Dynamic stability of cracked columns; the stiffness reduction method

Ranjbaran, Abdolrasoul; Rousta, Hamid; Ranjbaran, Mohammad

doi:10.1016/j.scient.2012.11.005

Cited by 5 publications

(2 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The governing differential equation for the dynamic stability analysis of beam-like structures is defined in Eq. (19), in which ( ) is the lateral displacement, ( P  ) is the load factor, and ( W  ) is the frequency factor [42,43].] (19) The method of Laplace Transform is used to solve Eq.…”

Section: Analytical Solution By the Laplace Transformmentioning

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

Section: Analytical Solution By the Laplace Transformmentioning

confidence: 99%

A Reliable Fracture Mechanics

Ranjbaran

2020

IJRRS

View full text Add to dashboard Cite

show abstract

“…The equation is used to obtain the analytical solution for the cracked beams and columns by Ranjbaran et al [16][17][18]. Analysis of cracked members is continued by the finite element formulation.…”

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