• Steel and Composite Structures
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• v.37 no.6
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• pp.663-678
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• 2020

This paper proposes a novel topology optimization method generating multiple materials for external linear plane crack structures based on the combination of IsoGeometric Analysis (IGA) and eXtended Finite Element Method (X-FEM). A so-called eXtended IsoGeometric Analysis (X-IGA) is derived for a mechanical description of a strong discontinuity state's continuous boundaries through the inherited special properties of X-FEM. In X-IGA, control points and patches play the same role with nodes and sub-domains in the finite element method. While being similar to X-FEM, enrichment functions are added to finite element approximation without any mesh generation. The geometry of structures based on basic functions of Non-Uniform Rational B-Splines (NURBS) provides accurate and reliable results. Moreover, the basis function to define the geometry becomes a systematic p-refinement to control the field approximation order without altering the geometry or its parameterization. The accuracy of analytical solutions of X-IGA for the crack problem, which is superior to a conventional X-FEM, guarantees the reliability of the optimal multi-material retrofitting against external cracks through using topology optimization. Topology optimization is applied to the minimal compliance design of two-dimensional plane linear cracked structures retrofitted by multiple distinct materials to prevent the propagation of the present crack pattern. The alternating active-phase algorithm with optimality criteria-based algorithms is employed to update design variables of element densities. Numerical results under different lengths, positions, and angles of given cracks verify the proposed method's efficiency and feasibility in using X-IGA compared to a conventional X-FEM.

• Structural Engineering and Mechanics
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• v.61 no.6
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• pp.693-700
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• 2017

Concrete cover cracking due to the corrosion of steel reinforcing bars is one of the main causes of deterioration in Reinforced Concrete (RC) structures. The oxidation level of the bars causes varying levels of expansion. The rebar expansions could lead to through-thickness cracking of the concrete cover, where depending on the cracking characteristics, the service life of the structures would be affected. In this paper, the effect of geometrical and material parameters, i.e., concrete cover thickness, reinforcing bar diameter, and concrete tensile strength, on the required pressure for concrete cover cracking due to corrosion has been investigated through detailed numerical simulations. ABAQUS finite element software is employed as a modeling platform where the concrete cracking is simulated by means of eXtended Finite Element Method (XFEM). The accuracy of the numerical simulations is verified by comparing the numerical results with experimental data obtained from the literature. Using a previously proposed empirical equation and the numerical model, the time from corrosion initiation to the cover cracking is predicted and then compared to the respective experimental data. Finally, a parametric study is undertaken to determine the optimum ratio of the rebar diameter to the reinforcing bars spacing in order to avoid concrete cover delamination.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.1870-1875
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• 2003

Optimization has been used in many engineering problems and must be one of the essential components during design process now. It is the process of maximizing the performance called an objective function of a system while satisfying some constraints, so finite element method is generally required in order to obtain these values during optimization. However, there are some difficulties to obtain them by means of FEM, where the changes of design variables cause the distortion and the regeneration of mesh that may result in inaccuracy and inefficiency. In order to overcome this problem, this paper proposed an alternative that the eXtended FEM introduced and developed by Ted Belytschko was applied to the optimization process because the key points of the X-FEM lie in that the discontinuity can be represented independently on the mesh by a function called in an enrichment function.

• Steel and Composite Structures
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• v.25 no.1
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• pp.57-65
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• 2017

The fatigue fracture of studs is the main reason for failure of composite beams based on massive engineering practices. Hence, studying the laws of cracks initiation and propagation are of great directive significance. eXtended Finite Element Method (XFEM) is an effective method in solving moving discontinuous problems in recent years. This paper extends our recent work on the fatigue damage analysis of stud shear connectors in the steel and crumble rubber concrete (RRFC) composite beams based on XFEM. The process of crack initiation to failure of the stud is simulated and an effective calculation criteria for the fatigue life of the composite beams is put forward. After the reliability of the numerical analysis is verified based on tests results, the extensive parametric study is conducted concerning effects of different rubber contents, shear connection degrees and the stress amplitudes. Results show that with the increasing rubber contents and shear connection degrees, the fatigue lives of composite beams increase obviously. Furthermore, the relationship between the fatigue life of the stud at the edge of the shear span and the whole composite beams is studied. Finally, the S-N curves of the single stud and the whole composite beams are put forward based on XFEM.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.11
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• pp.919-926
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• 2014

In this paper, the effect of material properties on fracture behavior was studied using cohesive zone model and extended finite element method. The rectangular tensile specimen with a central inclined initial crack was modeled by plane stress elements. In the CZM modeling, cohesive elements were inserted between every bulk elements in the predicted crack propagation region before analysis, while in the XFEM the enrichment to the elements was added as needed during analysis. The crack propagation behavior was examined for brittle and ductile materials. For thin specimen configuration, wrinkle deformation was accounted for by geometrically nonlinear post-buckling analysis and the effect of wrinkling on the crack propagation was investigated.

• Steel and Composite Structures
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• v.48 no.1
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• pp.73-88
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• 2023

This paper presents a novel implicit level set method for topology optimization of functionally graded (FG) structures with pre-existing discontinuities (pre-cracks) using radial basis functions (RBF). The mathematical formulation of the optimization problem is developed by incorporating RBF-based nodal densities as design variables and minimizing compliance as the objective function. To accurately capture crack-tip behavior, crack-tip enrichment functions are introduced, and an eXtended Finite Element Method (X-FEM) is employed for analyzing the mechanical response of FG structures with strong discontinuities. The enforcement of boundary conditions is achieved using the Hamilton-Jacobi method. The study provides detailed mathematical expressions for topology optimization of systems with defects using FG materials. Numerical examples are presented to demonstrate the efficiency and reliability of the proposed methodology.

• Composites Research
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• v.26 no.6
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• pp.363-372
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• 2013

Numerical simulation for Resin Transfer Molding manufacturing process is attempted by using the eXtended Finite Element Method (XFEM) combined with the level set method. XFEM allows to obtaining a good numerical precision of the pressure near the resin flow front, where its gradient is discontinuous. The enriched shape functions of XFEM are derived by using the level set values so as to correctly describe the interpolation with the resin flow front. In addition, the level set method is used to transport the resin flow front at each time step during the mold filling. The level set values are calculated by an implicit characteristic Galerkin FEM. The multi-frontal solver of IPSAP is adopted to solve the system. This work is validated by comparing the obtained results with analytic solutions. Moreover, a localization method of XFEM and level set method is proposed to increase the computing efficiency. The computation domain is reduced to the small region near the resin flow front. Therefore, the total computing time is strongly reduced by it. The efficiency test is made with a simple channel flow model. Several application examples are analyzed to demonstrate ability of this method.