3,390 research outputs found
Curve Skeleton and Moments of Area Supported Beam Parametrization in Multi-Objective Compliance Structural Optimization
This work addresses the end-to-end virtual automation of structural optimization up to the derivation of a parametric geometry model that can be used for application areas such as additive manufacturing or the verification of the structural optimization result with the finite element method.
A holistic design in structural optimization can be achieved with the weighted sum method, which can be automatically parameterized with curve skeletonization and cross-section regression to virtually verify the result and control the local size for additive manufacturing.
is investigated in general. In this paper, a holistic design is understood as a design that considers various compliances as an objective function. This parameterization uses the automated determination of beam parameters by so-called curve skeletonization with subsequent cross-section shape parameter estimation based on moments of area, especially for multi-objective optimized shapes. An essential contribution is the linking of the parameterization with the results of the structural optimization, e.g., to include properties such as boundary conditions, load conditions, sensitivities or even density variables in the curve skeleton parameterization.
The parameterization focuses on guiding the skeletonization based on the information provided by the optimization and the finite element model. In addition, the cross-section detection considers circular, elliptical, and tensor product spline cross-sections that can be applied to various shape descriptors such as convolutional surfaces, subdivision surfaces, or constructive solid geometry. The shape parameters of these cross-sections are estimated using stiffness distributions, moments of area of 2D images, and convolutional neural networks with a tailored loss function to moments of area. Each final geometry is designed by extruding the cross-section along the appropriate curve segment of the beam and joining it to other beams by using only unification operations.
The focus of multi-objective structural optimization considering 1D, 2D and 3D elements is on cases that can be modeled using equations by the Poisson equation and linear elasticity. This enables the development of designs in application areas such as thermal conduction, electrostatics, magnetostatics, potential flow, linear elasticity and diffusion, which can be optimized in combination or individually. Due to the simplicity of the cases defined by the Poisson equation, no experts are required, so that many conceptual designs can be generated and reconstructed by ordinary users with little effort.
Specifically for 1D elements, a element stiffness matrices for tensor product spline cross-sections are derived, which can be used to optimize a variety of lattice structures and automatically convert them into free-form surfaces. For 2D elements, non-local trigonometric interpolation functions are used, which should significantly increase interpretability of the density distribution. To further improve the optimization, a parameter-free mesh deformation is embedded so that the compliances can be further reduced by locally shifting the node positions.
Finally, the proposed end-to-end optimization and parameterization is applied to verify a linear elasto-static optimization result for and to satisfy local size constraint for the manufacturing with selective laser melting of a heat transfer optimization result for a heat sink of a CPU. For the elasto-static case, the parameterization is adjusted until a certain criterion (displacement) is satisfied, while for the heat transfer case, the manufacturing constraints are satisfied by automatically changing the local size with the proposed parameterization. This heat sink is then manufactured without manual adjustment and experimentally validated to limit the temperature of a CPU to a certain level.:TABLE OF CONTENT III
I LIST OF ABBREVIATIONS V
II LIST OF SYMBOLS V
III LIST OF FIGURES XIII
IV LIST OF TABLES XVIII
1. INTRODUCTION 1
1.1 RESEARCH DESIGN AND MOTIVATION 6
1.2 RESEARCH THESES AND CHAPTER OVERVIEW 9
2. PRELIMINARIES OF TOPOLOGY OPTIMIZATION 12
2.1 MATERIAL INTERPOLATION 16
2.2 TOPOLOGY OPTIMIZATION WITH PARAMETER-FREE SHAPE OPTIMIZATION 17
2.3 MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION WITH THE WEIGHTED SUM METHOD 18
3. SIMULTANEOUS SIZE, TOPOLOGY AND PARAMETER-FREE SHAPE OPTIMIZATION OF WIREFRAMES WITH B-SPLINE CROSS-SECTIONS 21
3.1 FUNDAMENTALS IN WIREFRAME OPTIMIZATION 22
3.2 SIZE AND TOPOLOGY OPTIMIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 27
3.3 PARAMETER-FREE SHAPE OPTIMIZATION EMBEDDED IN SIZE OPTIMIZATION 32
3.4 WEIGHTED SUM SIZE AND TOPOLOGY OPTIMIZATION 36
3.5 CROSS-SECTION COMPARISON 39
4. NON-LOCAL TRIGONOMETRIC INTERPOLATION IN TOPOLOGY OPTIMIZATION 41
4.1 FUNDAMENTALS IN MATERIAL INTERPOLATIONS 43
4.2 NON-LOCAL TRIGONOMETRIC SHAPE FUNCTIONS 45
4.3 NON-LOCAL PARAMETER-FREE SHAPE OPTIMIZATION WITH TRIGONOMETRIC SHAPE FUNCTIONS 49
4.4 NON-LOCAL AND PARAMETER-FREE MULTI-OBJECTIVE TOPOLOGY OPTIMIZATION 54
5. FUNDAMENTALS IN SKELETON GUIDED SHAPE PARAMETRIZATION IN TOPOLOGY OPTIMIZATION 58
5.1 SKELETONIZATION IN TOPOLOGY OPTIMIZATION 61
5.2 CROSS-SECTION RECOGNITION FOR IMAGES 66
5.3 SUBDIVISION SURFACES 67
5.4 CONVOLUTIONAL SURFACES WITH META BALL KERNEL 71
5.5 CONSTRUCTIVE SOLID GEOMETRY 73
6. CURVE SKELETON GUIDED BEAM PARAMETRIZATION OF TOPOLOGY OPTIMIZATION RESULTS 75
6.1 FUNDAMENTALS IN SKELETON SUPPORTED RECONSTRUCTION 76
6.2 SUBDIVISION SURFACE PARAMETRIZATION WITH PERIODIC B-SPLINE CROSS-SECTIONS 78
6.3 CURVE SKELETONIZATION TAILORED TO TOPOLOGY OPTIMIZATION WITH PRE-PROCESSING 82
6.4 SURFACE RECONSTRUCTION USING LOCAL STIFFNESS DISTRIBUTION 86
7. CROSS-SECTION SHAPE PARAMETRIZATION FOR PERIODIC B-SPLINES 96
7.1 PRELIMINARIES IN B-SPLINE CONTROL GRID ESTIMATION 97
7.2 CROSS-SECTION EXTRACTION OF 2D IMAGES 101
7.3 TENSOR SPLINE PARAMETRIZATION WITH MOMENTS OF AREA 105
7.4 B-SPLINE PARAMETRIZATION WITH MOMENTS OF AREA GUIDED CONVOLUTIONAL NEURAL NETWORK 110
8. FULLY AUTOMATED COMPLIANCE OPTIMIZATION AND CURVE-SKELETON PARAMETRIZATION FOR A CPU HEAT SINK WITH SIZE CONTROL FOR SLM 115
8.1 AUTOMATED 1D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINED SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 118
8.2 AUTOMATED 2D THERMAL COMPLIANCE MINIMIZATION, CONSTRAINT SURFACE RECONSTRUCTION AND ADDITIVE MANUFACTURING 120
8.3 USING THE HEAT SINK PROTOTYPES COOLING A CPU 123
9. CONCLUSION 127
10. OUTLOOK 131
LITERATURE 133
APPENDIX 147
A PREVIOUS STUDIES 147
B CROSS-SECTION PROPERTIES 149
C CASE STUDIES FOR THE CROSS-SECTION PARAMETRIZATION 155
D EXPERIMENTAL SETUP 15
Integration of geometric modeling and advanced finite element preprocessing
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development
The classical-quantum boundary for correlations: discord and related measures
One of the best signatures of nonclassicality in a quantum system is the
existence of correlations that have no classical counterpart. Different methods
for quantifying the quantum and classical parts of correlations are amongst the
more actively-studied topics of quantum information theory over the past
decade. Entanglement is the most prominent of these correlations, but in many
cases unentangled states exhibit nonclassical behavior too. Thus distinguishing
quantum correlations other than entanglement provides a better division between
the quantum and classical worlds, especially when considering mixed states.
Here we review different notions of classical and quantum correlations
quantified by quantum discord and other related measures. In the first half, we
review the mathematical properties of the measures of quantum correlations,
relate them to each other, and discuss the classical-quantum division that is
common among them. In the second half, we show that the measures identify and
quantify the deviation from classicality in various
quantum-information-processing tasks, quantum thermodynamics, open-system
dynamics, and many-body physics. We show that in many cases quantum
correlations indicate an advantage of quantum methods over classical ones.Comment: Close to the published versio
Geometric Algebra for Optimal Control with Applications in Manipulation Tasks
Many problems in robotics are fundamentally problems of geometry, which lead
to an increased research effort in geometric methods for robotics in recent
years. The results were algorithms using the various frameworks of screw
theory, Lie algebra and dual quaternions. A unification and generalization of
these popular formalisms can be found in geometric algebra. The aim of this
paper is to showcase the capabilities of geometric algebra when applied to
robot manipulation tasks. In particular the modelling of cost functions for
optimal control can be done uniformly across different geometric primitives
leading to a low symbolic complexity of the resulting expressions and a
geometric intuitiveness. We demonstrate the usefulness, simplicity and
computational efficiency of geometric algebra in several experiments using a
Franka Emika robot. The presented algorithms were implemented in c++20 and
resulted in the publicly available library \textit{gafro}. The benchmark shows
faster computation of the kinematics than state-of-the-art robotics libraries.Comment: 16 pages, 13 figures
A curvature-adapted anisotropic surface remeshing method
We present a new method for remeshing surfaces that respect the intrinsic anisotropy of the surfaces. In particular, we use the normal informations of the surfaces, and embed the surfaces into a higher dimensional space (here we use 6d). This allow us to form an isotropic mesh optimization problem in this embedded space. Starting from an initial mesh of a surface, we optimize the mesh by improving the mesh quality measured in the embedded space. The mesh is optimized by combining common local modifications operations, i.e., edge flip, edge contraction, vertex smoothing, and vertex insertion. All operations are applied directly on the 3d surface mesh. This method results a curvature-adapted mesh of the surface. This method can be easily adapted to mesh multi-patches surfaces, i.e., containing corner singularities and sharp features. We present examples of remeshed surfaces from implicit functions and CAD models
Feasible Form Parameter Design of Complex Ship Hull Form Geometry
This thesis introduces a new methodology for robust form parameter design of complex hull form geometry via constraint programming, automatic differentiation, interval arithmetic, and truncated hierarchical B- splines. To date, there has been no clearly stated methodology for assuring consistency of general (equality and inequality) constraints across an entire geometric form parameter ship hull design space. In contrast, the method to be given here can be used to produce guaranteed narrowing of the design space, such that infeasible portions are eliminated. Furthermore, we can guarantee that any set of form parameters generated by our method will be self consistent. It is for this reason that we use the title feasible form parameter design.
In form parameter design, a design space is represented by a tuple of design parameters which are extended in each design space dimension. In this representation, a single feasible design is a consistent set of real valued parameters, one for every component of the design space tuple. Using the methodology to be given here, we pick out designs which consist of consistent parameters, narrowed to any desired precision up to that of the machine, even for equality constraints. Furthermore, the method is developed to enable the generation of complex hull forms using an extension of the basic rules idea to allow for automated generation of rules networks, plus the use of the truncated hierarchical B-splines, a wavelet-adaptive extension of standard B-splines and hierarchical B-splines. The adaptive resolution methods are employed in order to allow an automated program the freedom to generate complex B-spline representations of the geometry in a robust manner across multiple levels of detail. Thus two complementary objectives are pursued: ensuring feasible starting sets of form parameters, and enabling the generation of complex hull form geometry
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