• 한국공간구조학회논문집
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• 제24권1호
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• pp.65-72
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• 2024

This paper aims to advance our understanding of extensible beams with multiple cracks by presenting a crack energy and motion equation, and mathematically justifying the energy functions of axial and bending deformations caused by cracks. Utilizing an extended form of Hamilton's principle, we derive a normalized governing equation for the motion of the extensible beam, taking into account crack energy. To achieve a closed-form solution of the beam equation, we employ a simple approach that incorporates the crack's patching condition into the eigenvalue problem associated with the linear part of the governing equation. This methodology not only yields a valuable eigenmode function but also significantly enhances our understanding of the dynamics of cracked extensible beams. Furthermore, we derive a governing equation that is an ordinary differential equation concerning time, based on orthogonal eigenmodes. This research lays the foundation for further studies, including experimental validations, applications, and the study of damage estimation and detection in the presence of cracks.

• 한국항공운항학회지
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• 제16권4호
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• pp.26-34
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• 2008

This article provides a comprehensive treatment of cracks in non-homogeneous structural materials such as functionally graded materials (FGMs). It is assumed that the material properties depend only on the coordinate perpendicular to the crack surfaces and vary continuously along the crack faces. By using laminated composite plate model to simulate the material non-homogeneity, we present an algorithm for solving the system based on Laplace transform and Fourier transform techniques. Unlike earlier studies that considered certain assumed property distributions and a single crack problem, the current investigation studies multiple crack problem in the FGMs with arbitrarily varying material properties. As a numerical illustration, transient thermal flow intensity factors for a metal-ceramic joint specimen with a functionally graded interlayer subjected to sudden heating on its boundary are presented. The results obtained demonstrate that the present model is an efficient tool in the fracture analysis of non-homogeneous material with properties varying in the thickness direction.

• 한국항공운항학회지
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• 제19권1호
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• pp.15-23
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• 2011

The purpose of this paper is to investigate the time behavior of a multiple crack problems. It is assumed that the medium contains cracks perpendicular to the crack surfaces, that the thermo-mechanical properties are continuous functions of the thickness coordinate. we use the laminated composite plate model to simulate the material non-homogeneity. By utilizing the Laplace transform and Fourier transform techniques, the multiple crack problems in the non-homogeneous medium is formulated. Singular integral equations are derived and solved to investigate the multiple crack problems. As a numerical illustration, transient thermal stress intensity factors(TSIFs) for a functionally graded material plate subjected to sudden heating on its boundary are provided. The variation in the TSIFs due to the change in material gradient and the crack position is studied.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1999년도 봄 학술발표회 논문집
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• pp.321-326
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• 1999

In this study, fatigue crack propagation problem of plate under multi-axial loading is mainly considered To analyze this special problem, recently developed technique called EFGM(Element-Free Galerkin Method), one of the Meshfree Methods, and general fatigue crack growth raw herein Paris law are used Using the Implemented scheme, paths of fatigue cracks by constant-amplitude load fluctuation and multiple-crack growth behavior are examined. The failure mechanism of steel plate due to crack propagation is studied. As a result, an algorithm that treats multiple fatigue crack problems is proposed. A numerical example shows that the prediction of growing paths can be achieved successfully and efficiently by proposed algorithm.

• 한국정밀공학회지
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• 제18권10호
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• pp.109-115
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• 2001

The compliance approach to the problem of load sharing between a cracked plate and multiple plate used to bridge the crack. The theory is validated by using calculated stress intensity factors for the multiple load path plate to reduce experimentally observed growth rate to a common base. Calculations are them made on the effect of multiple load path plate width on fatigue crack retardation in order to demonstrate the predictive capability of the technique.

• Structural Engineering and Mechanics
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• 제35권6호
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• pp.773-789
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• 2010

It is well known that the analytical vibration characteristic of a cracked beam depends largely on the crack model. In the forward analysis, an improved and simplified approach in modeling discrete open cracks in beams is presented. The effective length of the crack zone on both sides of a crack with stiffness reduction is formulated in terms of the crack depth. Both free and forced vibrations of cracked beams are studied in this paper and the results from the proposed modified crack model and other existing models are compared. The modified crack model gives very accurate predictions in the modal frequencies and time responses of the beams particularly with overlaps in the effective lengths with reduced stiffness. In the inverse analysis, the response sensitivity with respect to damage parameters (the location and depth of crack, etc.) is derived. And the dynamic response sensitivity is used to update the damage parameters. The identified results from both numerical simulations and experiment work illustrate the effectiveness of the proposed method.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2000년도 가을 학술발표회논문집
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• pp.315-322
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• 2000

In this study, an algorithm analyzing dynamic mutiple-crack propagation problem by Meshfree Method is proposed. A short description of Meshfree Method especially, Element-free Galerkin (EFG) method is presented and the elastodynamic fracture theory is summarized. A numerical implementation algorithm for dynamic analysis by Meshfree Method is discussed and an algorithm for mutlple-crack dynamic propagation is also presented. A couple of numerical examples of dynamic crack propagation problem illustrate the performance of the proposed technique. The accuracy of the algorithm is studied in the first example by being compared with experimental results, and the applicability and efficiency of the developed algorithm is studied in the second example.

• Smart Structures and Systems
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• 제9권4호
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• pp.355-371
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• 2012

A composite element method (CEM) is presented to analyze the free and forced vibrations of a cracked Euler-Bernoulli beam with axial force. The cracks are introduced by using Christides and Barr crack model with an adjustment on one crack parameter. The effects of the cracks and axial force on the reduction of natural frequencies and the dynamic responses of the beam are investigated. The time response sensitivities with respect to the crack parameters (i.e., crack location, crack depth) and the axial force are calculated. The natural frequencies obtained from the proposed method are compared with the analytical results in the literature, and good agreement is found. This study shows that the cracks in the beam may have significant effects on the dynamic responses of the beam. In the inverse problem, a response sensitivity-based model updating method is proposed to identify both a single crack and multiple cracks from measured dynamic responses. The cracks can be identified successfully even using simulated noisy acceleration responses.

• Steel and Composite Structures
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• 제37권6호
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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.

• Steel and Composite Structures
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• 제29권5호
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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.