Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
540
result(s) for
"Isogeometric Analysis"
Sort by:
Isosurfaces : geometry, topology, and algorithms
\"Ever since Lorensen and Cline published their paper on the marching cubes algorithm, isosurfaces have been a standard technique for the visualization of 3D volumetric data. Yet there is no book exclusively devoted to isosurfaces. This book presents the basic algorithms for isosurface construction and gives a rigorous mathematical perspective to some of the algorithms and results. It offers a solid introduction to research in this area as well as an organized overview of the various algorithms associated with isosurfaces\"-- Provided by publisher.
Book
Simulation of sheet metal forming processes by presenting a bending-dependent inverse isogeometric methodology
Recently, eliminating the gap between design and formability analysis of sheet metal parts has been studied to simulate sheet metal stamping processes. In this regard, a transfer-based inverse isogeometric formulation has been proposed. This method has various advantages such as solving the governing equations in two-dimensional networks without any concern about the convergence; however, it neglects the bending effect which is a major contributor in die/punch profile radii. The present work aims to consider the bending effects by introducing a bending-dependent inverse isogeometric formulation. The developed model deals with the minimization of potential energy, deformation theory of plasticity, classical plate theory, and considering a yield criterion in stress-resultant space. In addition to all advantages of the transfer-based inverse isogeometric formulation, one major benefit of this study is that the bending effects are included with a slight increase in the computation time. This methodology allows for accurately predicting the effects of changing die/punch profile radii and initial sheet thickness on the formability of the final part by presenting a new material updating process. To assess the credibility of this approach, an experimental setup and forward FEM software have been utilized to form a rectangular box. The results acquired by the developed method and those achieved by experiment and forward FEM reveal acceptable accuracy in the presented model. Also, strains and thicknesses predicted by the developed method, membrane inverse isogeometric model, and forward FEM for nine different values of punch radius to the sheet thickness ratio have been compared. Considering forward FEM as a reference method, the average of calculated error in the presented model for prediction of thickness at the middle of punch radius zone is around half of that in the membrane model. In solving the studied problems, the presented model requires only slightly more computation time (around 2%) than the membrane inverse isogeometric model and much less computation time than forward FEM. Therefore, the presented method is a valuable inverse forming solver especially when the bending effects are significant.
Journal Article
SYMBOL-BASED MULTIGRID METHODS FOR GALERKIN B-SPLINE ISOGEOMETRIC ANALYSIS
We consider the stiffness matrices arising from the Galerkin B-spline isogeometric analysis discretization of classical elliptic problems. By exploiting their specific spectral properties, compactly described by a symbol, we design an efficient multigrid method for the fast solution of the related linear systems. The convergence rate of general-purpose multigrid methods, based on classical stationary smoothers, is optimal (i.e., bounded independently of the matrix size), but it also worsens exponentially with respect to the spline degree. The symbol allows us to give a detailed theoretical explanation of this exponential worsening in the case of the two-grid scheme. In addition, thanks to a specific factorization of the symbol, we are able to design an ad hoc multigrid method with an effective preconditioned CG or GMRES smoother at the finest level, in the spirit of the multi-iterative idea. The convergence rate of this multi-iterative multigrid method is not only optimal but also robust (i.e., bounded substantially independently of the spline degree). This can again be explained by the symbol, in combination with the theory of generalized locally Toeplitz sequences. A selected set of numerical experiments confirms our symbol-based analysis, as well as the effectiveness of the proposed multi-iterative multigrid method, also for larger spline degree.
Journal Article
A MINIMAL STABILIZATION PROCEDURE FOR ISOGEOMETRIC METHODS ON TRIMMED GEOMETRIES
Trimming is a common operation in computer aided design and, in its simplest formulation, consists in removing superfluous parts from a geometric entity described via splines (a spline patch). After trimming, the geometric description of the patch remains unchanged, but the underlying mesh is unfitted with the physical object. We discuss the main problems arising when solving elliptic PDEs on a trimmed domain. First we prove that, even when Dirichlet boundary conditions are weakly enforced using Nitsche's method, the resulting method suffers lack of stability. Then, we develop novel stabilization techniques based on a modification of the variational formulation, which allow us to recover well-posedness and guarantee accuracy. Optimal a priori error estimates are proven, and numerical examples confirming the theoretical results are provided.
Journal Article
Finite Element Analysis of Structures through Unified Formulation
The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another.
Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same 'fundamental nucleus' that comes from geometrical relations and Hooke's law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D and 2D FEs that make use of 'real' physical surfaces rather than 'artificial' mathematical surfaces which are difficult to interface in CAD/CAE software.
Key features:
* Covers how the refined formulation can be easily and conveniently used to analyse laminated structures, such as sandwich and composite structures, and to deal with multifield problems
* Shows the performance of different FE models through the 'best theory diagram' which allows different models to be compared in terms of accuracy and computational cost
* Introduces an axiomatic/asymptotic approach that reduces the computational cost of the structural analysis without affecting the accuracy
* Introduces an innovative 'component-wise' approach to deal with complex structures
* Accompanied by a website hosting the dedicated software package MUL2 (www.mul2.com)
Finite Element Analysis of Structures Through Unified Formulation is a valuable reference for researchers and practitioners, and is also a useful source of information for graduate students in civil, mechanical and aerospace engineering.
eBook
ROBUST MULTIGRID FOR ISOGEOMETRIC ANALYSIS BASED ON STABLE SPLITTINGS OF SPLINE SPACES
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stable splitting of the spline space into a large subspace of 'Interior\" splines which satisfy a robust inverse inequality, as well as one or several smaller subspaces which capture the boundary effects responsible for the spectral outliers which occur in isogeometric analysis. We then construct a multigrid smoother based on an additive subspace correction approach, applying a different smoother to each of the subspaces. For the interior splines, we use a mass smoother, whereas the remaining components are treated with suitably chosen Kronecker product smoothers or direct solvers. We prove that the resulting multigrid method exhibits iteration numbers which are robust with respect to the spline degree and the mesh size. Furthermore, it can be efficiently realized for discretizations of problems in arbitrarily high geometric dimension. Some numerical examples illustrate the theoretical results and show that the iteration numbers also scale relatively mildly with the problem dimension.
Journal Article
A new surface parameterization method based on one-step inverse forming for isogeometric analysis-suited geometry
In an attempt to construct an isogeometric analysis-suited geometry for isogeometric analysis, a new surface parameterization method using the one-step inverse forming (SPIA) is proposed. Initial generation of watertight analysis-suitable geometry (NURBS surfaces) with complex shapes can be a significant bottleneck for isogeometric analysis because computer-aided design models often include ambiguities such as gaps and overlaps. Most of traditional surface parameterization techniques are based on geometric method and limited to finite meshes, while SPIA is a physics-based method using sheet metal forming technique with large elastic–plastic deformation and robust enough and rapid to deal with the finite elements mesh with over 100,000 nodes within 2 min without the necessity to simplify the meshes. Using Coons surface parameterization, global mesh parameterization, and NURBS reconstruction, we can rebuild new computer-aided design models with errors under any tolerance to which isogeometric analysis can be applied. The NURBS surfaces after reconstruction are also used for computer-aided manufacturing.
Journal Article
Computer simulations suggest that prostate enlargement due to benign prostatic hyperplasia mechanically impedes prostate cancer growth
Prostate cancer and benign prostatic hyperplasia are common genitourinary diseases in aging men. Both pathologies may coexist and share numerous similarities, which have suggested several connections or some interplay between them. However, solid evidence confirming their existence is lacking. Recent studies on extensive series of prostatectomy specimens have shown that tumors originating in larger prostates present favorable pathological features. Hence, large prostates may exert a protective effect against prostate cancer. In this work, we propose a mechanical explanation for this phenomenon. The mechanical stress fields that originate as tumors enlarge have been shown to slow down their dynamics. Benign prostatic hyperplasia contributes to these mechanical stress fields, hence further restraining prostate cancer growth. We derived a tissue-scale, patient-specific mechanically coupled mathematical model to qualitatively investigate the mechanical interaction of prostate cancer and benign prostatic hyperplasia. This model was calibrated by studying the deformation caused by each disease independently. Our simulations show that a history of benign prostatic hyperplasia creates mechanical stress fields in the prostate that impede prostatic tumor growth and limit its invasiveness. The technology presented herein may assist physicians in the clinical management of benign prostate hyperplasia and prostate cancer by predicting pathological outcomes on a tissue-scale, patient-specific basis.
Journal Article
Isogeometric iFEM Analysis of Thin Shell Structures
Shape sensing is one of most crucial components of typical structural health monitoring systems and has become a promising technology for future large-scale engineering structures to achieve significant improvement in their safety, reliability, and affordability. The inverse finite element method (iFEM) is an innovative shape-sensing technique that was introduced to perform three-dimensional displacement reconstruction of structures using in situ surface strain measurements. Moreover, isogeometric analysis (IGA) presents smooth function spaces such as non-uniform rational basis splines (NURBS), to numerically solve a number of engineering problems, and recently received a great deal of attention from both academy and industry. In this study, we propose a novel “isogeometric iFEM approach” for the shape sensing of thin and curved shell structures, through coupling the NURBS-based IGA together with the iFEM methodology. The main aim is to represent exact computational geometry, simplify mesh refinement, use smooth basis/shape functions, and allocate a lower number of strain sensors for shape sensing. For numerical implementation, a rotation-free isogeometric inverse-shell element (isogeometric Kirchhoff–Love inverse-shell element (iKLS)) is developed by utilizing the kinematics of the Kirchhoff–Love shell theory in convected curvilinear coordinates. Therefore, the isogeometric iFEM methodology presented herein minimizes a weighted-least-squares functional that uses membrane and bending section strains, consistent with the classical shell theory. Various validation and demonstration cases are presented, including Scordelis–Lo roof, pinched hemisphere, and partly clamped hyperbolic paraboloid. Finally, the effect of sensor locations, number of sensors, and the discretization of the geometry on solution accuracy is examined and the high accuracy and practical aspects of isogeometric iFEM analysis for linear/nonlinear shape sensing of curved shells are clearly demonstrated.
Journal Article
The Scaled Boundary Finite Element Method
An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method.
eBook