On curvature approximation in 2D and 3D parameter–free shape optimization

AbstractThere is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an existing design and proposing or ideally generating an optimal design using numerical optimization. In this context, efficient and robust realization of such a framework for numerical shape optimization is of prime importance. Another requirement of such a framework is modularity, such that the shape optimization can involve different physics. This requires that different physics solvers should be handled in black-box nature. The current contribution discusses the conceptualization and applications of a general framework for numerical shape optimization using the vertex morphing parametrization technique. We deal with both 2D and 3D shape optimization problems, of which 3D problems usually tend to be expensive and are candidates for special attention in terms of efficient and high-performance computing. The paper demonstrates the different aspects of the framework, together with the challenges in realizing them. Several numerical examples involving different physics and constraints are presented to show the flexibility and extendability of the framework.

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Density-based shape optimization for fail-safe design

Journal of Computational Design and Engineering ◽

10.1093/jcde/qwaa044 ◽

2020 ◽

Vol 7 (5) ◽

pp. 615-629

Author(s):

Olaf Ambrozkiewicz ◽

Benedikt Kriegesmann

Keyword(s):

Topology Optimization ◽

Shape Optimization ◽

Computational Cost ◽

Current Approach ◽

Element Mesh ◽

Local Volume ◽

Fail Safe ◽

Constraint Approach ◽

2D And 3D ◽

Safe Performance

Abstract This paper presents a two-stage procedure for density-based optimization towards a fail-safe design. Existing approaches either are computationally extremely expensive or do not explicitly consider fail-safe requirements in the optimization. The current approach trades off both aspects by employing two sequential optimizations to deliver redundant designs that offer robustness to partial failure. In the first stage, a common topology optimization or a topology optimization with local volume constraints is performed. The second stage is referred to as “density-based shape optimization” since it only alters the outline of the structure while still acting on a fixed voxel-type finite element mesh with pseudo-densities assigned to each element. The performance gain and computational efficiency of the current approach are demonstrated by application to various 2D and 3D examples. The results show that, in contrast to explicitly enforcing fail-safety in topology optimization, the current approach can be carried out with reasonable computational cost. Compared to the local volume constraint approach, the suggested procedure further increases the fail-safe performance by 47% for the example considered.

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Isogeometric Shape Optimization for Design Dependent Loads

10.1115/detc2021-70224 ◽

2021 ◽

Author(s):

Arkaprabho Pal ◽

Sourav Rakshit

Keyword(s):

Shape Optimization ◽

Optimization Problems ◽

Optimization Approach ◽

Analytical Sensitivity ◽

Control Points ◽

Minimum Compliance ◽

Design Variables ◽

Minimum Compliance Optimization ◽

Design Dependent Loads ◽

2D And 3D

Abstract This paper presents an isogeometric shape optimization approach for a special class of problems in structural optimization known as design dependent load problems. Isogeometric method has been widely used for structural analysis and shape optimization for its advantages in modeling smooth surfaces, high accuracy, local control, and interfacing with CAD tools. Isogeometric method may be of special advantage for shape optimization problems with design dependent loads as the loads in such class of problems depend on the geometry of the designed surface. The method outlined in this paper is applicable to design dependent load problems where there is a pressure load acting on the boundary of the structure, the direction of the pressure being normal to the profile of the designed structure. In this work minimum compliance optimization subject to volume constraint is considered and isogeometric formulations based on NURBS are presented for such class of problems. The control points of the boundaries of the NURBS geometries are taken as the design variables in the optimization problems. Analytical sensitivity formulations are derived for design dependent load problems and compared with numerically derived sensitivities. A few representative 2D and 3D examples are solved and compared with existing literature to demonstrate the application of the proposed method.

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Mesh Quality Preserving Shape Optimization Using Nonlinear Extension Operators

Journal of Optimization Theory and Applications ◽

10.1007/s10957-021-01837-8 ◽

2021 ◽

Vol 189 (1) ◽

pp. 291-316

Author(s):

Sofiya Onyshkevych ◽

Martin Siebenborn

Keyword(s):

Shape Optimization ◽

Numerical Test ◽

Extension Operator ◽

Navier Stokes ◽

Test Cases ◽

Mesh Quality ◽

Major Focus ◽

Nonlinear Advection ◽

High Level ◽

2D And 3D

AbstractIn this article, we propose a shape optimization algorithm which is able to handle large deformations while maintaining a high level of mesh quality. Based on the method of mappings, we introduce a nonlinear extension operator, which links a boundary control to domain deformations, ensuring admissibility of resulting shapes. The major focus is on comparisons between well-established approaches involving linear-elliptic operators for the extension and the effect of additional nonlinear advection on the set of reachable shapes. It is moreover discussed how the computational complexity of the proposed algorithm can be reduced. The benefit of the nonlinearity in the extension operator is substantiated by several numerical test cases of stationary, incompressible Navier–Stokes flows in 2d and 3d.

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Analysis of 2D and 3D defects associated with precipitation of Cu in silicon

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s042482010008866x ◽

1991 ◽

Vol 49 ◽

pp. 870-871

Author(s):

P.M. Rice ◽

MJ. Kim ◽

R.W. Carpenter

Keyword(s):

Colony Growth ◽

Dark Field ◽

Dark Side ◽

Silicide Phase ◽

Strain Fields ◽

Near Surface ◽

Unknown Composition ◽

Secondary Precipitates ◽

20 Nm ◽

2D And 3D

Extrinsic gettering of Cu on near-surface dislocations in Si has been the topic of recent investigation. It was shown that the Cu precipitated hetergeneously on dislocations as Cu silicide along with voids, and also with a secondary planar precipitate of unknown composition. Here we report the results of investigations of the sense of the strain fields about the large (~100 nm) silicide precipitates, and further analysis of the small (~10-20 nm) planar precipitates.Numerous dark field images were analyzed in accordance with Ashby and Brown's criteria for determining the sense of the strain fields about precipitates. While the situation is complicated by the presence of dislocations and secondary precipitates, micrographs like those shown in Fig. 1(a) and 1(b) tend to show anomalously wide strain fields with the dark side on the side of negative g, indicating the strain fields about the silicide precipitates are vacancy in nature. This is in conflict with information reported on the η'' phase (the Cu silicide phase presumed to precipitate within the bulk) whose interstitial strain field is considered responsible for the interstitial Si atoms which cause the bounding dislocation to expand during star colony growth.

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Covalent organic frameworks: an ideal platform for designing ordered materials and advanced applications

Chemical Society Reviews ◽

10.1039/d0cs00620c ◽

2021 ◽

Author(s):

Ruoyang Liu ◽

Ke Tian Tan ◽

Yifan Gong ◽

Yongzhi Chen ◽

Zhuoer Li ◽

...

Keyword(s):

Covalent Organic Frameworks ◽

2D And 3D ◽

Advanced Applications

Covalent organic frameworks offer a molecular platform for integrating organic units into periodically ordered yet extended 2D and 3D polymers to create topologically well-defined polygonal lattices and built-in discrete micropores and/or mesopores.

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