Abstract Nonlinear behaviors are commonplace in many engineering applications, e.g., metal forming and vehicle crash tests. Different from linear systems, nonlinear problems cannot be solved by using a system of linear equations and there is no guarantee that a unique solution can be found. In this work, we develop a unified framework, NLIGA (Non-Linear Isogeometric Analysis), for mainly solving two and three-dimensional nonlinear problems on the MATLAB platform by using the isogeometric method. Nonlinear hyperelastic and elastoplastic materials are primarily considered at this stage. The Newton-Raphson method is used to solve the nonlinear governing equations. A series of examples are performed to validate the procedures. First, we provide dozens of scripts to solve linear elastic benchmark problems including plane and solid problems, Poisson problems, plate and shell problems and compare the obtained numerical solutions with exact solutions and FEA solutions. Second, we further investigate several nonlinear examples considering hyperelastic and elastoplastic materials and compare the results with that obtained from commercial software. The visualization procedures are also developed in this framework to visualize the obtained results including displacements, stresses and numerical errors. Finally, NLIGA is an open-source framework and free to use ( http://nliga.sourceforge.net/ ).
Last. Howie Fang(UNCC: University of North Carolina at Charlotte)H-Index: 1
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Complex geometric models are usually built with multiple NURBS patches with non-conforming interfaces, which bring difficulties within the isogeometric analysis. In this paper, Nitsche’s method is employed to glue different patches for nonlinear isogeometric analysis of hyperelastic material models which are widely used to describe the material behavior of rubbers, foams, biological tissues, etc. Nitsche based weakly governing equations and discretized stiffness matrices are detailedly developed...
Abstract Recently, a new formation and assembly strategy was proposed in [1] , which resulted in significant speedups in the formation and assembly time of the Galerkin mass matrix in isogeometric analysis. The strategy relies on three key ingredients: (1) assembly row by row, instead of element by element; and an efficient formation strategy based on (2) sum factorization and (3) weighted quadrature, that is applied to each specific row of the matrix. Compared to traditional element procedures ...
#2Stefan Takacs(Austrian Academy of Sciences)H-Index: 9
Abstract The fast assembling of stiffness and mass matrices is a key issue in Isogeometric Analysis, particularly if the spline degree is increased. We present two algorithms based on the idea of sum factorization, one for matrix assembling and one for matrix-free methods, and study the behavior of their computational complexity in terms of the spline order p . Opposed to the standard approach, these algorithms do not apply the idea element-wise, but globally or on macro-elements. If this approa...
#1Changsheng Wang(DUT: Dalian University of Technology)H-Index: 8
#2Xiangkui Zhang(DUT: Dalian University of Technology)H-Index: 7
Last. Yang Wang(DUT: Dalian University of Technology)H-Index: 2
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Abstract Isogeometric analysis (IGA) has been used with great success when combined with incremental methods to simulate sheet metal forming. In this paper, we present the development of one-step inverse IGA based on the total deformation theory of plasticity. For a large number of industrial stamping parts, the membrane effects are dominant. Thus, we adopted an isogeometric membrane element to predict the flattened contour of the initial blank from the energy-based initial solution estimation a...
#1Oliver Weeger(SUTD: Singapore University of Technology and Design)H-Index: 13
#2Bharath Narayanan(SUTD: Singapore University of Technology and Design)H-Index: 3
Last. Martin L. Dunn(University of Colorado Denver)H-Index: 36
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Abstract Straight beams, rods and trusses are common elements in structural and mechanical engineering, but recent advances in additive manufacturing now also enable efficient freeform fabrication of curved, deformable beams and beam structures, such as microstructures, metamaterials and conformal lattices. To exploit this new design freedom for applications with nonlinear mechanical behavior, we introduce an isogeometric method for shape optimization of curved 3D beams and beam structures. The ...
Last. Tinh Quoc Bui(TITech: Tokyo Institute of Technology)H-Index: 54
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The isogeometric analysis (IGA), which employs non-uniform rational B-splines (NURBS) basis as shape functions for both representation of geometry and approximation of the field variables, owns several inherent advantages to become an effective numerical method such as an exact geometry description with fewer control points, high-order continuity, and high accuracy. Unlike the C0-continuity shape functions in the conventional finite element method (FEM), the high-order basis functions in IGA are...
Abstract This paper introduces tIGAr , a library for using the open-source finite element (FE) automation software FEniCS to perform isogeometric analysis (IGA). The library uses a global variant of Bezier extraction to avoid modifying the finite element assembly procedures of FEniCS . This makes much of the convenient functionality of FEniCS directly available for IGA. General rational splines are implemented through an abstraction that sees only an extracted representation of the IGA function ...
Abstract A simple skew-symmetric Nitsche’s formulation is introduced into the framework of isogeometric analysis (IGA) to deal with various problems in small strain elasticity: essential boundary conditions, symmetry conditions for Kirchhoff plates, patch coupling in statics and in modal analysis as well as Signorini contact conditions. For linear boundary or interface conditions, the skew-symmetric formulation is parameter-free. For contact conditions, it remains stable and accurate for a wide ...
We review the treatment of trimmed geometries in the context of design, data exchange, and computational simulation. Such models are omnipresent in current engineering modeling and play a key role for the integration of design and analysis. The problems induced by trimming are often underestimated due to the conceptional simplicity of the procedure. In this work, several challenges and pitfalls are described.
#1Eduardo Mario Garau(CONICET: National Scientific and Technical Research Council)H-Index: 3
#2Rafael Vázquez(EPFL: École Polytechnique Fédérale de Lausanne)H-Index: 16
In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the pape...
#2Weiyin Ma(CityU: City University of Hong Kong)H-Index: 22
Abstract null null Analysis-suitable parameterization is a fundamental problem in IGA (IsoGeometric Analysis) implementation which significantly influences computational accuracy and efficiency. This paper proposes a variational framework to address the problem of producing a smooth parameterization of a computational domain represented in B-spline form. In order to control both angle and area distortions, a weighted and modified Liao functional is constructed. The weighting function is a modifi...
