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Free in-plane vibration analysis of curved beams by the generalized/extended finite element method

EUROPEAN JOURNAL OF MECHANICS A-SOLIDS 2021年 88卷 104244-104244页

作者： Correa, Ramon Macedo Arndt, Marcos Machado, Roberto Dalledone Univ Fed Parana PPGMNE Grad Program Numer Methods Engn Mailbox 19011 BR-81531990 Curitiba Parana Brazil Univ Fed Parana PPGECC Grad Program Civil Construct Engn Mailbox 19011 BR-81531980 Curitiba Parana Brazil

Arches and curved beams are solved here by the G/XFEM in the context of free vibration problems. This hierarchical enrichment method has been used in many complex applications, however it has not been examined for dynamic of curved beams yet. The focus of the present work is to apply the G/XFEM for free vibration analysis of thin and thick curved beam models. The accuracy of frequencies values, the convergence to reach them, and the frequency spectrum are some of the points to be discussed. Four examples are carried out and the results are compared with standard FEM, the p-Fourier method and analytical solutions. Even with coarse meshes, G/XFEM presents competitiveness and can reach good precision for large range of frequencies with few enrichment levels. It is also shown that the ill conditioning of mass and stiffness matrices for higher enrichment levels does not affect the G/XFEM competitiveness, since it converges faster with few enrichment levels.

关键词： Free vibration Curved beam generalized/extended finite element method finite element method

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Two-dimensional fracture modeling with the generalized/extended finite element method: An object-oriented programming approach

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ADVANCES IN ENGINEERING SOFTWARE 2018年 115卷 168-193页

作者： Malekan, Mohammad Silva, Leandro L. Barros, Felicio B. Pitangueira, Roque L. S. Penna, Samuel S. Fed Univ Minas Gerais UFMG Sch Engn Grad Program Struct Engn PROPEEs Belo Horizonte MG Brazil

This work presents an object-oriented implementation of the G/XFEM to model the crack nucleation and propagation in structures made of either linear or nonlinear materials. A discontinuous function along with the asymptotic crack-tip displacement fields are used to represent the crack without explicitly meshing its surfaces. Different approach are explained in detail that are used to capture the crack nucleation within the model and also determine the crack propagation path for various problems. Stress intensity factor and singularity of the localization tensor (which provides the classical strain localization condition) can be used to determine the crack propagation direction for linear elastic materials and nonlinear material models, respectively. For nonlinear material model, the cohesive forces acting on the crack plane are simulated in the enrichment process by incorporating a discrete constitutive model. Several algorithms and strategies have been implemented, within an object-oriented framework in Java, called INSANE. This implementation will be presented in detail by solving different two-dimensional problems, for both linear and nonlinear material models, in order to show the robustness and accuracy of the proposed method. The numerical results are compared with the reference solutions from the analytical, numerical or experimental results, where applicable.

关键词： generalized/extended finite element method Fracture mechanics Object-oriented programming Linear and nonlinear materials

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Simulation of fracture behavior in seawater and sea-sand mixed recycled coarse aggregate concrete under three-point bending

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THEORETICAL AND APPLIED FRACTURE MECHANICS 2024年 131卷

作者： Mukhtar, Faisal King Fahd Univ Petr & Minerals Dept Civil & Environm Engn Dhahran 31261 Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Construct & Bldg Mat Dhahran 31261 Saudi Arabia

This paper presents a comprehensive fracture analysis of seawater -mixed concrete containing seasand and recycled concrete coarse aggregate based on the extended finite element method. Capable of simulating fracture problems without the need for a conforming mesh, the model was validated using a set of literature experimental results for specimens containing different compositions of the sustainable materials (seawater, seasand, and recycled concrete aggregate) under three-point bending test configurations. A series of parametric studies was then conducted to invesitgate the effects of beam size and notch -to -depth ratio for seawater -mixed specimens containing natural aggregates, followed by another parametric study on the effects of modulus of rupture, total fracture energy, concrete elastic modulus, and Poisson's ratio of the material. The exercise resulted in a total of 32 simulation runs based on which the model presents unique attributes on the fracture behavior of this nonconventional sustainable material whose response has not been simulated previously although its fracture behavior could differ from that of normal concrete.

关键词： Sustainability Concrete Recycled coarse aggregate Sea sand Seawater Cohesive zone model Fracture behavior generalized/extended finite element method

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extended isogeometric analysis: a two-scale coupling FEM/IGA for 2D elastic fracture problems

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COMPUTATIONAL MECHANICS 2024年第3期73卷 639-665页

作者： Santos, K. F. Barros, F. B. Silva, R. P. Fed Univ Minas Gerais UFMG Dept Struct Engn Sch Engn Ave Antonio Carlos6627 Pampulha BR-31270901 Belo Horizonte MG Brazil

Some of the key features of the isogeometric analysis, IGA, are the capacity of exactly representing the problem geometry, the use of the same basis functions to describe the geometry and the solution field, and a straightforward and automatic discretization refining scheme. The higher order continuity of the isogeometric approximation, important to correctly represent the domain geometry, can be a problem to approximate the displacement field in the neighbourhood of a crack. The extended Isogeometric Analysis (XIGA) overcomes this obstacle, enlarging the approximate space of IGA. This is achieved by incorporating customized functions, using the enrichment strategy of the generalized/extended finite element method. When these functions are unknown, they can be computed from the solution of local boundary value problems embracing the crack, and a global-local iterative procedure is established. Here this procedure is firstly proposed to combine FEM and isogeometric approximations, denoted XIGAgl\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>\text {gl}$$\end{document}. The effectiveness of this approach is investigated in terms of convergence rates and numerical stability. The method is applied to two-dimensional fracture mechanics problems. The numerical experiments show the importance of using the isogeometric approximation to recover more accurate solutions and minimize the deterioration of the conditioning of the related stiffness matrix.

关键词： extended isogeometric analysis method generalized/extended finite element method Global-local strategy Fracture mechanics Condition number

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Assessment of the flat-top stable GFEM for free vibration analysis

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2022年第0期117卷 271-283页

作者： da Silva, Ivan Assing Machado, Roberto Dalledone Arndt, Marcos Weinhardt, Paulo de Oliveira Univ Fed Parana R Cel Francisco H dos Santos 210 BR-81531980 Curitiba Parana Brazil PPGMNE Numer Methods Engn Grad Program Curitiba Parana Brazil PPGEC Civil Engn Grad Program Curitiba Parana Brazil

The stable generalized finite element method, SGFEM, has been used for numerical stabilization of the generalized finite element method during enrichment process of shape functions. However, some troubles persist in dynamic analysis. The flat-topstrategy is an alternative to hold up the SGFEM but, despite its good performance in quasi-static problems, for dynamic problems some points remain opened, such as the accuracy of natural frequencies, the computational effort to reach a desired degree of precision (for each natural frequency), and the conditioning of mass and stiffness matrices. The main objective of this work is to assess the performance of the flat-topSGFEM in the context of free vibration analysis Based in many numerical simulations, the sensitivity of the method is verified for different parameters, such as, the size of the flat-toppartition of unity (PU) intervals, the smoothness of enriched functions, and the stabilization parameter. Despite the flat-topSGFEM improves the numerical stability for modal analysis, it is shown that the convergence rates can be degraded.

关键词： SGFEM generalized/extended finite element method Flat-top PU Non-polynomial enrichment Free vibration Structural dynamic

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Coupled multiphysics 3-D generalized finite element method simulations of hydraulic fracture propagation experiments

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ENGINEERING FRACTURE MECHANICS 2022年第PartA期276卷

作者： Mukhtar, Faisal M. Duarte, C. Armando King Fahd Univ Petr & Minerals Dept Civil & Environm Engn Dhahran 31261 Saudi Arabia King Fahd Univ Petr & Minerals Interdisciplinary Res Ctr Construct & Bldg Mat Dhahran 31261 Saudi Arabia Univ Illinois Dept Civil & Environm Engn 205 North Mathews Av Urbana IL 61801 USA

Intentional creation and propagation of fractures driven by fluid under high pressure have several applications in oil and gas exploration, geological mining, disposal of toxic waste, flow of molten magma within crevices/fissures, etc. Due to the need to design hydraulic fractures, especially in the oil and gas industry, and the limitation of their full scale/field testing, the use of laboratory experiments and/or numerical simulations remain viable alternatives. While several computational methods for this class of problems exist in the literature, their reliability and robustness hinge on their ability to replicate experimental results with acceptable confidence. This paper presents the application of a coupled multiphysics 3-D generalized finite element method (GFEM) for the simulation of hydraulic fracture experiments based on a regularized Irwin criterion and adaptive mesh refinement. Built with an automatic time step search, the algorithm computes the time step size that ensures the satisfaction of the propagation criterion. Modes I, II, and III stress intensity factors are computed using the displacement correlation method, while the fracture propagation direction is determined using the Schollmann's criterion, which is a generalization of the maximum tangential stress criterion for 3-D stress state. The GFEM is validated against a hydraulic fracture experiment on PMMA specimen, on one hand, and against four different cases of experimental fractures within concrete (a granitelike) material which serves as the pioneer application of the algorithm to verify hydraulic fracture simulation in non-PMMA materials. The influence of the initial shear stresses along the fracture plane (assuming unnotched condition) on the resulting propagation paths in the latter benchmarked problem is also assessed and found to have good agreement with experimental observations.

关键词： Multiphysics simulation generalized/extended finite element method Discrete fractures Hydraulic fracture propagation Validation against experimental tests

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Effect of in-plane deformation on the cohesive failure of heterogeneous adhesives

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JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS 2013年第7期61卷 1600-1611页

作者： Aragon, Alejandro M. Soghrati, Soheil Geubelle, Philippe H. Univ Illinois Dept Aerosp Engn Urbana IL 61801 USA Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA

The effect of in-plane deformations on the failure response of heterogeneous adhesives with a second phase of spherical elastic particles is investigated numerically using a 3D cohesive framework. The methodology includes a new interface-enriched generalized finite element scheme for the solution of structural problems with weak discontinuities, allowing for the efficient and accurate prediction of the stress and displacement fields in the adhesive based on finite element meshes that do not conform to the heterogeneities. A rate-dependent isotropic failure model is adopted to capture the failure in the matrix, while the stiff inclusions are assumed to be linearly elastic. Cohesive failure envelopes resulting from the micro-to-macro analysis are extracted for a wide variety of failure mode conditions. A study of 1611 the impact of in-plane tensile and shear strains on the macroscopic failure response under tensile (mode I) loading is also presented. (C) 2013 Elsevier Ltd. All rights reserved.

关键词： Cohesive modeling Micro-to-macro analysis generalized/extended finite element method Heterogeneous adhesives Homogenization Viscous damage model

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generalized finite element method enrichment functions for curved singularities in 3D fracture mechanics problems

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COMPUTATIONAL MECHANICS 2009年第1期44卷 73-92页

作者： Pereira, J. P. Duarte, C. A. Jiao, X. Guoy, D. Univ Illinois Dept Civil & Environm Engn Urbana IL 61801 USA SUNY Stony Brook Dept Appl Math & Stat Stony Brook NY 11794 USA Univ Illinois Ctr Simulat Adv Rockets Urbana IL 61801 USA

This paper presents a study of generalized enrichment functions for 3D curved crack fronts. Two coordinate systems used in the definition of singular curved crack front enrichment functions are analyzed. In the first one, a set of Cartesian coordinate systems defined along the crack front is used. In the second case, the geometry of the crack front is approximated by a set of curvilinear coordinate systems. A description of the computation of derivatives of enrichment functions and curvilinear base vectors is presented. The coordinate systems are automatically defined using geometrical information provided by an explicit representation of the crack surface. A detailed procedure to accurately evaluate the surface normal, conormal and tangent vectors along curvilinear crack fronts in explicit crack surface representations is also presented. An accurate and robust definition of orthonormal vectors along crack fronts is crucial for the proper definition of enrichment functions. Numerical experiments illustrate the accuracy and robustness of the proposed approaches.

关键词： Partition of unity methods generalized/extended finite element method 3D fracture mechanics Crack front enrichments

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