Part of thecivil and environmental engineering commons this thesis is brought to you for free and open access by byu scholarsarchive. Isogeometric boundary element analysis with matlab this code holds all the matlab files necessary to run a 2d isogeometric code for elastostatic analysis. Isogeometric analysis using tsplines hal archive ouverte. The construction of the thbsplines t is based on the re nability of bsplines. Finite element and isogeometric correlation analysis using. Designs are encapsulated in computer aided design cad systems. Isogeometric collocation using analysissuitable tsplines of.
The b splines allows to make a unstructured grid which represents the eld of the solution of the pde. A simple definition of twodimensional t splines is given and bezier extraction is introduced. The drawback of the cardinal bsplines is the lack of interpolatory functions that allow us to impose, in a strong form, dirichlet boundary conditions. Highlights we couple isogeometric boundary element methods and unstructured t spline surfaces.
In this study, we develop an isogeometric analysis igabased level. Isogeometric collocation using analysissuitable tsplines of arbitrary degree hugo casqueroa. Lewis a research paper submitted in partial ful llment of the requirements for the degree of masters of science in the eld of mathematics approved by. The drawback of the cardinal b splines is the lack of interpolatory functions that allow us to impose, in a strong form, dirichlet boundary conditions. The present code uses nonuniform rational b splines but it should be noted that the cagd community is making headway towards other descriptions of the geometry, overcoming the.
Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis fea into conventional nurbsbased cad design tools. Isogeometric finite element analysis using tsplines jingang li brigham young university provo follow this and additional works at. Numerical method for shape optimization using tspline. Nurbs, t splines and rhtsplines, cannot be seamlessly extracted from ex. Macstyle strategy is able to better determine the modal. T splines also need to be thoroughly researched and compared with traditional finite element methodology on a wider variety of analysis applications. A generalized finite element formulation for arbitrary basis. We refer also to 62 for iga combined with finite element based local.
For the head modeled by nurbs and t splines in figs. Isogeometric finite element analysis using t splines jingang li brigham young university provo follow this and additional works at. Nurbs, tsplines and rhtsplines, cannot be seamlessly extracted from ex. Mac strategy, which is widely used in experimental structural dynamics 24, 25. Finite element analysis shows whether a product will break, wear out, or work the way it was designed. Currently, it is necessary to convert data between cad and fea packages to analyse new designs during development, a difficult task since the two computational geometric approaches are different. For more guidance, it is probably a good idea to have a look through the code repository, and more recent updates to the code may also be present here. While the cad community uses geometry descriptions like e. Pdf a performance study of nurbsbased isogeometric analysis. Matlab code for conducting isogeometric analysis using nurbs. Isogeometric analysis using tsplines oden institute. Isogeometric analysis using tsplines was introduced in bazilevs et al. The present code uses nonuniform rational bsplines but it should be.
The finite element method fem is the most widely used method for solving problems of engineering and mathematical models. Isogeometric analysis using t splines was introduced in bazilevs et al. Isogeometric finite element analysis of nonlinear structural. Our collocation procedure correctly accounts for sharp edges and corners, extraordinary points, and t junctions. The principle of the isogeometric nite element method is to use functions from cadcomputeraided design like b splines to determine the eld where the pde takes place and to numerically solve it. Moreover, tsplines are completely backward compatible. This can be done through the development of new types of finite element models using the same basis functions as those used in. A computer software for analyzing displacement, stress, etc. Macbased modetracking in structural topology optimization. Computer methods in applied mechanics and engineering 317, pp. We begin the mathematical study of isogeometric analysis based on nurbs nonuniform rational bsplines. Isogeometric boundaryelement analysis for the wave.
Typically a mac matrix is calculated, collecting mac values between. Our collocation procedure correctly accounts for sharp edges and corners, extraordinary points, and tjunctions. The fiveaxis nc machining based on t spline was introduced in gan et al. Basis functions generated from nurbs nonuniform rational bsplines are employed to construct an exact geometric model. Isogeometric boundary element analysis with matlab. The principle of the isogeometric nite element method is to use functions from cadcomputeraided design like bsplines to determine the eld where the pde takes place and to numerically solve it.
Load design finite element analysis software for mac os x. Fem that aims at bridging the gap between design and analysis by in. The fem is a particular numerical method for solving. Finite element analysis shows whether a product will break, wear out or work the way it was designed.
The analytical and fea results are compared and validated with experimental results. Finite element analysis fea is a computerised method for predicting how a product reacts to realworld forces, vibration, heat, fluid flow and other physical effects. Usplines are compatible with bezier, nurbs, tsplines, fea quaddominant meshes. We extend the definition of analysissuitable tsplines to encompass unstructured control grids. We extend the definition of analysis suitable t splines to encompass unstructured control grids. About isogeometric analysis and the new nurbsbased finite. Currently, it is necessary to convert data between cad and fea packages to analyse new designs during development, a difficult task since the two computational geometric approaches are diffe. The standard finite element method fem, albeit very popular in various fields of sciences. Locally refined bsplines for isogeometric representation and. The approach is applied to several threedimensional problems, including a realworld t. Recent citations isogeometric analysis for elliptical. Tsplines also need to be thoroughly researched and compared with traditional finite element methodology on a wider variety of analysis applications. Isogeometric analysis using tsplines archive ouverte hal.
Finite element methods with b splines describes new weighted approximation techniques, combining the computational advantages of b splines and standard finite elements. Usplines satisfy the smoothness and exactness requirements of cad, while satisfying the rigorous requirements for fea. Isogeometric analysis with local adaptivity based on a. Then we explain the principle of finite element analysis and the isogeometric analysis using nurbs basis functions.
A partial row of control points terminates in a t junction, hence the name t splines. Highlights we couple isogeometric boundary element methods and unstructured tspline surfaces. Tsplines seem to be a very appealing way of unifying the cad and cae communities, not only for its ease of integrating into existing cadprograms, but also for its powerful properties within both. A partial row of control points terminates in a tjunction, hence the name tsplines. A hamiltonianbased derivation of scaled boundary finite element method for elasticity problems zhiqiang hu, gao lin, yi wang et al. This book is very original, and if you want to have a basic idea of this method, i would recommend you to read a journal paper titled isogeometric analysis. Universit at stuttgart finite element analysis with bsplines avignon, june 2010 12. Isogeometric analysis with local adaptivity based on a posterior error. This chapter provides an introduction to the use of t splines in isogeometric analysis. The fiveaxis nc machining based on tspline was introduced in gan et al.
Inspired by the new paradigm of isogeometric analysis introduced in 16, we propose an algorithm based on the use of bivariate bsplines. Isogeometric boundary element analysis using unstructured t. Isogeometric analysis 1,2 was created to address the major impediment to the process of engineering product development, namely, the conversion of cad descriptions to analysissuitable formats leading to finite element meshes. The invention of usplines was an important step in the development of analysissuitable geometry for splinebased simulation. We extend the definition of analysissuitable tsplines to encompass unstructured control grids unstructured meshes and develop basis functions which are smooth rational polynomials defined in terms of the bezier extraction framework and which. Nonlinear finite element analysis of solids and structures. A simple definition of twodimensional tsplines is given and bezier extraction is introduced. In particular, no grid generation is necessary, which eliminates a difficult and often timeconsuming preprocessing step.
The basic details for implementation of t splines as finite element shape functions are given. However, the finite element based shape design sensitivity analysis and optimization have experienced some bottleneck problems such as design parameterization and design remodeling during optimization. This perhaps explains why the geometric representations in. Acknowledgements we wish to thank omar ghattas for helpful insights into the relationship between.
The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite element program but that permits the use of arbitrary sets of basis functions that are. Cad, finite elements, nurbs, exact geometry and mesh refinement. Acknowledgements we wish to thank omar ghattas for helpful insights into the relationship between isogeometric analysis and highperformance computing. This chapter provides an introduction to the use of tsplines in isogeometric analysis. Multigrid methods for isogeometric analysis with thbsplines. Overview on use of feap university of california, berkeley. Tsplines nurbs isogeometric analysis cad fea fluid dynamics structural analysis pbsplines we explore tsplines, a generalization of nurbs enabling local re. Stability of finite element models for distributedparameter optimization and topology design. Design cad systems, needs to be translated to an analysissuitable geometry for mesh generation and use in a finite element analysis fea. To this end, t splines have been recently developed to overcome the. Weighted isogeometric bsplines for linear elasticity. We begin the mathematical study of isogeometric analysis based on nurbs nonuniform rational b splines.
Nonlinear finite element analysis of solids and structures, 2nd edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics. In this paper, as a remedy for these problems, an isogeometric based shape. We couple collocated isogeometric boundary element methods and unstructured analysissuitable tspline surfaces for linear elastostatic problems. Gregory budzban, chair gregory budzban issa tall nazeih botros graduate school southern illinois university carbondale. The basic details for implementation of tsplines as finite element shape functions are given. An isogeometric analysis for elliptic homogenization problems. We will show how to construt a spline space where all basis functions vanish on the boundary. Scott university of texas at austin t splines, inc. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential.
To conclude, we compare the results obtained using the mac modal. This can be done through the development of new types of finite element models using the same basis functions as those used in cad models defining exact geometry. Isogeometric boundary element analysis using unstructured. Isogeometric analysis based on tsplines springerlink.
Numerical methods for shape design sensitivity analysis and optimization have been developed for several decades. In this system, x, y, z is the global coordinate system, and x, y, z is the local coordinate system for the element i. In the second part we develop a twodimensional mesh that we will explore with the two methods, the classical finite element and isogemetric finite element. Isogeometric analysis 2011 austin, texas january 15, 2011. Presently, cad is a much bigger industry than analysis. Finite element methods with bsplines describes new weighted approximation techniques, combining the computational advantages of bsplines and standard finite elements. Isogeometric analysis using tsplines sciencedirect. The present code uses nonuniform rational b splines but it should be.
Isogeometric analysis has been widely applied in many areas since the authors proposed this method in 2005. Isogeometric finite element analysis using polynomial splines over hierarchical tmeshes nhon nguyenthanh, hung nguyenxuan, stephane p a bordas et al. Isogeometric finite element analysis using tsplines. Isogeometric analysis has been proposed as a methodology for bridging the gap. The bsplines allows to make a unstructured grid which represents the eld of the solution of the pde. Finite element analysis fea is a computerized method for predicting how a product reacts to realworld forces, vibration, heat, fluid flow, and other physical effects.