The applicability of isogeometric analysis to shape optimization has. Isogeometric method in shape optimization, the analysis model will be naturally merged by design model, which eliminates the desired link between the design and analysis models in optimization process. Rd, which represents a deformable solid subject to external forces g, in d 2 or d 3 dimensions. It is shown that a new shape optimization algorithm has advantages in conical shape representation and in the treatment for location of control points in the limited space cases. The shape derivative can be computed by solving the primal and adjoint problems with the igbem. We formulate the shape optimization problem by introducing a trackingtype cost functional to match a desired pressure distribution in the focal region. Isogeometrical analysis based shape optimization numa jku.
The modal analysis of threedimension gun barrel using. Structural optimization, as an important tool in the product design process. Optimal design of multiphysics systems topology optimization aims to determine optimal shape and connectivity of material distributions under physical constraints. Recent years, wang and colleagues 8 10 extended the application fields of isogeometric shape optimization to the quasistatic design problems, the transient heat conduction design problems, and the lattice structure design problems. Isogeometric analysis, hape optimization, topology. The aim of structural shape optimization is to find the. Evans of the department of aerospace engineering sciences, pioneers new approaches to the modeling and simulation of aerospace, naval, and energy systems by leveraging synergies between computational mechanics, geometry, and approximation theory. In this case the design ariablev that describes the design is the crosssection area of the bars in the truss. Isogeometric shape optimization for scattering problems 3 parametrization. A framework for shape optimization in the context of. The seventh international conference on isogeometric analysis iga 2019 will be organized in munich, germany, on 1820 september 2019. Isogeometric shape optimization in fluidstructure interaction.
A notable departure from the optimization of control point weights. Pdf isogeometric shape optimization on triangulations. Introduction shape optimization of three dimensional and shell structures has drawn the attention of many disciplines in industry for its role in improving the structural performance. The advantages of isogeometric analysis for shape optimization are further elaborated in e. Typically, sizing optimization is used to optimize truss structures. Christoph heinrich, regis duvigneau, louis blanchard. The objective of the optimization is to modify the shape of the horn bell to improve the efficiency of the speaker. Topology optimization with isogeometric analysis in a phase field approach l. Iso geometric shape optimization of magnetic density separators june 5, 2014 abstract purpose the waste recycling industry increasingly relies on magnetic density separators. Jens gravesen dtu mathematics isogeometric analysis and shape optimisation saga, 48 october 2010 3 26. Isogeometric layout optimization of shell structures using trimmed nurbs surfaces. Software computational mechanics and geometry laboratory. Application of isogeometric analysis in structural shape optimization. Shape gradient for isogeometric structural design 3 2 isogeometric analysis in linear elasticity we consider an open domain.
Hirschler t, bouclier r, duval a, elguedj t and morlier j 2019 isogeometric sizing and shape optimization of thin structures with a solidshell approach, structural and multidisciplinary optimization, 59. Multiplegradient descent algorithm for isogeometric shape. The structures are modelled with nonuniform rational bspline based isogeometric kirchhofflove shell. Isogeometric analysis finite element analysis standard nite element analysis i triangulate the domain i use piecewise linear functions as basis functions or sometimes higher order polynomials. Isogeometric analysis is a computational approach that offers the possibility of integrating finite element analysis fea into conventional nurbsbased cad design tools. It thus inherits the advantages of isogeometric analysis and the resulting shape can be directly imported into cad systems, leading to closer integration of design and analysis.
Isogeometric shape optimization 810 is an iga based shape. The first 9 natural frequencies were calculated respectively by iga and traditional finite element method abaqus, and compared with the test results. Mma method is used to implement the iga shape optimization based on fcm. Multiresolution topology optimization using isogeometric. Isogeometric shape optimization 9, 10, 11 is a shap e. A method for conducting isogeometric shape optimization on triangulations. His technical contributions span several subfields, including geometric modeling, topology optimization, shape optimization and isogeometric analysis. Isogeometric shape optimization of trimmed shell structures. Abstract this paper proposes a multiscale isogeometric topology optimization ito method where the configuration and layout of microstructures are optimized simultaneously. Isogeometric shape optimization software for iga and cad integration applications of iga. 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 aim of wp6 in exciting is to assemble an isogeometric toolbox to support isogeometric analysis and shape optimization. Li k, qian xp 2011 isogeometric analysis and shape optimization via boundary integral. The intention of this paper is to show that isogeometric analysis offers a potential and promising way out of this dilemma.
Fixedgrid holeshape optimization for opening structures. The computational mechanics and geometry laboratory cmglab, led by dr. Also, a numerical analysis tool is developed, which uses the nurbs basis functions for. Anything in here will be replaced on browsers that support the canvas element. Triga is a software package for constructing unstructured isogeometric triangular and tetrahedral meshes from a set of boundary nurbs curves in two spatial dimensions or nurbstspline surfaces in three spatial dimensions. The substitution of the traditional finite elements not only makes the mesh model geometrically exact but also avoids the laborious mesh regeneration. Isogeometric analysis is a new development in computational analysis which aims to close this gap by using the same mathematical description for the design and the analysis model. Topology optimization with isogeometric analysis in a. A framework of shape optimisation based on the isogeometric. The delivery contains basic geometric support tools. In isogeometric approach, however, the geometric properties of design are embedded into the nurbs basis functions and the control points whose perturbation naturally results in shape changes. These devices generate an upward magnetic force in ferrouids allowing to separate the immersed particles according to their mass density. Computational design, isogeometric analysis, geometry processing.
Shape optimization of lift and thrust generating surfaces. Automatic model generation for isogeometric analysis 6. The isogeometric shape optimization method based on finite cell method p. Isogeometric shape optimization of three dimensional problems. We present an energy penalization method for isogeometric topology optimization using moving morphable components itommc, propose an itommc with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an itommc with a symmetric constraint. The formulation of the exterior potentialflow problem reduces to a boundaryintegral equation bie for the associated velocity potential exploiting the nullpressure jump kutta condition at the trailing edge.
A multipatch nonsingular isogeometric boundary element. Isogeometric shape optimization for nonlinear ultrasound. Therefore, this study is devoted to the estimation of shape derivatives in this particular context. Thus, exact geometric models can be used in both response and shape sensitivity analyses, where. One can dispose the differentiation of analysis and design model, the smoothness of the boundaries can be achieved easily and flexibly, and the promising analysis quality together with refinement strategies ensure the desired accuracy. This paper proposes a multiscale isogeometric topology optimization ito method where the configuration and layout of microstructures are optimized simultaneously. Lowfidelity aeroelasticity, isogeometric analysis, morphing airfoil, potential. One order and two order implicit curves are used to the outer boundary representation of elastic optimization problem, and their coefficients are taken as design variable. Isogeometric shape optimization of magnetic density. During regular iterations we work with quadratic optimization problems whose optimality conditions are linear systems based on a second order taylor series expansion of the nonlinear winslow functional around the reference parametrization. In the twodimensional shape optimization of a magnetic density separator was proposed, and in the optimization of ferromagnetic materials in a magnetic actuator was shown. Isogeometric topology optimization based on energy. A framework for parametric design optimization using. Isogeometric shape optimization of general curved geometry.
Shape optimization, isogeometric analysis, nurbs, control point, weight 3. In shape optimization the design ariablev is given by the whole or a part of the boundary. Department of naval architecture and ocean engineering, kunsan national university, 558 daehakro, gunsan, jeonbuk, 573701, republic of korea. Pdf structural design optimization using isogeometric analysis. Pdf isogeometric shape optimization for electromagnetic.
Furthermore, the concept of isogeometric analysis is extended to isogeometric shape optimization. In this paper, the isogeometric analysis iga is applied to make the modal analysis for 3d gun barrel. Computational mechanics and geometry laboratory university. The goal of this work is to improve focusing of highintensity ultrasound by modifying the geometry of acoustic lenses through shape optimization. Full analytical sensitivities in nurbs based isogeometric shape optimization xiaoping qian illinois institute of technology chicago, il 60062 february 27, 2010 abstract nonuniform rational bspline nurbs has been widely used as an e ective shape parameterization technique for structural optimization due to its compact and powerful shape. Multiscale isogeometric topology optimization with unified. Nurbs nonuniform rational bsplines are the most widespread functions in cad and hence they are used as basis functions for the isogeometric analysis. Establish an optimization framework that allows the automatic shape optimization of the geometric entities under investigation.
His research interests are in the area of computational design, he is interested in developing design methods and computer tools to advance multiphysics applications. All this make isogeometric analysis an ideal tool for shape opti mization. In this paper we apply iso geometric shape optimization to. Adaptive topology optimization of shell structures aiaa journal. Kiendl j, schmidt r, wuchner r, bletzinger ku 2014 isogeometric shape optimization of shells using semianalytical sensitivity analysis and sensitivity weighting. Topology optimization with isogeometric analysis in a phase. Geopdes is a suite of software tools for research on isogeometric analysis of partial differential equations.
Isogeometric shape optimization, is a shape optimization method where the same basis are also used to parameterize the shape, in addition to being used for analysis. We are studying methods for topology optimization of multiphysics systems, where human intuition is often inadequate to cope with the coupling nature of multiphysics systems. Isogeometric structural shape optimization combining the isogeometric approach for structural analysis with shape optimal design seems especially appealing. Isogeometric topology optimization based on energy penalization for. Isogeometric analysis and shape optimization in fluid. Finite element based shape optimization has some difficulties in the parameterization of design domain. Isogeometric shape optimization for nonlinear ultrasound focusing. The geometry of iga is modeled by noneuniform rational bsplines nurbs which is exact and smooth even at the coarsest mesh level. Shapeoptimization of 2d hydrofoils using an isogeometric bem. Isogeometric shape optimization of trimmed shell structures 21 november 2015 structural and multidisciplinary optimization, vol. The structures are modelled with nonuniform rational bspline based isogeometric kirchhofflove shell elements.
Isogeometric structural shape optimization sciencedirect. Adaptive topology optimization of shell structures aiaa. Shape optimization for natural frequency with isogeometric. Isogeometric layout optimization of shell structures using. Optimal analysisaware parameterization of computational. Isogeometric shape optimization of magnetic density separators. Nurbsbased isogeometric shape optimization using a boundary integral method. Shapeoptimization of 2d hydrofoils using an isogeometric bem solver k.
The library is licensed under the mozilla public license v2. In isogeometric approach, however, the geometric pr thus, exact geometric models can be used in both response and shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be obtained. Office of naval research 04272010 universita degli studi di pavia institute for computational engineering and sciences the university of texas at austin. A fast shape optimization strategy for free form shell structure design with structural dynamics criteria is proposed in this paper. Full analytical sensitivities in nurbs based isogeometric. A fast shape optimization strategy for free form shell structure design with. Researchers and practitioners from academia and industry are invited to share their original work by submitting research and application papers for this issue.
Also a material distribution function is considered to define the topology of the structure. In particular, complex shapes can be represented with relatively. 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. Isogeometric analysis and shape optimization in electromagnetism ph. Jan 10, 2020 we present an energy penalization method for isogeometric topology optimization using moving morphable components itommc, propose an itommc with an additional bilateral or periodic symmetric constraint for symmetric structures, and then extend the proposed energy penalization method to an itommc with a symmetric constraint. The sensitivity of the mean compliance equation 7 is given as follows 15, 17. Isogeometric analysis uses for the analysis the same basis function as the cad model, which makes the. The isogeometric shape optimization method based on finite. May 30, 2008 finite element based shape optimization has some difficulties in the parameterization of design domain. Additionally, isogeometric shape optimization has been used to address problems of electromagnetic scattering, vibrating membranes, heat conduction, fluid mechanics.
Topics of interest include but are not restricted to. Isogeometric shape optimization for electromagnetic scattering problems. Triga is still actively in development, but an alpha release in matlab with twodimensional capabilities is available. This framework is promising for the commercial software. Shape optimization is an iterative procedure and geometries vary at each step, thus leading to cumbersome remeshing procedures, which occupy around 80% of the total problem solving time for linear problems at each iterative step and accumulate to an unaffordable computational burden.
Isogeometric shape optimization on triangulations sciencedirect. Isogeometric analysis and analysissuitable parameterization methods 2. At micro scale, a shape deformation method is presented to transform a prototype microstructure pm for obtaining a series of graded microstructures gms, where microstructural skeleton based on the level set framework is. Subsequently, we map our shape optimisation problems to nonlinear programming problems in order to exploit a generalpurpose software for the latter problems. The role of pdebased parameterization techniques in. Shape gradient computation in isogeometric analysis for. Isogeometric shape optimization in fluid mechanics dtu orbit.
In all researches related with isogeometric optimization of structures 25, gradient methods are used in optimization process. Applicable to complex topology and allow local refinement. Isogeometric shape optimization of beam structures and vibrating. This paper proposes a shape optimization algorithm based on the principles of isogeometric analysis iga in which the parameterization of the geometry enters. At micro scale, a shape deformation method is presented to transform a prototype microstructure pm for obtaining a series of graded microstructures gms, where microstructural skeleton based on the level set framework is applied to retain more topology features and improve the connectability. Bezier triangles are used to represent both the geometry and physical fields. An application of isogeometric shape optimization in. Shape optimization of 2d hydrofoils using an isogeometric bem solver k.
Recent advances of isogeometric analysis in computational. Our approach for solving this problem is based on shape optimization and isogeometric analysis. Recently, researchers have also started to investigate isogeometric analysis of integral equations in the context of electrical engineering, e. The energy penalization method can solve the problems of. Coarse mesh to maintain parameterization validity for computational efficiency. Isogeometric topology optimization of structures by using mma 315 problems is briefly explained. In this paper, an optimization procedure, based on an isogeometric bem solver for the potential flow, is developed and used for the shape optimization of hydrofoils. An old dilemma in structural shape optimization is the needed tight link between design model or geometric description and analysis model.
Section 3 is devoted to the concise definition of topology optimization problem. Iga2d is an educational suite of software tools for isogeometric analysis of systems of twodimensional partial differential equations including heat conduction, linear elasticity, structural vibrations and wave propagation, elastodynamics, hyperelasticity, and incompressible fluid flow. It aims at providing access to high quality, opensource software to the isogeometric numerical simulation community and beyond. Lieu and jaehong lee, an isogeometric multimesh design approach for size and shape optimization of multidirectional functionally graded plates, computer methods in applied mechanics and engineering, 10. Vuong adepartment of mathematics,technische universit at kaiserslautern, paulehrlichstra. Shapeoptimization of 2d hydrofoils using an isogeometric. Isogeometric analysis and shape optimisation jens gravesen, anton evgrafov, allan roulund gersborgy, nguyen dang manh, peter n. Apply these tools in design, simulation, and optimization of functional freeform surfaces, which are of significance in aeronautical, shipbuilding and green energy technologies. The arrival of isogeometric analysis iga 7 provided the subject of shape optimization with a new direction of development.