New Finite-Element Formulation for Buckling Analysis of Cracked Structures

Ranjbaran, Abdolrasoul; Ranjbaran, Mohammad

doi:10.1061/(asce)em.1943-7889.0000734

Cited by 22 publications

(10 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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

View full text Add to dashboard Cite

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.

show abstract

Section: List Of Symbolsmentioning

confidence: 99%

State functions: the milestone of fracture

Ranjbaran

2016

Arch Appl Mech

View full text Add to dashboard Cite

show abstract

“…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%

“…SS k ) and( SS f ), the (ART) detected (great detection)a fact that, the flexibility-and the stiffness-of the crack, as shown in Eq. (45),are proportional to each other (while for structures the stiffness and the flexibility are inverse of each other).Based on the definition of the state functions, the (stiffness) ratio of ( C k ) over ( S k ) is set equal to the state ratio ( R ), which after some manipulation led into an explicit definition for the ( N c )as defined in Eq (46)…”

mentioning

confidence: 99%

A Reliable Fracture Mechanics

Ranjbaran

2020

IJRRS

View full text Add to dashboard Cite

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.

show abstract

“…The main aim of the presented work is to propose a certain probability function, based on sound mathematical foundation. Toward the aim, in the first two decades of 21st century, our research team, conducted an extensive research for analysis of phenomena which are partly published in references (Amirian and Ranjbaran, 2019;Baharvand and Ranjbaran, 2020a-b;Ranjbaran et al, 2011;2013;2020a-b;Ranjbaran and Ranjbaran, 2014;2017a-b;2018;Hoseini et al, 2018;Ranjbaran, 2010;. More detailed information may be obtained in (Ranjbaran et al, 2020b).…”

Section: Introductionmentioning

confidence: 99%

Building Probability Functions by Persian Curve

Ranjbaran¹,

Ranjbaran²,

Ranjbaran³

2020

International Journal of Structural Glass and Advanced Material

View full text Add to dashboard Cite

Construction of a probability function for a given random data is the main theme of several branches of human knowledge, where it is an active area of study. In spite of great developments, the solution needs extensive effort and the results contain epistemic uncertainty. In this study, making use of the logical reasoning and concise mathematical logics, a method called the change of state philosophy, which is digested in the Persian curves, is derived. The Persian curves that have the necessary and sufficient condition for a probability function, are explicitly derived, via the ordinates of four specific points on the random data. The proposed Persian curves are free of epistemic uncertainty and their flexibility provide the possibility for the insertion of the expert's will. The work is validated via concise logical formulation and comparison of the results with those of the others.

show abstract

New Finite-Element Formulation for Buckling Analysis of Cracked Structures

Cited by 22 publications

References 19 publications

State functions: the milestone of fracture

State functions: the milestone of fracture

A Reliable Fracture Mechanics

Building Probability Functions by Persian Curve

Contact Info

Product

Resources

About