Numerical analysis of natural frequency and stress intensity factor in Euler–Bernoulli cracked beam

Circumferential crack modeling of thin cylindrical shells in modal deformation

“…This technique, which was already applied over cracked beams [16][17][18], is implemented by dividing a cracked element into three parts including two sub-elements and a rotational spring. The finite element method is used to obtain the enriched stiffness matrix from the strain energy of the three parts.…”

“…[13][14][15]. Alijani et al [16][17][18] presented a novel technique in the finite element method to include cracks into a beam element. They enriched components of the stiffness matrices by using crack properties modeled as a rotational spring.…”

“…Two techniques are used to enrich the stiffness matrix. The first technique, which was already applied for the analysis of cracked beams called the conversion technique [16][17][18], has been originally implemented to formulate the finite element relations for the cracked cylindrical shell. The second technique, called spring set, is applied by considering the crack as an element, whose stiffness matrix is assembled with the standard stiffness matrices of other elements.…”

A Lagrange Multiplier-based Technique within the Nonlinear Finite Element Method in Cracked Columns

“…and C L , C R and C Spring can be found in [25]. Table 2 shows the material properties of the metal-ceramic FGM beam used as a case study in mechanical and thermal post-buckling analysis, in which length, height, and width are considered as L = 2 m, h = 0.1 m and b = 0.1 m, respectively.…”

“…The LM technique is originally implemented for the mechanical and thermal post-buckling analysis. Moreover, The CM technique which has been already introduced to involve the crack in the beam, see [25], is briefly reviewed. The main difference between the two techniques is highlighted where the geometrical nonlinearity and material inhomogeneity should be considered in the analysis.…”