Abstract in English:Abstract Natural frequencies are important dynamic characteristics of a structure where they are required for the forced vibration analysis and solution of resonant response. Therefore, the exact solution to free vibration of elastically restrained Timoshenko beam on an arbitrary variable elastic foundation using Green Function is presented in this paper. An accurate and direct modeling technique is introduced for modeling uniform Timoshenko beam with arbitrary boundary conditions. The applied method is based on the Green Function. Thus, the effect of the translational along with rotational support flexibilities, as well as, the elastic coefficient of Winkler foundation and other parameters are assessed. Finally, some numerical examples are shown to present the efficiency and simplicity of the Green Function in the new formulation.
Abstract in English:Abstract Multiple flaws are frequently occurred in actual components, such as pressure vessels and power plants. These flaws will in some circumstances lead to more severe effects than single flaw alone. Assessment of the interaction behavior is based on the evaluation of alignment and combination of these multiple flaws. In the current standards, multiple cracks are treated as an equivalent single crack if the distance between two cracks satisfies a prescribed criterion. First, this study introduces the current alignment and combination rules for through-wall cracks. Following, to investigate the effects of the interaction of cracks, brittle fracture of a plate containing two offset cracks is simulated. The effect of cracks distances and crack lengths on stress intensity factors is evaluated. In addition, crack growth behavior is simulated based on linear elastic fracture mechanics approach. The extended finite element method has been utilized to model the problem. This method enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack propagation simulations can be carried out without remeshing. Based on the results, a new alignment and combination rule is proposed.
Abstract in English:Abstract In this paper, natural frequency based forward and inverse methods are proposed for identifying multiple cracks in beams. Forward methods include simplified definition of the natural frequency drops caused by the cracks. The ratios between natural frequencies obtained from multi-cracked and un-cracked beams are determined by an approach that uses the local flexibility model of cracks. This approach does not consider nonlinear crack effects that can be easily neglected when the number of cracks is not excessive. In addition, an expression, which removes the necessity of repeating natural frequency analyses, is given for identifying the connection between the crack depths and natural frequency drops. These simplified approaches play crucial role in solving inverse problem using constituted crack detection methodology. Solution needs a number of measured modal frequency knowledge two times more than the number of cracks to be detected. Efficiencies of the methods are verified using the natural frequency ratios obtained by the finite element package. The crack detection methodology is also validated using some experimental natural frequency ratios given in current literature. Results show that the locations and depths ratios of cracks are successfully predicted by using the methods presented.
Abstract in English:Abstract A modified computational scheme of the stochastic perturbation finite element method (SPFEM) is developed for structures with low-level uncertainties. The proposed scheme can provide second-order estimates of the mean and variance without differentiating the system matrices with respect to the random variables. When the proposed scheme is used, it involves finite analyses of deterministic systems. In the case of one random variable with a symmetric probability density function, the proposed computational scheme can even provide a result with fifth-order accuracy. Compared with the traditional computational scheme of SPFEM, the proposed scheme is more convenient for numerical implementation. Four numerical examples demonstrate that the proposed scheme can be used in linear or nonlinear structures with correlated or uncorrelated random variables.
Abstract in English:Abstract This paper is concerned with the fatigue prediction models for estimating the multiaxial fatigue limit. An equivalent loading approach with zero out-of-phase angles intended for fatigue limit evaluation under multiaxial loading is used. Based on experimental data found in literatures, the equivalent stress is validated in Crossland and Sines criteria and predictions compared to the predictions of existing multiaxial fatigue; results over 87 experimental items show that the equivalent stress approach is very efﬁcient.
Abstract in English:Abstract Use of Tuned Mass Dampers (TMDs) to reduce the wind-induced torsional response of structures has been investigated in the literature by assuming that the wind excitations can be approximated by harmonic forces or white noise random processes; however, such an assumption is not realistic. Further, wind load effects are correlated. This study is focused on the effectiveness of different linear/nonlinear TMDs configurations to reduce the wind induced response. For the analyses, the structure is modeled as a multi-degree of freedom system under correlated wind load effects. The results show that the selection of optimum dampers is affected by the consideration of the correlated wind load effects.
Abstract in English:Abstract This paper investigates the cracking process of reinforced concrete slabs subjected to vertical load, involving their crack pattern and the load-displacement capacity curve. Concrete was discretized with hexahedral finite elements with embedded discontinuities; whereas steel reinforcement was represented by 3D bar elements, placed along the edges of the solid elements, both kinds of elements have three degrees of freedom per node. The constitutive behaviour of concrete considers the softening deformation after reaching a failure surface, whereas the hardening of the reinforcing steel is represented by a 1D rate independent plasticity model with isotropic hardening. The coupling of solid and bar finite elements was validated with a reinforced concrete slab reported in the literature; other two slabs were also investigated showing their cracking patters at the top and at the bottom surfaces.
Abstract in English:Abstract The generalized magneto-thermoelastic problem of an infinite homogeneous isotropic microstretch half-space with temperature-dependent material properties placed in a transverse magnetic field is investigated in the context of different generalized thermoelastic theories. The upper surface of the half-space is subjected to a zonal time-dependent heat shock. By solving finite element governing equations, the solution to the problem is obtained, from which the transient magneto-thermoelastic responses, including temperature, stresses, displacements, microstretch, microrotation, induced magnetic field and induced electric field are presented graphically. Comparisons are made in the results obtained under different generalized thermoelastic theories to show some unique features of generalized thermoelasticity, and comparisons are made in the results obtained under three forms of temperature dependent material properties (absolute temperature dependent, reference temperature dependent and temperature-independent) to show the effects of absolute temperature and reference temperature. Weibull or Log-normal.
Abstract in English:Abstract Traditionally, classical methods of structural analysis such as slope-deflection and moment distribution methods (Cross method) are used for primary analysis of structures and also controlling the results of computer programs. The main objective of this paper is to introduce a new method for classical computing and extending it to a matrix formulation. The proposed approach, named the "Slope Distribution Method (SDM)", is based on a Jacobi iterative procedure, in which without forming the system of linear equations, structural displacement values are obtained. Also, to make the method applicable and to use it in computer softwares, the matrix formulation of the approach is developed, where there is no need for iterative procedures and the nodal rotations are obtained through solving only one matrix equation. The SDM is able to analyze frames with non-vertical columns and those with nodal vertical displacement. Whereas current analysis softwares have some elimination for the analysis of non-prismatic members, the proposed method can be applied to analyze structures with any non-prismatic member. The SDM process is also developed for the analysis of dual lateral load resisting systems (moment resisting frames with other lateral load resisting elements such as bracings and shear walls). The advantages of the method over previous ones and also, its accuracy and reliability are presented through the article.
Abstract in English:Abstract The Rayleigh-Ritz-Meirovitch substructure synthesis method (RRMSSM) is extended to buckling analysis in framed structures. The objective is a computational procedure capable of yielding very accurate critical loads through solution of very-low-order eigenvalue problems. In this regard, numerical examples demonstrate that the convergence characteristics of the proposed RRMSSM for stability analysis are superior to those associated with the finite element method.