Approximation of derivatives in semi-analytical structural optimization

Bletzinger, K.‐U.; Firl, M.; Daoud, Fernaß

doi:10.1016/j.compstruc.2007.04.014

Cited by 36 publications

(16 citation statements)

References 13 publications

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“…So, to ensure satisfactory mesh quality, the interior nodes must be relocated during the optimization. Many shape optimization methods place the interior nodes in the design set so the optimizer updates all but the fixed surface node coordinates while others update only surface design nodes [49,50,8]. We follow the latter approaches and hence we must relocate the interior nodes to avoid mesh distortion.…”

Section: Interior Node Updatementioning

confidence: 98%

A gradient-based, parameter-free approach to shape optimization

Bruns

Tortorelli

2011

Computer Methods in Applied Mechanics and Engineering

136

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Section: Interior Node Updatementioning

confidence: 98%

A gradient-based, parameter-free approach to shape optimization

Bruns

Tortorelli

2011

Computer Methods in Applied Mechanics and Engineering

136

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“…When using a B-Spline as geometrical model the selected finite elements are the ones affected by the region There is a source of error associated to shape optimisation which increases with mesh refinement. It arises with respect to the rigid body rotation behaviour of the approximated stiffness matrix derivative (37) . The finite elements that are affected are the ones which stiffness depends on different powers of the independent variables as it is the case of elements including bending stiffness (36) .…”

Section: Shape Optimisationmentioning

confidence: 99%

“…The finite elements that are affected are the ones which stiffness depends on different powers of the independent variables as it is the case of elements including bending stiffness (36) . There exist several solutions to the problem (37) . The examples shown later were calculated using central difference approximation of the stiffness matrix.…”

Section: Shape Optimisationmentioning

confidence: 99%

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Shape optimisation in the design of thin-walled shells as components of aerospace structures

Espinoza

Bletzinger

Hörnlein³

et al. 2012

Aeronaut. j. (1968)

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One of the most resent efforts in aircraft design is the replacement of aluminium structures by carbon fibre reinforced polymer composites. Due to lower material and manufacturing costs, doubly curved shapes covering big areas are preferred over simpler surfaces which integrate stiffening profiles. In this context, CAD parameterisation of surfaces allows design solutions by means of classical shape optimisation. Related geometrical parameters are manipulated towards optimal design, generating innovative geometries and detailing.The presented structure is optimised by reducing the overall weight. The final optimum is guided using stability and strength restrictions in order to assure the safety of the component. Geometrical considerations are also included due to operational reasons. A hierarchical design procedure is developed which results in a work flow from preliminary 'parameter-free' form finding motivated by solving the minimal surface problem. The geometrical model for optimisation is recovered by generating B-Spline surface patches to preserve continuity requirements over large regions. The number of geometrical coefficients are defined by the accuracy in surface generation and the required freedom in surface control. The hierarchical approach reduces the possibilities of ending with an unsatisfactory optimum when several local minima characterise the non-linear problem, as it is usually the case in shape optimal design. A geometrical non-linear analysis is used to verify the performance of the optimum.

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“…enhanced strain elements) in existing codes. To avoid the known numerical problems with the semi-analytic approach (Barthelemy and Haftka 1990), the approximation of ∂K ∂ x j is corrected with the exact semi-analytic method as introduced by Bletzinger et al (2008). This method is based on the findings of Cheng and Olhoff (1993) but avoids the need for a different implementation for each element.…”

Section: The Adjoint Exact Semi-analytic Approachmentioning

confidence: 99%

Parameter free shape and thickness optimisation considering stress response

Arnout

Firl

Bletzinger

2011

Struct Multidisc Optim

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In the parameter free approach, FE-based data are used as design variables, such as nodal coordinates and nodal thickness. During shape and thickness optimisation, this approach provides much design freedom for a limited modelling effort. Stress results are, however, very sensitive to the local shape changes that can occur during parameter free optimisation. When stress results are used as response function, this irregularity can complicate the optimisation. As a solution, the Kreisselmeier-Steinhauser function for the stresses is introduced as a response function for parameter free shape optimisation. In this function, the local stress results are aggregated to obtain a global measure of stress in a structure. This measure can be used as an objective to reduce the overall stress in the structure or as a constraint to limit the stress in the structure to a maximum allowable value. As a result, the optimal structures are smooth and material efficient. Several examples are presented in this paper to illustrate the use of the parameter free design approach in combination with the stress response function.

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Approximation of derivatives in semi-analytical structural optimization

Cited by 36 publications

References 13 publications

A gradient-based, parameter-free approach to shape optimization

A gradient-based, parameter-free approach to shape optimization

Shape optimisation in the design of thin-walled shells as components of aerospace structures

Parameter free shape and thickness optimisation considering stress response

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