• Advances in materials Research
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• v.12 no.4
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• pp.273-286
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• 2023

The fracture mechanics make it possible to characterize the behavior with cracking of structures using parameters quantifiable in the sense of the engineer, in particular the stress field, the size of the crack, and the resistance to cracking of the material. Any structure contains defects, whether they were introduced during the production of the part (machining or molding defects for example). The aim of this work is to determine numerically by the finite element method the stress concentration factor Kt of a plate subjected to a tensile loading containing a lateral form defect with different sizes: a semicircle of different radii, a notch with different opening angles and a crack of different lengths. The crack propagation is then determined using the extended finite element technique (X-FEM). The modeling was carried out using the ABAQUS calculation code.

• Interaction and multiscale mechanics
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• v.2 no.1
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• pp.45-68
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• 2009

An aim of the study is to develop an efficient numerical simulation technique that can handle the two-scale analysis of fluid permeation filters fabricated by the partial sintering technique of small spherical ceramics. A solid-fluid mixture homogenization method is introduced to predict the mechanical characters such as rigidity and permeability of the porous ceramic filters from the micro-scale geometry and configuration of partially-sintered particles. An extended finite element (X-FE) discretization technique based on the enriched interpolations of respective characteristic functions at fluid-solid interfaces is proposed for the non-interface-fitted mesh solution of the micro-scale analysis that needs non-slip condition at the interface between solid and fluid phases of the unit cell. The homogenization and localization performances of the proposed method are shown in a typical two-dimensional benchmark problem whose model has a hole in center. Three-dimensional applications to the body-centered cubic (BCC) and face-centered cubic (FCC) unit cell models are also shown in the paper. The 3D application is prepared toward the computer-aided optimal design of ceramic filters. The accuracy and stability of the X-FEM based method are comparable to those of the standard interface-fitted FEM, and are superior to those of the voxel type FEM that is often used in such complex micro geometry cases.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2011.04a
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• pp.697-700
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• 2011

본 논문에서는 X-FEM을 사용하여 혼합모드 하중 상태에서의 이차원 선형탄성체의 균열문제에 대한 형상 설계민감도 해석을 수행하였다. X-FEM이란 균열과 같은 특수한 해를 근사하는 방법으로써, 확장함수를 도입하여 FEM의 한계를 극복하는 방법론이다. X-FEM 하에서 해를 근사하는 데 쓰이는 확장함수들은 불연속성과 특이성을 포함하고 있어 물리적 영역에 의존한다. 이는 설계민감도 해석을 수행하는 과정에서 그러한 의존성을 고려해주는 것이 필요하다. 따라서 본 논문에서는 X-FEM 기반의 형상 설계민감도 해석해를 제안하고자 한다. 식의 유도는 전 미분 공식에 기초하고 있으며, 형상함수의 설계변분에 대한 의존성에 관한 항을 추가시켰다. 또한, 균열 주위의 국부적인 공간에서의 확장된 자유도에 설계속도를 가한다. 이에 대한 몇 가지 수치 예제를 통하여 개발된 방법론의 타당성을 확인하였다.

• 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.

• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.125-150
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• 2013

This paper intends to present an application of isogeometric analysis in crack problems. An isogeometric formula is developed based on NURBS basis functions - enriched and adopted via X-FEM enrichment functions. The proposed method which is represented by the combination of the two above-mentioned methods, first by using NURBS functions models the geometry exactly and then by defining level set function on domain, identifies available discontinuity in elements. Additional DOFs are allocated to elements containing the crack and X-FEM enrichment functions enrich approximate solution. Moreover, a subelement refinement technique is used to improve the accuracy of integration by the Gauss quadrature rule. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of the proposed method during calculation of crack parameters.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• Steel and Composite Structures
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• v.29 no.5
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• pp.635-645
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• 2018

Beam-column joints play a significant role in static and dynamic performances of reinforced concrete frame structures. This study contributes a numerical approach of topologically optimal design of carbon fiber reinforced plastics (CFRP) to retrofit existing beam-column connections with crack patterns. In recent, CFRP is used commonly in the rehabilitation and strengthening of concrete members due to the remarkable properties, such as lightweight, anti-corrosion and simplicity to execute construction. With the target to provide an optimal CFRP configuration to effectively retrofit the beam-column connection under semi-failure situation such as given cracks, extended finite element method (X-FEM) is used by combining with multi-material topology optimization (MTO) as a mechanical description approach for strong discontinuity state to mechanically model cracked structures. The well founded mathematical formulation of topology optimization problem for cracked structures by using multiple materials is described in detail in this study. In addition, moved and regularized Heaviside functions (MRHF), that have the role of a filter in multiple materials case, is also considered. The numerical example results illustrated in two cases of beam-column joints with stationary cracks verify the validity, benefit and supremacy of the proposed method.

• Structural Monitoring and Maintenance
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• v.10 no.3
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• pp.221-242
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• 2023

Internal and external corrosion are common in pressure pipes used in a variety of industries, often resulting in defects that compromise their integrity. This economically and industrially significant problem calls for both preventive and curative technical solutions to guarantee the reliability of these structures. With this in mind, our study focuses on the influence of composite and metallic patch repairs on the limit loads of pipes, particularly elbows, the critical component of piping systems. To this end, we used the nonlinear extended finite element method (X-FEM) to study elbows, a priori corroded on the internal surface of the extrados section, then repaired with composite and metallic patches. In addition, the effect of the geometry of composite materials and metal patches was examined, in particular the effect of their thickness and material on the increase in limit loads of repaired structures. The results obtained provide information on the effectiveness and optimization of patch repair of corroded elbows, with the aim of increasing their service life.

• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.405-412
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• 2016

Bone is a living material with a complex hierarchical structure that gives it remarkable mechanical properties. Bone constantly undergoes mechanical. Its quality and resistance to fracture is constantly changing over time through the process of bone remodeling. Numerical modeling allows the study of the bone mechanical behavior and the prediction of different trauma caused by accidents without expose humans to real tests. The aim of this work is the modeling of the femur fracture under static solicitation to create a numerical model to simulate this element fracture. This modeling will contribute to improve the design of the indoor environment to be better safe for the passengers' transportation means. Results show that vertical loading leads to the femur neck fracture and horizontal loading leads to the fracture of the femur diaphysis. The isotropic consideration of the bone leads to bone fracture by crack propagation but the orthotropic consideration leads to the fragmentation of the bone.