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Effect of Crack Severity on a Curved Cantilever Beam Using Differential Quadrature Element Method

  • Baharul Islam
  • Prases K. MohantyEmail author
  • Dayal R. Parhi
Conference paper
  • 52 Downloads
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

Abstract

In the present paper, investigation of a crack in a curved cantilever beam is studied. The crack in the beam is modeled using a rotational spring with stiffness defined in terms of depth of the crack. The equation of motion for the cracked cantilever beam is solved using Differential Quadrature Element Method (DQEM). The Finite Element Analysis (FEA) using ANSYS is also carried out for the cracked curved beam. The severity of the crack with its location on cross-section of the beam is studied using DQEM and FEA. Many numerical examples are demonstrated to verify the aforementioned effects. It is concluded that both the approaches are very close to each other for different crack locations and severities.

Keywords

Crack Differential quadrature element method Curved beam FEA 

Nomenclature

\(\overrightarrow {\tau } (\phi ,t)\)

Shear force

\(\overrightarrow {{F_{n} }} (\phi ,t)\)

Normal force

\(\overrightarrow {M} (\phi ,t)\)

Bending moment of curved beam

t

Time period

A1

Cross-sectional area of curved beam

I

Moment of inertia of the curved beam

R

Mean radius of the circular arc

\(\gamma\)

Mass per unit volume of curved beam

E

Modulus of elasticity of the curved beam

\(\alpha\)

Bending slope

\(v\)

Inward radial displacement

x

Tangential displacement

\(\phi_{t}\)

Total angle between deformed and undeformed neutral axis

\(K_{o}\)

Rotational spring stiffness

k

Numerical share factor of cross section

G

Modulus of rigidity

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Baharul Islam
    • 1
  • Prases K. Mohanty
    • 1
    Email author
  • Dayal R. Parhi
    • 2
  1. 1.National Institute of Technology Arunachal PradeshYupiaIndia
  2. 2.National Institute of Technology RourkelaRourkelaIndia

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