Iterative surface warping to shape craters in micro-EDM simulation

This paper introduces a new method for simulating the micro-EDM process in order to predict both the tool’s wear and the workpiece’s roughness. The tool and workpiece are defined by NURBS patches whose shapes result from an iterative crater-by-crater deformation technique driven by physical parameters. Through hundreds of thousands of local surface warping, the method is able to compute the global as well as the local shapes of the tool and workpiece. At each step, the warping vector and function are computed so as to be able to generate a spherical crater whose volume is also controlled. While acting very locally to simulate the real physical phenomenon, not only the method can evaluate the tool’s wear from the overall final shape at a low resolution level, but it can also estimate the workpiece’s roughness from the high resolution level. The simulation method is validated through a comparison with experimental data. Different simulations are presented with an increase in computation accuracy in order to study its influence on the results and their deviation from expected values

Iterative surface warping to shape craters in micro‐EDM simulation

This paper introduces a new method for simulat- ing the micro-EDM process in order to predict both the tool’s wear and the workpiece’s roughness. The tool and workpiece are de ned by NURBS patches whose shapes result from an iterative crater-by-crater deformation technique driven by physical parameters. Through hundreds of thousands of local surface warping, the method is able to compute the global as well as the local shapes of the tool and workpiece. At each step, the warping vector and function are computed so as to be able to generate a spherical crater whose volume is also controlled. While acting very locally to simulate the real physical phenomenon, not only the method can evaluate the tool’s wear from the overall nal shape at a low resolu- tion level, but it can also estimate the workpiece’s roughness from the high resolution level. The simulation method is validated through a comparison with experimental data. Dif- ferent simulations are presented with an increase in compu- tation accuracy in order to study its in uence on the results and their deviation from expected values

Fast character modeling with sketch-based PDE surfaces

© 2020, The Author(s). Virtual characters are 3D geometric models of characters. They have a lot of applications in multimedia. In this paper, we propose a new physics-based deformation method and efficient character modelling framework for creation of detailed 3D virtual character models. Our proposed physics-based deformation method uses PDE surfaces. Here PDE is the abbreviation of Partial Differential Equation, and PDE surfaces are defined as sculpting force-driven shape representations of interpolation surfaces. Interpolation surfaces are obtained by interpolating key cross-section profile curves and the sculpting force-driven shape representation uses an analytical solution to a vector-valued partial differential equation involving sculpting forces to quickly obtain deformed shapes. Our proposed character modelling framework consists of global modeling and local modeling. The global modeling is also called model building, which is a process of creating a whole character model quickly with sketch-guided and template-based modeling techniques. The local modeling produces local details efficiently to improve the realism of the created character model with four shape manipulation techniques. The sketch-guided global modeling generates a character model from three different levels of sketched profile curves called primary, secondary and key cross-section curves in three orthographic views. The template-based global modeling obtains a new character model by deforming a template model to match the three different levels of profile curves. Four shape manipulation techniques for local modeling are investigated and integrated into the new modelling framework. They include: partial differential equation-based shape manipulation, generalized elliptic curve-driven shape manipulation, sketch assisted shape manipulation, and template-based shape manipulation. These new local modeling techniques have both global and local shape control functions and are efficient in local shape manipulation. The final character models are represented with a collection of surfaces, which are modeled with two types of geometric entities: generalized elliptic curves (GECs) and partial differential equation-based surfaces. Our experiments indicate that the proposed modeling approach can build detailed and realistic character models easily and quickly

Processing free form objects within a Product Development Process framework

The purpose of the chapter is then to review: (1) the stages of a product development pro- cess (PDP) where free-form shapes appear and are subjected to aesthetic and functional require- ments; (2) the modeling, sketching, and modification activities illustrating how free-form surfaces can be processed and what are the corresponding difficulties faced during these tasks; (3) the con- tributions of our community to solve some of these issues, and the problems which are still open

Adaptive parameterization for Aerodynamic Shape Optimization in Aeronautical Applications

Cílem mé disertační práce je analyzovat a vyvinout parametrizační metodu pro 2D a 3D tvarové optimalizace v kontextu průmyslového aerodynamického návrhu letounu založeném na CFD simulacích. Aerodynamická tvarová optimalizace je efektivní nástroj, který si klade za cíl snížení nákladů na návrh letounů. Nástroj založený na automatickém hledání optimálního tvaru. Klíčovou částí úspěšného optimalizačního procesu je použití vhodné parametrizační metody, metody schopné garantovat možnost dosažení optimálního tvaru. Parametrizační metody obecně používané v oblasti aerodynamické tvarové optimalizace momentálně nejsou připravený na komplikované průmyslové aplikace vyskytující se u moderních dopravních letounů, které mají šípová zalomená křídla s winglety a motorovými gondolami, přechodové prvky spojující např. trup s křídlem atd.. Existuje tedy potřeba nalezení obecné parametrizační metody, která bude aplikovatelná na širokou škálu různých geometrických tvarů. Free-Form Deformation (FFD[1]) parametrizace může, vzhledem ke svým schopnostem při zacházení s geometrií, být odpovědí na tuto potřebu. Adaptivní parametrizace by se měla být schopna automaticky přizpůsobit danému tvaru tak, aby byly její kontrolní body vhodně rozmístěny. Což umožní dostatečnou kontrolu deformací objektu, která zaručí možnost vytvoření optimálního tvaru objektu a splnění geometrických omezení. Primární aplikací takové parametrizační metody je deformace tvaru objektu. Dalším navrhovaným cílem je modifikace FFD parametrizační metody pro současné deformace tvaru objektu a CFD výpočetní sítě, umožnující velké deformace objektu při zachování kvality výpočetní sítě.The goal of this doctoral thesis is to analyze and develop parameterization algorithms for 2D and 3D shape optimization in the context of industrial aircraft aerodynamic design based on simulations with CFD. Aerodynamic shape optimization is an efficient tool that aims at reducing the cost of the process of aircraft design. A tool that is based on automatization of the search for the optimum shape. Key part of successful aerodynamic shape optimization is the use of appropriate parameterization method, a method that should guarantee the possibility of reaching optimum shape. The parameterization methods used in aerodynamic shape optimizations are still not ready for complex industrial applications, which are present on modern passenger aircrafts with swept cranked wings with winglets and engine pylons, fuselage-wing interactions etc. So there is a need for general parameterization method that applies on wide variety of different geometries.The Free-Form Deformation (FFD[1]) parameterization can, thanks to its geometry handling qualities, be the answer to this need. Adaptive parameterization should automatically modify parameterization grid (lattice) to get appropriate lattice in regions of interest. Such that will allow sufficient control of deformations of the object with respect to reaching optimum shape and fulfilling optimization constraints. First application is in the surface deformation. The other proposed goal is development of the FFD parameterization that can do both surface deformations and CFD mesh deformations, while enabling large object deformations and preserving the level of mesh quality during the process.

기하학적으로 정밀한 비선형 구조물의 아이소-지오메트릭 형상 설계 민감도 해석

학위논문 (박사)-- 서울대학교 대학원 : 공과대학 조선해양공학과, 2019. 2. 조선호.In this thesis, a continuum-based analytical adjoint configuration design sensitivity analysis (DSA) method is developed for gradient-based optimal design of curved built-up structures undergoing finite deformations. First, we investigate basic invariance property of linearized strain measures of a planar Timoshenko beam model which is combined with the selective reduced integration and B-bar projection method to alleviate shear and membrane locking. For a nonlinear structural analysis, geometrically exact beam and shell structural models are basically employed. A planar Kirchhoff beam problem is solved using the rotation-free discretization capability of isogeometric analysis (IGA) due to higher order continuity of NURBS basis function whose superior per-DOF(degree-of-freedom) accuracy over the conventional finite element analysis using Hermite basis function is verified. Various inter-patch continuity conditions including rotation continuity are enforced using Lagrage multiplier and penalty methods. This formulation is combined with a phenomenological constitutive model of shape memory polymer (SMP), and shape programming and recovery processes of SMP structures are simulated. Furthermore, for shear-deformable structures, a multiplicative update of finite rotations by an exponential map of a skew-symmetric matrix is employed. A procedure of explicit parameterization of local orthonormal frames in a spatial curve is presented using the smallest rotation method within the IGA framework. In the configuration DSA, the material derivative is applied to a variational equation, and an orientation design variation of curved structure is identified as a change of embedded local orthonormal frames. In a shell model, we use a regularized variational equation with a drilling rotational DOF. The material derivative of the orthogonal transformation matrix can be evaluated at final equilibrium configuration, which enables to compute design sensitivity using the tangent stiffness at the equilibrium without further iterations. A design optimization method for a constrained structure in a curved domain is also developed, which focuses on a lattice structure design on a specified surface. We define a lattice structure and its design variables on a rectangular plane, and utilize a concept of free-form deformation and a global curve interpolation to obtain an analytical expression for the control net of the structure on curved surface. The material derivative of the analytical expression eventually leads to precise design velocity field. Using this method, the number of design variables is reduced and design parameterization becomes more straightforward. In demonstrative examples, we verify the developed analytical adjoint DSA method in beam and shell structural problems undergoing finite deformations with various kinematic and force boundary conditions. The method is also applied to practical optimal design problems of curved built-up structures. For example, we extremize auxeticity of lattice structures, and experimentally verify nearly constant negative Poisson's ratio during large tensile and compressive deformations by using the 3-D printing and optical deformation measurement technologies. Also, we architect phononic band gap structures having significantly large band gap for mitigating noise in low audible frequency ranges.본 연구에서는 대변형을 고려한 휘어진 조립 구조물의 연속체 기반 해석적 애조인 형상 설계 민감도 해석 기법을 개발하였다. 평면 Timoshenko 빔의 선형화된 변형률의 invariance 특성을 고찰하였고 invariant 정식화를 선택적 축소적분(selective reduced integration) 기법 및 B-bar projection 기법과 결합하여 shear 및 membrane 잠김 현상을 해소하였다. 비선형 구조 모델로서 기하학적으로 정밀한 빔 및 쉘 모델을 활용하였다. 평면 Kirchhoff 빔 모델을 NURBS 기저함수의 고차 연속성에 따른 아이소-지오메트릭 해석 기반 rotation-free 이산화를 활용하여 다루었으며, 기존의 Hermite 기저함수 기반의 유한요소법에 비해 자유도당 해의 정확도가 높음을 검증하였다. 라그랑지 승수법 및 벌칙 기법을 도입하여 회전의 연속성을 포함한 다양한 다중패치간 연속 조건을 고려하였다. 이러한 기법을 현상학적 (phenomenological) 형상기억폴리머 (SMP) 재료 구성방정식과 결합하여 형상의 프로그래밍과 회복 과정을 시뮬레이션하였다. 전단변형을 겪는 (shear-deformable) 구조 모델에 대하여 대회전의 갱신을 교대 행렬의 exponential map에 의한 곱의 형태로 수행하였다. 공간상의 곡선 모델에서 최소회전 (smallest rotation) 기법을 통해 국소 정규직교좌표계의 명시적 매개화를 수행하였다. 형상 설계 민감도 해석을 위하여 전미분을 변분 방정식에 적용하였으며 휘어진 구조물의 배향 설계 변화는 국소 정규직교좌표계의 회전에 의하여 기술된다. 최종 변형 형상에서 직교 변환 행렬의 전미분을 계산함으로써 대회전 문제에서 추가적인 반복 계산없이 변형 해석에서의 접선강성행렬에 의해 해석적 설계 민감도를 계산할 수 있다. 쉘 구조물의 경우 면내 회전 자유도 및 안정화된 변분 방정식을 활용하여 보강재(stiffener)의 모델링을 용이하게 하였다. 또한 본 연구에서는 휘어진 영역에 구속되어있는 구조물에 대한 설계 속도장 계산 및 최적 설계기법을 제안하며 특히 곡면에 구속된 빔 구조물의 설계를 집중적으로 다룬다. 자유형상변형(Free-form deformation)기법과 전역 곡선 보간기법을 활용하여 직사각 평면에서 형상 및 설계 변수를 정의하고 곡면상의 곡선 형상을 나타내는 조정점 위치를 해석적으로 표현할 수 있으며 이의 전미분을 통해 정확한 설계속도장을 계산한다. 이를 통해 설계 변수의 개수를 줄일 수 있고 설계의 매개화가 간편해진다. 개발된 방법론은 다양한 하중 및 운동학적 경계조건을 갖는 빔과 쉘의 대변형 문제를 통해 검증되며 여러가지 휘어진 조립 구조물의 최적 설계에 적용된다. 대표적으로, 전단 강성 및 충격 흡수 특성과 같은 기계적 물성치의 개선을 위해 활용되는 오그제틱 (auxetic) 특성이 극대화된 격자 구조를 설계하며 인장 및 압축 대변형 모두에서 일정한 음의 포아송비를 나타냄을 3차원 프린팅과 광학적 변형 측정 기술을 이용하여 실험적으로 검증한다. 또한 우리는 소음의 저감을 위해 활용되는 가청 저주파수 영역대에서의 밴드갭이 극대화된 격자 구조를 제시한다.Abstract 1. Introduction 2. Isogeometric analysis of geometrically exact nonlinear structures 3. Isogeometric confinguration DSA of geometrically exact nonlinear structures 4. Numerical examples 5. Conclusions and future works A. Supplements to the geometrically exact Kirchhoff beam model B. Supplements to the geometrically exact shear-deformable beam model C. Supplements to the geometrically exact shear-deformable shell model D. Supplements to the invariant formulations E. Supplements to the geometric constraints in design optimization F. Supplements to the design of auxetic structures 초록Docto

Review of research in feature-based design

Research in feature-based design is reviewed. Feature-based design is regarded as a key factor towards CAD/CAPP integration from a process planning point of view. From a design point of view, feature-based design offers possibilities for supporting the design process better than current CAD systems do. The evolution of feature definitions is briefly discussed. Features and their role in the design process and as representatives of design-objects and design-object knowledge are discussed. The main research issues related to feature-based design are outlined. These are: feature representation, features and tolerances, feature validation, multiple viewpoints towards features, features and standardization, and features and languages. An overview of some academic feature-based design systems is provided. Future research issues in feature-based design are outlined. The conclusion is that feature-based design is still in its infancy, and that more research is needed for a better support of the design process and better integration with manufacturing, although major advances have already been made

Towards a better integration of modelers and black box constraint solvers within the Product Design Process

This paper presents a new way of interaction between modelers and solvers to support the Product Development Process (PDP). The proposed approach extends the functionalities and the power of the solvers by taking into account procedural constraints. A procedural constraint requires calling a procedure or a function of the modeler. This procedure performs a series of actions and geometric computations in a certain order. The modeler calls the solver for solving a main problem, the solver calls the modeler’s procedures, and similarly procedures of the modeler can call the solver for solving sub-problems. The features, specificities, advantages and drawbacks of the proposed approach are presented and discussed. Several examples are also provided to illustrate this approach