A Nonlinear Crack Model for Concrete Structure Based on an Extended Scaled Boundary Finite Element Method

Li, Jianbo; Gao, Xin; Fu, Xing-an; Wu, Chenglin; Lin, Gao

doi:10.3390/app8071067

Cited by 21 publications

(9 citation statements)

References 31 publications

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“…In order to solve the homogeneous second-order differential equation (19), the concept of "boundary dynamic stiffness" S(kc, ξ) is introduced and defined as:…”

Section: The Generalized Eigenvalue Equationmentioning

confidence: 99%

“…The SBFEM [15,16] as a semi-analysis approach has been widely used to analyze different problems, such as fracture mechanics [17][18][19], electromagnetic field [20][21][22], hydraulic structures [23][24][25][26][27], heat conduction [28], and so on. The SBFEM inherits the advantages of the BEM and FEM with some unique properties of its own.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of Quadruple Corner-Cut Ridged Elliptical Waveguide by NURBS Enhanced Scaled Boundary Finite Element Method

Xue

Lei

et al. 2021

IEEE Access

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The scaled boundary finite element method(SBFEM) is a semi-analysis method, combing the advantages of boundary element method and finite element method. However, in solving the quadruple corner-cut ridged elliptical(QCRE) waveguide, the traditional SBFEM employ the Lagrange polynomials as the basis functions which leads to the curved boundaries cannot be exactly represented and the continuity order across element is low. In this paper, a non-uniform rational B-spline (NURBS) enhanced SBFEM is firstly extended to solve the QCRE waveguide, which can exactly describe the curved boundaries, reduce the spatial dimensions by one and obtain analytically results in the radial direction. According to its symmetry, only a quarter of the ridged elliptical waveguide needs to be simulated and subdivided into several subdomains. The curved boundaries and straight boundaries of the subdomains are described and discretized by the NURBS and Lagrange basis functions, respectively. The side-face boundaries do not need to be discretized. Then, the NURBS enhanced SBFEM governing equation of the waveguide eigenvalue problem is derived based on the vibrational principle and scaled boundary coordinate transforming. Finally, a generalized eigenvalue equation respecting to the cut-off wave numbers is established by introducing the boundary dynamic stiffness and employing a continued fraction solution. Numerical results verify the high computational efficiency and accuracy of the NURBS enhanced SBFEM with exactly describing the curved boundaries. The influence of the corner-cut on the cut-off wave numbers of several modes and single-mode bandwidth are investigated in details.INDEX TERMS scaled boundary finite element method, elliptical waveguide, NURBS basis function, quadruple corner-cut ridge, cut-off wave number.

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“…In order to solve the homogeneous second-order differential equation (19), the concept of "boundary dynamic stiffness" S(kc, ξ) is introduced and defined as:…”

Section: The Generalized Eigenvalue Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of Quadruple Corner-Cut Ridged Elliptical Waveguide by NURBS Enhanced Scaled Boundary Finite Element Method

Xue

Lei

et al. 2021

IEEE Access

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“…To prevent the load from falling, or when it was necessary to move more slowly, two brakes could be used that braked the AA axle (4) or the EE axle (9) independently. For this, each axle had an inertia flywheel on which the brake was held, so that when pulling one of the braking levers (20) and (21), a collar embraced the wheels (8) and (5), respectively, and reduced the speed of the axles by friction.…”

Section: Downward Movementmentioning

confidence: 99%

“…The ultimate goal of this research is to perform a static analysis [19] of the Hay inclined plane using the finite element method (FEM) [20] under real operating conditions, in order to determine whether it was well dimensioned and functioned properly. Its scientific interest lies in the fact that from the point of view of industrial archaeology and the study of technical historical heritage, there is no existing study, worldwide, on this outstanding example of industrial historical heritage, which marked a historic milestone in the Industrial Revolution (1760-1840).…”

Section: Introductionmentioning

confidence: 99%

The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Analysis through Computer-Aided Engineering

Rojas‐Sola¹,

Fuente²

2019

Applied Sciences

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This article analyzes the ‘Hay inclined plane’ designed by the English engineer and entrepreneur William Reynolds and put into operation in 1792 to facilitate the transport of vessels between channels at different levels using an inclined plane. To this end, a study of computer-aided engineering (CAE) was carried out using the parametric software Autodesk Inventor Professional, consisting of a static analysis using the finite-element method (FEM) of the 3D model of the invention under real operating conditions. The results obtained after subjecting the mechanism to the two most unfavorable situations (blockage situation of the inertia flywheel and emergency braking situation) indicate that, with the exception of the braking bar, the rest of the assembly is perfectly designed and dimensioned. In particular, for the blockage situation, the point with the greatest stress is at the junction between the inertia flywheel and the axle to which it is attached, the maximum value of von Mises stress being at that point (186.9 MPa) lower than the elastic limit of the cast iron. Also, at this point the deformation is very low (0.13% of its length), as well as the maximum displacement that takes place in the inertia flywheel itself (22.98 mm), and the lowest safety factor has a value of 3.51 (located on the wooden shaft support), which indicates that the mechanism is clearly oversized. On the other hand, the emergency braking situation, which is technically impossible with a manual operation, indicates that the braking bar supports a maximum von Mises stress of 1025 MPa, above the elastic limit of the material, so it would break. However, other than that element, the rest of the elements have lower stresses, with a maximum value of 390.7 MPa, and with safety factors higher than 1.7, which indicates that the mechanism was well dimensioned.

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“…To ensure the good working performance of concrete dams, one of the prerequisites is to prevent and control the formation and propagation of concrete cracks that may appear during the construction and operation periods. In fact, cracking is a very common, classical, but also complicated problem in concrete structures in real-life service conditions [4], which has been studied comprehensively from different perspectives by many researchers [5][6][7][8][9]. In terms of cracking risk analysis, the true fracture toughness K c and tensile strength f t of the concrete are the key material parameters that should be provided.…”

Section: Introductionmentioning

confidence: 99%

Determination of Fracture Properties of Concrete Using Size and Boundary Effect Models

et al. 2019

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Tensile strength and fracture toughness are two essential material parameters for the study of concrete fracture. The experimental procedures to measure these two fracture parameters might be complicated due to their dependence on the specimen size or test method. Alternatively, based on the fracture test results only, size and boundary effect models can determine both parameters simultaneously. In this study, different versions of boundary effect models developed by Hu et al. were summarized, and a modified Hu-Guan’s boundary effect model with a more appropriate equivalent crack length definition is proposed. The proposed model can correctly combine the contributions of material strength and linear elastic fracture mechanics on the failure of concrete material with any maximum aggregate size. Another size and boundary model developed based on the local energy concept is also introduced, and its capability to predict the fracture parameters from the fracture test results of wedge-splitting and compact tension specimens is first validated. In addition, the classical Bažant’s Type 2 size effect law is transformed to its boundary effect shape with the same equivalent crack length as Koval-Gao’s size and boundary effect model. This improvement could extend the applicability of the model to infer the material parameters from the test results of different types of specimens, including the geometrically similar specimens with constant crack-length-to-height ratios and specimens with different initial crack-length-to-height ratios. The test results of different types of specimens are adopted to verify the applicability of different size and boundary effect models for the determination of fracture toughness and tensile strength of concrete material. The quality of the extrapolated fracture parameters of the different models are compared and discussed in detail, and the corresponding recommendations for predicting the fracture parameters for dam concrete are proposed.

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A Nonlinear Crack Model for Concrete Structure Based on an Extended Scaled Boundary Finite Element Method

Cited by 21 publications

References 31 publications

Analysis of Quadruple Corner-Cut Ridged Elliptical Waveguide by NURBS Enhanced Scaled Boundary Finite Element Method

Analysis of Quadruple Corner-Cut Ridged Elliptical Waveguide by NURBS Enhanced Scaled Boundary Finite Element Method

The Hay Inclined Plane in Coalbrookdale (Shropshire, England): Analysis through Computer-Aided Engineering

Determination of Fracture Properties of Concrete Using Size and Boundary Effect Models

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