in Ranjbaran [24].…”

Section: List Of Symbolsmentioning

confidence: 99%

State functions: the milestone of fracture

Ranjbaran

2016

Arch Appl Mech

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The fracture phenomenon is defined via the change of state of structure (entity) between the intact and the fractured end states as the function of the state variable. The twin state functions are defined for the transition of unit of the entity between its two end states. The state ratio is defined as the ratio of the two state functions. The property of the cracked structure is defined as the product of the structure property and the state ratio. The work is then used to derive the main parameters of the fracture mechanics. The work is verified via five examples.

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Section: List Of Symbolsmentioning

confidence: 99%

State functions: the milestone of fracture

Ranjbaran

2016

Arch Appl Mech

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“…It is found that the initial crack-stiffness matrix as defined in Eq. (27) is not correct and should be modified [44][45][46]! For several bar members and several beam members, via hundreds of trial free vibration analyses, the numerical values for the survive function ( R S ) (A coefficient to be multiplied by the initial crack integral to obtain the correct result) are defined as in Table 2.…”

Section:  (25)mentioning

confidence: 99%

A Reliable Fracture Mechanics

Ranjbaran

2020

IJRRS

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A branch of human knowledge, which treats the behavior of cracked structures, is called fracture mechanics. Since there is no intact structure in the world, then the paramount importance of fracture mechanics in human life is accentuated. The main parameter of fracture mechanics is called crack compliance, which is the amount of flexibility added to the flexibility of the intact structure due to the presence of a crack with specified size. The compliance, similar to flexibility, is the sole characteristics of the cracked structure. In this way for a given structure with a specified crack, there should be a single compliance. Unfortunately, in classical fracture mechanics that is not the case! The number of crack compliances for a clacked structure is equal to the number of researchers who treated the case! This diversity in the results stems from the presence of epistemic uncertainty in the mathematical basis of classical fracture mechanics. In view of the need for remedy, the Abdolrasoul Ranjbaran Team (ART), investigated the case and proposed a reliable fracture mechanics, which is based on sound logical reasoning. The proposed reliable fracture mechanics is described in the presented paper. The paper is managed via fourteen titles as, introduction, the mathematical basis of the classical fracture mechanics, birthplace of the state based philosophy, strong form of governing equation, analytical solution by Laplace transform, the weak form equation, the finite element equation, logical basis of the state based philosophy, state functions, Persian curves, reliable crack compliance, energy release rate, stress intensity factor, and weight function for the stress intensity factor in sections one to fourteen respectively. The paper concludes with a list of cited references.

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“…The state of the art of the (FAD) contains epistemic uncertainty, that should be modified. The current authors research team detected the need for remedy and after extensive research (Ranjbaran, 2010;Ranjbaran et al, 2013;Ranjbaran and Ranjbaran, 2014;Ranjbaran et al, 2020a;2020b;2020c;2020d;2021;Amirian and Ranjbaran, 2019;Baharvand and Ranjbaran, 2020), in the last two decades, proposed the Change of State Philosophy (CSP) which digested in the Persian Curves (PC) (Ranjbaran et al, 2020a), that is used for the development of a reliable (FAD). The validity of the work is verified via concise mathematical logics and comparison of the results with those of the others as follows.…”

Section: Introductionmentioning

confidence: 99%

Development of a Reliable Failure Assessment Diagram by Persian Curve

Ranjbaran¹,

Ranjbaran²,

Ranjbaran³

2021

International Journal of Structural Glass and Advanced Material

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A conventional tool for assessing the integrity of structures containing flaws is, the Failure Assessment Diagram (FAD). The (FAD) is a combination of the limiting conditions for load, the flaw size and fracture toughness or yielding stress. The abscissa is the load ratio and the ordinate is the toughness ratio. The toughness ratio is defined as a function of the load ratio. Three options are available for this function. The (FAD) drive is based on parameters of fracture mechanics. Classical fracture mechanics contains epistemic uncertainty and is unreliable. As a result, the state of the art for the (FAD) is also unreliable. The present authors' team, conducted an extensive investigation in the past two decades, which led to the birth of the change of state philosophy that is digested in the Persian Curve. In the present paper the Persian Curve is used for development of a reliable (FAD). The validity of the work is verified via concise mathematical logics and comparison of the results with those of the others.

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A necessary modification for the finite element analysis of cracked members detection, construction, and justification

Cited by 10 publications

References 10 publications

State functions: the milestone of fracture

State functions: the milestone of fracture

A Reliable Fracture Mechanics

Development of a Reliable Failure Assessment Diagram by Persian Curve

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