Constructing analysis-suitable parameterization of computational domain from CAD boundary by variational harmonic method

In isogeometric anlaysis, parameterization of computational domain has great effects as mesh generation in finite element analysis. In this paper, based on the concept of harmonic mapping from the computational domain to parametric domain, a variational harmonic approach is proposed to construct analysis-suitable parameterization of computational domain from CAD boundary for 2D and 3D isogeometric applications. Different from the previous elliptic mesh generation method in finite element analysis, the proposed method focus on isogeometric version, and converts the elliptic PDE into a nonlinear optimization problem, in which a regular term is integrated into the optimization formulation to achieve more uniform and orthogonal isoparametric structure near convex (concave) parts of the boundary. Several examples are presented to show the efficiency of the proposed method in 2D and 3D isogeometric analysis

Parametric Design and Isogeometric Analysis of Tunnel Linings within the Building Information Modelling Framework

Both planning and design phase of large infrastructural project require analysis, modelling, visualization, and numerical analysis. To perform these tasks, different tools such as Building Information Modelling (BIM) and numerical analysis software are commonly employed. However, in current engineering practice, there are no systematic solutions for the exchange between design and analysis models, and these tasks usually involve manual and error-prone model generation, setup and update. In this paper, focussing on tunnelling engineering, we demonstrate a systematic and versatile approach to efficiently generate a tunnel design and analyse the lining in different practical scenarios. To this end, a BIM-based approach is developed, which connects a user-friendly industry-standard BIM software with effective simulation tools for high-performance computing. A fully automatized design-through-analysis workflow solution for segmented tunnel lining is developed based on a fully parametric design model and an isogeometric analysis software, connected through an interface implemented with a Revit plugin

Constructing IGA-suitable planar parameterization from complex CAD boundary by domain partition and global/local optimization

In this paper, we propose a general framework for constructing IGA-suitable planar B-spline parameterizations from given complex CAD boundaries consisting of a set of B-spline curves. Instead of forming the computational domain by a simple boundary, planar domains with high genus and more complex boundary curves are considered. Firstly, some pre-processing operations including B\'ezier extraction and subdivision are performed on each boundary curve in order to generate a high-quality planar parameterization; then a robust planar domain partition framework is proposed to construct high-quality patch-meshing results with few singularities from the discrete boundary formed by connecting the end points of the resulting boundary segments. After the topology information generation of quadrilateral decomposition, the optimal placement of interior B\'ezier curves corresponding to the interior edges of the quadrangulation is constructed by a global optimization method to achieve a patch-partition with high quality. Finally, after the imposition of C1=G1-continuity constraints on the interface of neighboring B\'ezier patches with respect to each quad in the quadrangulation, the high-quality B\'ezier patch parameterization is obtained by a C1-constrained local optimization method to achieve uniform and orthogonal iso-parametric structures while keeping the continuity conditions between patches. The efficiency and robustness of the proposed method are demonstrated by several examples which are compared to results obtained by the skeleton-based parameterization approach

Exact conversion from Bézier tetrahedra to Bézier hexahedra

International audienceModeling and computing of trivariate parametric volumes is an important research topic in the field of three-dimensional isogeo-metric analysis. In this paper, we propose two kinds of exact conversion approaches from Bézier tetrahedra to Bézier hexahedra with the same degree by reparametrization technique. In the first method, a Bézier tetrahedron is converted into a degenerate Bézier hexahedron, and in the second approach, a non-degenerate Bézier tetrahedron is converted into four non-degenerate Bézier hexahedra. For the proposed methods, explicit formulas are given to compute the control points of the resulting tensor-product Bézier hexahedra. Furthermore, in the second method, we prove that tetrahedral spline solids with C k-continuity can be converted into a set of tensor-product Bézier volumes with G k-continuity. The proposed methods can be used for the volumetric data exchange problems between different trivariate spline representations in CAD/CAE. Several experimental results are presented to show the effectiveness of the proposed methods

An interactive geometry modeling and parametric design platform for isogeometric analysis

In this paper an interactive parametric design-through-analysis platform is proposed to help design engineers and analysts make more effective use of Isogeometric Analysis (IGA) to improve their product design and performance. We develop several Rhinoceros (Rhino) plug-ins to take input design parameters through a user-friendly interface, generate appropriate surface and/or volumetric models, perform mechanical analysis, and visualize the solution fields, all within the same Computer-Aided Design (CAD) program. As part of this effort we propose and implement graphical generative algorithms for IGA model creation and visualization based on Grasshopper, a visual programming interface to Rhino. The developed platform is demonstrated on two structural mechanics examples—an actual wind turbine blade and a model of an integrally bladed rotor (IBR). In the latter example we demonstrate how the Rhino functionality may be utilized to create conforming volumetric models for IGA

Convergence rates with singular parameterizations for solving elliptic boundary value problems in isogeometric analysis

International audienceIn this paper, we present convergence rates for solving elliptic boundary value problems with singular parameterizations in isogeometric analysis. First, the approximation errors with the $L^2(\Omega)$-norm and the $H^1(\Omega)$-seminorm are estimated locally. The impact of singularities is considered in this framework. Second, the convergence rates for solving PDEs with singular parameterizations are discussed. These results are based on a weak solution space that contains all of the weak solutions of elliptic boundary value problems with smooth coefficients. For the smooth weak solutions obtained by isogeometric analysis with singular parameterizations and the finite element method, both are shown to have the optimal convergence rates. For non-smooth weak solutions, the optimal convergence rates are reached by setting proper singularities of a controllable parameterization, even though convergence rates are not optimal by finite element method, and the convergence rates by isogeometric analysis with singular parameterizations are better than the ones by the finite element method

정적 전기장 문제에 대한 형상 최적화 설계

학위논문(석사)--서울대학교 대학원 :공과대학 조선해양공학과,2019. 8. 조선호.The electric field generated by the electrode can be applied in various fields in engineering. In the shipbuilding marine engineering field, electric field analysis is carried out in the process of disinfecting ship ballast water. IMO regulations have made regulations on the quality of ballast water discharged to the oceans more stringent. Therefore, there has been actively studied an electrolysis method capable of sterilizing the ballast water simply and effectively. In order to conduct research in this direction, it is necessary to observe how the shape change of the electrode changes the electric field. It is also possible to find an optimal electrode shape from the tendency. From the governing equation of the electrostatic problem, a weak form for finite element analysis was derived. And from that equation, a continuum-based design sensitivity analysis (DSA) method is developed for electrostatic problem. To consider high order objective function, we use 9-node FEM basis function for analysis and DSA method. Specifying design variables in shape optimization is an important issue. If there are too many design variables, it is likely to result in an optimal shape that cannot be produced. Since design variables are parameterized with B-spline function, we can obtain smooth boundary variations. In addition, the mesh quality may drop sharply due to the shape change of the structure during optimization. To solve mesh entanglement problem in optimization process, mesh regularization scheme is used. By minimizing Dirichlet energy functional, mesh uniformity can be automatically obtained. For verifying our numerical simulation, numerical examples are compared with Comsol software results. The analysis results will be verified by comparison with the Comsol software results, and the change in the sensitivity value will be verified by the Finite Difference Method. The obtained optimal electrode geometry characteristics and optimization histories are specifically discussed. Finally, for the further study, an electrode shape parametric study was performed in 3D environment. This is because optimization in 3D requires too much computation cost to proceed with the simulation. Based on the results obtained through the parametric study, the orientation of electrode shape optimization in the 3D environment is presented.전극에 의해 생성 된 전기장은 공학을 다룸에 있어 다양한 분야에 적용될 수 있다. 조선 해양 공학 분야에서는 선박 평형 수의 소독 과정에서 이용되는 전처리 장치를 하나의 예로 생각할 수 있다. 전처리 장치가 이용되는 연구 배경으로는 최근에 발효된 IMO 규정이 그 원인이다. 새로 발효된 IMO 규정은 해양에 배출되는 밸러스트 수의 품질에 대한 규제를 더욱 엄격하게 만들었다. 따라서, 밸러스트 수를 간단하고 효과적으로 살균 할 수 있는 방법에 대한 연구가 전 세계적으로 활발히 진행되고 있다. 본 연구는 그 중 하나의 방법인 전처리 장치를 이용한 살균 처리법에 주 관심을 두고 있다. 전처리 장치의 효율을 높이는 방법에는 물리적인 방법이나 화학적인 방법, 생물학적인 방법 등 여러 가지 접근법이 존재하지만, 물리적인 방법 중 하나인 전극이 생성한 전기장 분포에 대한 연구는 아직 활발히 이루어지지 않았다. 따라서 본 논문은 전극의 형상 변화가 전기장을 어떻게 변화시키는 지에 대한 경향성 및 최적화 연구를 목표로 두었다. 얻어진 연구 결과로부터 어떤 형상의 전극이 최적의 전기 분해 효율을 가져오는지 알아낼 수 있다. 본 논문은 다음과 같은 내용으로 구성되어있다. 정전기 문제의 지배 방정식으로부터, 유한 요소 해석을 위한 약식(weak form)이 유도되었다. 그리고 그 방정식으로부터 정전기 문제에 대한 연속체 기반 설계 감도 분석 (DSA) 방법이 유도 되었습니다. 이 때, 고차 목적 함수를 고려하기 위한 해석 및 DSA 방법을 위해 9 노드 FEM 기반 함수를 형상 함수로서 사용한다. DSA 방법을 통해 얻어진 민감도 값을 목적 함수에 대한 설계 변수의 경향성으로 생각할 수 있고, 이를 이용해 최적화 연구를 진행한다. 최적화를 진행할 때, 형상 최적화 설계에서 설계 변수를 지정하는 것은 중요한 이슈이다. 설계 변수가 너무 많으면 생산할 수 없는 불규칙한 경계를 가진 최적 형상을 결과로서 제시할 가능성이 있기 때문이다. 이를 방지 하기 위해 설계 변수를 B- 스플라인 함수로 매개 변수화 하였고, 부드러운 경계 변형을 얻어내었다. 또한 최적화 설계의 고질적인 문제로서 매 최적화 시행 마다 구조물의 모양이 변경되어 메쉬 품질이 크게 떨어지는 문제가 있다. 최적화 과정에서 메쉬 얽힘 문제를 해결하기 위해 메쉬 정규화 방법(Mesh regularization scheme)이 사용되었다. 본 방법에서는 디리쉴릿(dirichlet) 에너지 함수를 최소화함으로써 메쉬 균일 성을 자동으로 얻을 수 있다. 연구 결과의 수치 시뮬레이션을 검증하기 위해 수치 예제를 Comsol 소프트웨어 결과와 비교하였다. 해석 결과는 Comsol 소프트웨어 결과와 비교 분석하였고, DSA 방법을 통해 얻어진 민감도 값은 잘 알려진 유한차분법을 통해 검증되었다. 얻어진 민감도 값과 형상 설계 최적화 기법을 이용해 주어진 목적 함수와 제한 조건하에서 최적의 전극 형상을 얻어낸다. 목적함수를 전기 분해 효율과 관련된 값으로 두어 최적 전극 형상의 기하 특성 및 최적화 진행 과정을 구체적으로 논의한다. 마지막으로, 향후 연구를 위해 전극 형태의 파라 메트릭 연구가 3D 환경에서 수행되었다. 3D에서의 형상 설계 최적화를 진행하려면 너무 많은 계산 비용을 필요로 하기 때문에 파라 메트릭 연구를 통해, 전극의 기하 특성과 전기 분해 효율에 대한 경향성연구만을 진행한다. 파라 메트릭 연구를 통해 얻은 결과를 기반으로 3D 환경에서 전극 형상 최적화의 방향을 제시하는 것으로 본 연구를 마무리하였다.1. Introduction 1 2. Finite element analysis of electrostatic problem 5 2.1 Governing equations 5 2.2 Finite element formulation 7 3. Shape design optimization 3.1 Material derivative 9 3.2 Shape sensitivity analysis - direct differentiation method 11 3.3 Shape sensitivity analysis - adjoint variable method 12 4. Shape design optimization techniques in finite element analysis 15 4.1 Design variable parameterization 15 4.2 Mesh regularization scheme 17 5. Numerical examples 21 5.1 Comparison of analysis results with Comsol software 21 5.2 Shape design sensitivity verification 24 5.3 Shape design optimization for 2D electrodes 26 5.4 Parametric study result for 3D electrodes 37 6. Conclusion 51Maste