Elastic analysis of a circumferential crack in an isotropic curved beam using modified mapping-collocation method

Amireghbali, Aydın
The modified mapping-collocation (MMC) method is applied to analyze a circumferential crack in an isotropic curved beam. Based on the method a MATLAB code was developed to obtain the stress field. Incorporating the stress correlation technique, the opening and sliding fracture mode stress intensity factors (SIF)s of the crack for the beam under pure bending moment load case are calculated. The MMC method aims to solve two-dimensional problems of linear elastic fracture mechanics (LEFM) by combining the power of analytic tools of complex analysis (Muskhelishvili formulation, conformal mapping, and extension arguments) with simplicity of applying the boundary collocation method as a numerical solution approach. Qualitatively, a good agreement between the computed stress contours and the fringe shapes obtained from the photoelastic experiment on a plexiglass specimen is observed. Quantitatively, the results are compared with that of ANSYS finite element analysis software. The effect of crack size, crack position and beam thickness variation on SIF values and mode mixity is investigated.


Elastic analysis of a circumferential crack in an isotropic curved beam using the modified mapping-collocation method
Amireghbali, Aydin; Çöker, Demirkan (2014-07-01)
The modified mapping-collocation (MMC) method was applied to the boundary value problem (BVP) of a circumferential crack in an isotropic elastic curved beam subjected to pure bending moment loading. The stress correlation technique is then used to determine opening and sliding mode stress intensity factor (SIF) values based on the computed stress field near the crack tip. The MMC method aims at solving two-dimensional BVP of linear elastic fracture mechanics (LEFM) circumventing the need for direct treatmen...
Static and free vibration analyses of small - scale functionally graded beams possessing a variable length scale parameter using different beam theories
Aghazadeh, Reza; Dağ, Serkan; Ciğeroğlu, Ender; Department of Mechanical Engineering (2013)
This study presents static and free vibration analyses of functionally graded (FG) micro - beams on the basis of higher order continuum mechanics used in conjunction with classical and higher order shear deformation beam theories. Unlike conventional ones, higher order elastic theories consider the size effect for the beam. Strain gradient theory (SGT) and modified couple stress theory (MCST) are the two common non-classical continuum approaches capable of capturing the size effect. Shear deformation beam t...
Nonlinear Vibrations of a Beam with a Breathing Edge Crack
Batihan, Ali C.; Ciğeroğlu, Ender (2015-02-05)
In this paper, nonlinear transverse vibration analysis of a beam with a single edge crack is studied. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonlinear behavior due to opening and closing of the crack region. In this paper, a...
Amireghbali, A.; Çöker, Demirkan (2014-07-25)
The modified mapping-collocation (MMC) method is applied to the problem of an isotropic curved beam with a circumferential crack under pure bending moment. Using least squares method to solve the overdetermined system of boundary condition equations causes numerical difficulties. Alternatively zeroth-order Tikhonov regularization is applied to solve the system. The regularization technique appears brilliantly helpful in eliminating the convergence problems associated with ill-posedness of the problem. The b...
Modeling and fabrication of electrostatically actuated diaphragms for on-chip valving of MEMS-compatible microfluidic systems
Atik, Ali Can; Ozkan, Metin Dundar; Ozgur, Ebru; Külah, Haluk; Yıldırım, Ender (IOP Publishing, 2020-11-01)
This paper presents an analytical model to estimate the actuation potential of an electrostatic parylene-C diaphragm, processed on a glass wafer using standard microelectromechanical systems (MEMS) process technology, and integrable to polydimethylsiloxane (PDMS) based lab-on-a-chip systems to construct a normally-closed microvalve for flow manipulation. The accurate estimation of the pull-in voltage of the diaphragm is critical to preserve the feasibility of integration. Thus, we introduced an analytical m...
Citation Formats
A. Amireghbali, “Elastic analysis of a circumferential crack in an isotropic curved beam using modified mapping-collocation method,” M.S. - Master of Science, Middle East Technical University, 2013.