390 research outputs found
CAD-CAE integration and isogeometric analysis: trivariate multipatch and applications
This PhD thesis is focused on the issues related to one of the critical steps during the lifecycle of a product design and manufacturing process: the transition between the geometrical and functional definition of a product, and the virtual prototyping with numerical simulations, also known as CAD (Computer-Aided Design) / CAE (Computer-Aided Engineering) transition.
The isogeometric methodologies developed by Hughes et Al. [1, 2] has the ambition to close the gap in CAD/CAE integration, allowing the two environments to underlay on the same framework, taking advantage of the isoparametric concept, widely used in Finite Elements world, coupled with the Non-Uniform Rational B-Splines (NURBS) that are a standard in CAD systems in the mathematical representation of geometries.
Even though the first paper was published 10 years ago, the method is not yet used in industrial applications and only few commercial software are able to handle isogeometric elements.
In this thesis a step towards the possibility of application in industry by developing a multi-patch coupling method where the geometry at the interface does not allow a compatible mesh.
This improvement opens new frontiers for applications in both static and dynamic solutions.
Another issue that is analysed in this thesis is the possibility to improve the geometry-to-analysis integration by conversion of the information that comes from CAD software, in terms of representation of the external surfaces, to solid information that is necessary to be suitable for a structural simulation
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
๊ธฐํํ์ ์ผ๋ก ์ ๋ฐํ ๋น์ ํ ๊ตฌ์กฐ๋ฌผ์ ์์ด์-์ง์ค๋ฉํธ๋ฆญ ํ์ ์ค๊ณ ๋ฏผ๊ฐ๋ ํด์
ํ์๋
ผ๋ฌธ (๋ฐ์ฌ)-- ์์ธ๋ํ๊ต ๋ํ์ : ๊ณต๊ณผ๋ํ ์กฐ์ ํด์๊ณตํ๊ณผ, 2019. 2. ์กฐ์ ํธ.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.๋ณธ ์ฐ๊ตฌ์์๋ ๋๋ณํ์ ๊ณ ๋ คํ ํ์ด์ง ์กฐ๋ฆฝ ๊ตฌ์กฐ๋ฌผ์ ์ฐ์์ฒด ๊ธฐ๋ฐ ํด์์ ์ ์กฐ์ธ ํ์ ์ค๊ณ ๋ฏผ๊ฐ๋ ํด์ ๊ธฐ๋ฒ์ ๊ฐ๋ฐํ์๋ค. ํ๋ฉด Timoshenko ๋น์ ์ ํํ๋ ๋ณํ๋ฅ ์ invariance ํน์ฑ์ ๊ณ ์ฐฐํ์๊ณ invariant ์ ์ํ๋ฅผ ์ ํ์ ์ถ์์ ๋ถ(selective reduced integration) ๊ธฐ๋ฒ ๋ฐ B-bar projection ๊ธฐ๋ฒ๊ณผ ๊ฒฐํฉํ์ฌ shear ๋ฐ membrane ์ ๊น ํ์์ ํด์ํ์๋ค. ๋น์ ํ ๊ตฌ์กฐ ๋ชจ๋ธ๋ก์ ๊ธฐํํ์ ์ผ๋ก ์ ๋ฐํ ๋น ๋ฐ ์ ๋ชจ๋ธ์ ํ์ฉํ์๋ค. ํ๋ฉด Kirchhoff ๋น ๋ชจ๋ธ์ NURBS ๊ธฐ์ ํจ์์ ๊ณ ์ฐจ ์ฐ์์ฑ์ ๋ฐ๋ฅธ ์์ด์-์ง์ค๋ฉํธ๋ฆญ ํด์ ๊ธฐ๋ฐ rotation-free ์ด์ฐํ๋ฅผ ํ์ฉํ์ฌ ๋ค๋ฃจ์์ผ๋ฉฐ, ๊ธฐ์กด์ Hermite ๊ธฐ์ ํจ์ ๊ธฐ๋ฐ์ ์ ํ์์๋ฒ์ ๋นํด ์์ ๋๋น ํด์ ์ ํ๋๊ฐ ๋์์ ๊ฒ์ฆํ์๋ค. ๋ผ๊ทธ๋์ง ์น์๋ฒ ๋ฐ ๋ฒ์น ๊ธฐ๋ฒ์ ๋์
ํ์ฌ ํ์ ์ ์ฐ์์ฑ์ ํฌํจํ ๋ค์ํ ๋ค์คํจ์น๊ฐ ์ฐ์ ์กฐ๊ฑด์ ๊ณ ๋ คํ์๋ค. ์ด๋ฌํ ๊ธฐ๋ฒ์ ํ์ํ์ (phenomenological) ํ์๊ธฐ์ตํด๋ฆฌ๋จธ (SMP) ์ฌ๋ฃ ๊ตฌ์ฑ๋ฐฉ์ ์๊ณผ ๊ฒฐํฉํ์ฌ ํ์์ ํ๋ก๊ทธ๋๋ฐ๊ณผ ํ๋ณต ๊ณผ์ ์ ์๋ฎฌ๋ ์ด์
ํ์๋ค. ์ ๋จ๋ณํ์ ๊ฒช๋ (shear-deformable) ๊ตฌ์กฐ ๋ชจ๋ธ์ ๋ํ์ฌ ๋ํ์ ์ ๊ฐฑ์ ์ ๊ต๋ ํ๋ ฌ์ exponential map์ ์ํ ๊ณฑ์ ํํ๋ก ์ํํ์๋ค. ๊ณต๊ฐ์์ ๊ณก์ ๋ชจ๋ธ์์ ์ต์ํ์ (smallest rotation) ๊ธฐ๋ฒ์ ํตํด ๊ตญ์ ์ ๊ท์ง๊ต์ขํ๊ณ์ ๋ช
์์ ๋งค๊ฐํ๋ฅผ ์ํํ์๋ค. ํ์ ์ค๊ณ ๋ฏผ๊ฐ๋ ํด์์ ์ํ์ฌ ์ ๋ฏธ๋ถ์ ๋ณ๋ถ ๋ฐฉ์ ์์ ์ ์ฉํ์์ผ๋ฉฐ ํ์ด์ง ๊ตฌ์กฐ๋ฌผ์ ๋ฐฐํฅ ์ค๊ณ ๋ณํ๋ ๊ตญ์ ์ ๊ท์ง๊ต์ขํ๊ณ์ ํ์ ์ ์ํ์ฌ ๊ธฐ์ ๋๋ค. ์ต์ข
๋ณํ ํ์์์ ์ง๊ต ๋ณํ ํ๋ ฌ์ ์ ๋ฏธ๋ถ์ ๊ณ์ฐํจ์ผ๋ก์จ ๋ํ์ ๋ฌธ์ ์์ ์ถ๊ฐ์ ์ธ ๋ฐ๋ณต ๊ณ์ฐ์์ด ๋ณํ ํด์์์์ ์ ์ ๊ฐ์ฑํ๋ ฌ์ ์ํด ํด์์ ์ค๊ณ ๋ฏผ๊ฐ๋๋ฅผ ๊ณ์ฐํ ์ ์๋ค. ์ ๊ตฌ์กฐ๋ฌผ์ ๊ฒฝ์ฐ ๋ฉด๋ด ํ์ ์์ ๋ ๋ฐ ์์ ํ๋ ๋ณ๋ถ ๋ฐฉ์ ์์ ํ์ฉํ์ฌ ๋ณด๊ฐ์ฌ(stiffener)์ ๋ชจ๋ธ๋ง์ ์ฉ์ดํ๊ฒ ํ์๋ค. ๋ํ ๋ณธ ์ฐ๊ตฌ์์๋ ํ์ด์ง ์์ญ์ ๊ตฌ์๋์ด์๋ ๊ตฌ์กฐ๋ฌผ์ ๋ํ ์ค๊ณ ์๋์ฅ ๊ณ์ฐ ๋ฐ ์ต์ ์ค๊ณ๊ธฐ๋ฒ์ ์ ์ํ๋ฉฐ ํนํ ๊ณก๋ฉด์ ๊ตฌ์๋ ๋น ๊ตฌ์กฐ๋ฌผ์ ์ค๊ณ๋ฅผ ์ง์ค์ ์ผ๋ก ๋ค๋ฃฌ๋ค. ์์ ํ์๋ณํ(Free-form deformation)๊ธฐ๋ฒ๊ณผ ์ ์ญ ๊ณก์ ๋ณด๊ฐ๊ธฐ๋ฒ์ ํ์ฉํ์ฌ ์ง์ฌ๊ฐ ํ๋ฉด์์ ํ์ ๋ฐ ์ค๊ณ ๋ณ์๋ฅผ ์ ์ํ๊ณ ๊ณก๋ฉด์์ ๊ณก์ ํ์์ ๋ํ๋ด๋ ์กฐ์ ์ ์์น๋ฅผ ํด์์ ์ผ๋ก ํํํ ์ ์์ผ๋ฉฐ ์ด์ ์ ๋ฏธ๋ถ์ ํตํด ์ ํํ ์ค๊ณ์๋์ฅ์ ๊ณ์ฐํ๋ค. ์ด๋ฅผ ํตํด ์ค๊ณ ๋ณ์์ ๊ฐ์๋ฅผ ์ค์ผ ์ ์๊ณ ์ค๊ณ์ ๋งค๊ฐํ๊ฐ ๊ฐํธํด์ง๋ค. ๊ฐ๋ฐ๋ ๋ฐฉ๋ฒ๋ก ์ ๋ค์ํ ํ์ค ๋ฐ ์ด๋ํ์ ๊ฒฝ๊ณ์กฐ๊ฑด์ ๊ฐ๋ ๋น๊ณผ ์์ ๋๋ณํ ๋ฌธ์ ๋ฅผ ํตํด ๊ฒ์ฆ๋๋ฉฐ ์ฌ๋ฌ๊ฐ์ง ํ์ด์ง ์กฐ๋ฆฝ ๊ตฌ์กฐ๋ฌผ์ ์ต์ ์ค๊ณ์ ์ ์ฉ๋๋ค. ๋ํ์ ์ผ๋ก, ์ ๋จ ๊ฐ์ฑ ๋ฐ ์ถฉ๊ฒฉ ํก์ ํน์ฑ๊ณผ ๊ฐ์ ๊ธฐ๊ณ์ ๋ฌผ์ฑ์น์ ๊ฐ์ ์ ์ํด ํ์ฉ๋๋ ์ค๊ทธ์ ํฑ (auxetic) ํน์ฑ์ด ๊ทน๋ํ๋ ๊ฒฉ์ ๊ตฌ์กฐ๋ฅผ ์ค๊ณํ๋ฉฐ ์ธ์ฅ ๋ฐ ์์ถ ๋๋ณํ ๋ชจ๋์์ ์ผ์ ํ ์์ ํฌ์์ก๋น๋ฅผ ๋ํ๋์ 3์ฐจ์ ํ๋ฆฐํ
๊ณผ ๊ดํ์ ๋ณํ ์ธก์ ๊ธฐ์ ์ ์ด์ฉํ์ฌ ์คํ์ ์ผ๋ก ๊ฒ์ฆํ๋ค. ๋ํ ์ฐ๋ฆฌ๋ ์์์ ์ ๊ฐ์ ์ํด ํ์ฉ๋๋ ๊ฐ์ฒญ ์ ์ฃผํ์ ์์ญ๋์์์ ๋ฐด๋๊ฐญ์ด ๊ทน๋ํ๋ ๊ฒฉ์ ๊ตฌ์กฐ๋ฅผ ์ ์ํ๋ค.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
์ด๋กDocto
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Smooth quasi-developable surfaces bounded by smooth curves
Computing a quasi-developable strip surface bounded by design curves finds
wide industrial applications. Existing methods compute discrete surfaces
composed of developable lines connecting sampling points on input curves which
are not adequate for generating smooth quasi-developable surfaces. We propose
the first method which is capable of exploring the full solution space of
continuous input curves to compute a smooth quasi-developable ruled surface
with as large developability as possible. The resulting surface is exactly
bounded by the input smooth curves and is guaranteed to have no
self-intersections. The main contribution is a variational approach to compute
a continuous mapping of parameters of input curves by minimizing a function
evaluating surface developability. Moreover, we also present an algorithm to
represent a resulting surface as a B-spline surface when input curves are
B-spline curves.Comment: 18 page
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
Powell-Sabin B-splines and unstructured standard T-splines for the solution of the Kirchhoff-Love plate theory exploiting Bรฉzier extraction
The equations that govern KirchhoffโLove plate theory are solved using quadratic PowellโSabin B-splines and unstructured standard T-splines. Bรฉzier extraction is exploited to make the formulation computationally efficient. Because quadratic PowellโSabin B-splines result in inline image-continuous shape functions, they are of sufficiently high continuity to capture KirchhoffโLove plate theory when cast in a weak form. Unlike non-uniform rational B-splines (NURBS), which are commonly used in isogeometric analysis, PowellโSabin B-splines do not necessarily capture the geometry exactly. However, the fact that they are defined on triangles instead of on quadrilaterals increases their flexibility in meshing and can make them competitive with respect to NURBS, as no bending strip method for joined NURBS patches is needed. This paper further illustrates how unstructured T-splines can be modified such that they are inline image-continuous around extraordinary points, and that the blending functions fulfil the partition of unity property. The performance of quadratic NURBS, unstructured T-splines, PowellโSabin B-splines and NURBS-to-NURPS (non-uniform rational PowellโSabin B-splines, which are obtained by a transformation from a NURBS patch) is compared in a study of a circular plat
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