The three analytical, finite element and experimental methods are applied to study the nonlinear buckling of cracked columns. The original aim of this research is to investigate the validity of the common analytical method in an analogy with the experimental method and the finite element method of MATLAB programming-based. The literature review shows that papers applied this analytical method without considering its drawbacks to determine the post-buckling results. Results in the linear part of the analytical method are in close accordance with the two others, while a clear difference in the nonlinear part of the analytical method is observed with the actual results obtained from the experimental tests and numerical results of the finite element method. An in-depth discussion is represented to find out the main reasons of this difference. The conversion matrix technique in the finite element method and dividing the column into two segments in the analytical method are used to include the crack parameters in relations according to the continuity conditions in the crack tip. An investigation is performed to study the effect of the crack depth and position on the critical buckling load and the post-buckling path. پرونده مقاله

This paper investigates the dynamic and quasi-static plastic behavior of single and nested mild steel square tubes under lateral loadings experimentally and numerically. The dynamic experimental tests are carried out using a gas gun and the dynamic force-time responses are measured with a load cell. Also, the quasi-static experimental tests are performed in a universal test machine. The dynamic experimental tests are also simulated with the finite element software Abaqus. Furthermore, the square tubes’ combinations in the nested systems are investigated in the present work. It is revealed that the amount of peak load decreases significantly when the form of the single tube changes from square to lozenge. It is also observed that in the nested tube structures, by changing each of the outer or inner tubes or both of them from the square form to lozenge one, the amount of peak load decreases meanwhile the energy absorption capacity decreases too, which is not desirable for energy absorbers. By comparing the impact results of both the single and nested square tubes which have the same mass, it can result that the nested square tubes behave better as energy absorbers compared with the single tubes. پرونده مقاله

In this paper, the extended finite element method (XFEM) is employed to investigate the statics and vibration problems of cracked isotropic bars and beams. Three kinds of elements namely the standard, the blended and the enriched elements are utilized to discretize the structure and model cracks. Two techniques referred as the increase of the number of Gauss integration points and the rectangle sub-grid are applied to refine the integration within the blended and enriched elements of the beam in which the priority of the developed rectangle sub-grid technique is identified. The stiffness and the mass matrices of the beam are extended by considering the Heaviside and the crack tip functions. In a plane stress analysis, the effects of various crack positions and depths, different boundary conditions and other geometric parameters on the displacement and the stress contours are detected. Moreover, in a free vibration analysis, changes of the natural frequencies and the mode shapes due to the aforementioned effects are determined. پرونده مقاله

In this paper, a discontinuity in beams whose intensity is adjusted by the spring stiffness factor is modeled using a torsional spring. Adapting two analyses in strong and weak forms for discontinuous beams, the improved governing differential equations and the modified stiffness matrix are derived respectively. In the strong form, two different solution methods have been presented to make an analogy between the formulation of the Euler-Bernoulli and Timoshenko theories that indicates the influence of the shear deformation in discontinuous beams. The flexural stiffness of discontinuous beams is corrected by using the Dirac’s delta function. In the weak form, the reduced stiffness matrix is derived from the strain energy equation established by the continuity, kinematics and constitutive equations. The linearity assumption of the geometry and material is considered to construct the kinematics and constitutive equations respectively. The continuity conditions mathematically connect two divided parts of the Euler-Bernoulli beam for which an improved Hermitian shape function is employed to interpolate displacement field. An application shows the comparison and validation of the results of the strong and weak forms, and also the static behavior of discontinuous beams پرونده مقاله