Abstract Limit analysis, without the complicated elasto-plastic computation, is an efficient method for estimating safety load of engineering structures. This paper develops a novel computational approach by integrating second-order cone programming (SOCP) into adaptive extended isogemetric elements (XIGA) for upper-bound limit analysis of cracked structures. The advantage of XIGA is to model cracks without considering the location of crack faces by introducing enrichment functions. The local refined (LR) B-splines, which have versatile and flexible local refinement ability, are adopted as basis functions in the XIGA. We use structured mesh refinement strategy to implement local refinement based on the indicator of L 2 -norm of plastic strain rates. Cracked structures are assumed under plane stress condition, and the von Mises yield criterion is used. Kinematic formulation of the limit analysis is translated into the form of SOCP, then is solved by the Mosek tool. The developed model is implemented and its accuracy and effectiveness are illustrated through several numerical examples. In addition, numerical results illustrate that the convergence rate of adaptive XIGA is faster than that of traditional XIGA.
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract This paper presents an error-controlled adaptive extended isogeometric analysis (XIGA) for assessment of fracture behavior for through-cracked Mindlin-Reissner plates. The locally refined (LR) B-splines that facilitate the local refinement are used as the basis functions for the approximations, while the kinematics of plates are described in terms of the Mindlin-Reissner plate theory. Appropriate enrichment functions for cracked plates are incorporated into the formulation to represent ...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract We present in this paper an efficient computational approach based on an adaptive extended isogeometric analysis (XIGA) for simulation of arbitrary holes in orthotropic materials. The interfaces of holes are described by multiple level set functions so that the developed XIGA can capture the hole geometry without considering its interfaces. The approach is further enhanced by using the locally refined (LR) B-spline basis functions, which dominate over B-spline or non-uniform rational B-...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract This paper is concerned with the numerical investigation of fracture mechanics parameters for cracked orthotropic composite structures by using an efficient computational approach. The adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines is thus developed. This adaptive XIGA is enhanced by both signed-distance and orthotropic crack-tip enrichment functions to represent strong discontinuity and singularity induced by crack, respectively. In addition, to ...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract This paper aims at investigating fracture behavior of single and multiple cracks in two-dimensional solids by an adaptive extended isogeometric analysis (XIGA) based on locally refined (LR) B-splines. The adaptive XIGA is capable of modeling cracks without considering the location of crack faces due to the local enrichment technique based on partition-of-unity concept. The XIGA approximation is locally enriched by Heaviside function and crack tip enrichment functions to capture the disc...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract In this paper, we present an effective computational approach that combines an adaptive extended isogeometric analysis (XIGA) method with locally refined (LR) B-splines and level set methods for modeling multiple inclusions in two-dimensional (2D) elasticity problems. The advantage of XIGA is to model inclusions without considering internal inclusion interfaces by additional functions. Multiple level set functions are used to represent the location of inclusion interfaces and to define ...
Abstract Limit analysis is a useful tool for design and safety assessment of structures in civil and geotechnical engineering. In the present study, a newly developed high order algorithm-the weak form quadrature element method is reformulated for upper bound limit analysis. The dual formulations of the kinematic theorem are employed with the nodal stresses chosen as the optimization variables. The weak form equilibrium constraint is numerically integrated by Lobatto integration and then the nod...
Summary Adaptive local refinement is one of the main issues for isogeometric analysis (IGA). In this paper, an adaptive extended IGA (XIGA) approach based on polynomial splines over hierarchical T-meshes (PHT-splines) for modeling crack propagation is presented. The PHT-splines overcome certain limitations of non-uniform rational B-splines (NURBS)-based formulations; in particular, they make local refinements feasible. To drive the adaptive mesh refinement, we present a recovery-based error esti...
Last. Kun Zhou(NTU: Nanyang Technological University)H-Index: 63
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In this paper, the buckling analysis for the Mindlin–Reissner plates is performed by applying the isogeometric analysis (IGA) coupled with Bezier extraction operator. The Bezier extraction operator allows the incorporation of non-uniform rational B-spline-based IGA into the existing finite element method (FEM) work frame. For cracked plates, the extended IGA (XIGA) is employed. Unlike previous FEM approaches, the present method is expected to be more accurate and to achieve higher convergence as...
#1S.K. Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 6
#2Indra Vir Singh(IITR: Indian Institute of Technology Roorkee)H-Index: 31
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract In the present work, a simple, efficient and accurate Bezier extraction based T-spline XIGA (BEBT-XIGA) has been proposed for the crack simulations. Bezier extraction maps T-spline basis functions over the element in the forms of Bernstein polynomial basis defined over the Bezier element. T-spline basis functions over the element can be written as linear combination of Bernstein polynomials basis. Bezier extraction approach generates an element extraction operator and Bezier element for...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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Abstract The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche’s method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partitio...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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This paper is devoted to numerical investigations on mechanical behavior of cracked composite functionally graded (FG) plates. We thus develop an efficient adaptive approach in terms of the extended isogeometric analysis (XIGA) enhanced by locally refined non-uniform rational B-spline (LR NURBS) for natural frequency and buckling analysis of cracked FG Mindlin–Reissner plates. In this setting, the crack geometries, which are described by the level sets, are independent of the computational mesh;...