Optimal shapes of mechanically motivated surfaces

Bletzinger, K.‐U.; Firl, M.; Linhard, Johannes; Wüchner, Roland

doi:10.1016/j.cma.2008.09.009

Cited by 100 publications

(64 citation statements)

References 13 publications

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“…As the number of design control points go up, more complex shapes can be designed. This comes, however, on the cost of numerical challenges, a well-known issue from finite element methods (Bletzinger et al 2010). These challenges, and solution strategies to remedy them, are discussed in this section.…”

Section: Regularizationmentioning

confidence: 99%

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Isogeometric shape optimization in fluid mechanics

Nørtoft

Gravesen

2013

Struct Multidisc Optim

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Document Version Isogeometric Shape Optimization in Fluid MechanicsPeter Nørtoft · Jens Gravesen Abstract The subject of this work is numerical shape optimization in fluid mechanics, based on isogeometric analysis. The generic goal is to design the shape of a 2-dimensional flow domain to minimize some prescribed objective while satisfying given geometric constraints. As part of the design problem, the steady-state, incompressible Navier-Stokes equations, governing a laminar flow in the domain, must be solved. Based on isogeometric analysis, we use B-splines as the basis for both the design optimization and the flow analysis, thereby unifying the models for geometry and analysis, and, at the same time, facilitating a compact representation of complex geometries and smooth approximations of the flow fields. To drive the shape optimization, we use a gradient-based approach, and to avoid inappropriate parametrizations during optimization, we regularize the optimization problem by adding to the objective function a measure of the quality of the boundary parametrization. A detailed description of the methodology is given, and three different numerical examples are considered, through which we investigate the effects of the regularization, of the number of geometric design variables, and of variations in the analysis resolution, initial design and Reynolds number, and thereby demonstrate the robustness of the methodology.

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Section: Regularizationmentioning

confidence: 99%

“…An inherent challenge in numerical shape optimization is to maintain a high quality of the computational mesh as the shape of the domain changes during optimization (Mohammadi and Pironneau 2004;Bletzinger et al 2010). This also applies in an isogeometric approach.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric shape optimization in fluid mechanics

Nørtoft

Gravesen

2013

Struct Multidisc Optim

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“…Here the final form is the direct result of equilibrium and is influenced intensively by the materiality and the boundary condition applied. [8,17,18] (fig 1c)  Topology optimization: The last stream can be resumed under topology and shape optimization problems. These methods combined with evolutionary algorithms, often result in free-form spatial objects, which although have been generated based on a structural criteria, fall into the first category, where they are geometrically approximated in order to be built.…”

Section: Geometry Of Space Structures: a Survey On "Form-element" Reamentioning

confidence: 99%

“…These methods combined with evolutionary algorithms, often result in free-form spatial objects, which although have been generated based on a structural criteria, fall into the first category, where they are geometrically approximated in order to be built. [1](b) Free-form design and panelling approximation [2](c) Equilibrium forms either in tension or compression [8](d) Free-form obtained from a topology optimization process [10] In fact, according to the free-form design, it starts generally with a "complex form" which ends up with multiple typologies of elements in a top-bottom process, and "complex connection technologies", where structural elements follow offsets of the external form. Indeed, we ask the question whether the same free-form practice should be followed in context of timber construction.…”

Section: Geometry Of Space Structures: a Survey On "Form-element" Reamentioning

confidence: 99%

Geometrical Description and Structural Analysis of a Modular Timber Structure

Nabaei

Weinand

2011

International Journal of Space Structures

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SummaryThe ambitious goal of the ongoing research at IBOIS, the Laboratory of timber constructions at the Ecole Polytechnique Fédérale de Lausanne (EPFL) is to develop a next generation of timber constructions made out of innovative timber-derived products, through applying textile principles on the building scale. The presented structure is a modular composition of timber folded panels, notably demonstrates an example of applying the geometric techniques used to produce modular patterns and lattices to timber construction context. Effectively, it is shown that complex space structures can be designed using simple connection technology between elements. Moreover, by taking advantage of advanced CAM process, complex planar timber elements are cut in large scale and assembled with high precision as for the prototype of the structure presented in this paper. The folding concept corresponds to a planar reciprocal frame structure. The basic module is consisted of two mutually supporting timber folded panels which are slipped in, consecutively, along their cuts, to build up an arch. The inter-module connection's stability is provided by contact boundary condition over the slide joints. The fundamental mechanical properties of the structure are examined using Finite Element Method and considering the non-linear contact boundary condition. The static behavior is studied under the self-weight load case as well as the modal dynamic response. According to analysis results, and by aid of a CAD parametric model, structural and geometrical alternatives are proposed to improve the structural performance. A prototype based on this geometric principal has been fabricated and assembled to explore feasibility of the concept in the building scale.

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“…In general, the underlying mechanical statement for the computation of prestressed surfaces is the demand for equilibrium, which resembles the geometrical explanation of minimizing the area content in the case of isotropic prestress fields [3,5,6,9]. The latter fact is the conclusion of the well-known soap film analogy.…”

Section: Introduction: Plateau's Problem and Its Numerical Solutionmentioning

confidence: 99%

Plateau regularization method for structural shape optimization and geometric mesh control

Wüchner

Firl

Linhard

et al. 2008

Proc Appl Math and Mech

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Within this contribution the algorithmic treatment of the inverse problem of finding mechanically motivated membrane shapes is discussed and the key point, that the corresponding numerical methods have a broader spectrum of applications which enables their adoption to similar problems from other disciplines, is highlighted. The presented adaptive scheme is the Updated Reference Strategy (URS) enhanced by a newly derived "element distortion control". The key feature is the ability of the proposed stabilized scheme to overcome the singular problem of finding equilibrium shapes of prestressed membranes which is due to the non-uniqueness of nodal positions in the finite element mesh and the purposeful adjustment of the underlying stress state based on a local geometrical criterion in case of incompatible stress states. Therefore, the derived methodology is -beside the mere computation of equilibrium configurations-able to distribute (probably very local) deformations of the mesh in a smooth way to the whole domain by at the same time conserving specific mesh characteristics which guarantees regular meshes with high quality concerning the element shape. This results in robust computations even for complex and problematic geometrical situations. Due to the effective mesh control of this approach a transfer of the developed methodology to other fields of application like e.g. mesh smoothing, large displacement mesh moving problems and stabilized CAD-free shape optimization of shells is promising and therefore accomplished.

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Optimal shapes of mechanically motivated surfaces

Cited by 100 publications

References 13 publications

Isogeometric shape optimization in fluid mechanics

Isogeometric shape optimization in fluid mechanics

Geometrical Description and Structural Analysis of a Modular Timber Structure

Plateau regularization method for structural shape optimization and geometric mesh control

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