Improvements on a non-invasive, parameter-free approach to inverse form finding

Landkammer, Philipp; Caspari, M. O. B.; Steinmann, Paul

doi:10.1007/s00466-017-1468-2

Cited by 9 publications

(12 citation statements)

References 36 publications

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“…The values at the Gauss points of the adjoining elements of a design node are smoothed to the corresponding nodal value. Various possibilities for this procedure were also examined in [5]. As suggested by a detailed analysis, the superconvergent patch recovery technique as proposed in [11] is eventually used.…”

Section: Description Of An Update Stepmentioning

confidence: 99%

“…Equation 19 is further converted by approximation of the Hessian matrix. Different Quasi-Newton methods, outlined in [5], serve this purpose. Therein, numerical investigations suggest that the use of the Gauss-Newton approximation works most efficient and sufficiently accurate.…”

Section: Description Of An Update Stepmentioning

confidence: 99%

“…The update step is necessarily complemented by a linesearch parameter α which is controlled by Armijo-Backtracking [5] and that ensures a suited update without severe distortion of a single element. Equation 18 includes the first derivative (Jacobian) and the inverse of the second deriva- …”

Section: Description Of An Update Stepmentioning

confidence: 99%

“…Equation 17 represents a global treatment, however we decide to only locally perform the update step of the optimization procedure, so that the new material position of each Table 1 The node-based optimization problem for inverse form finding [5] Objective function…”

Section: Description Of An Update Stepmentioning

confidence: 99%

“…Various enhancements to improve the algorithm in terms of both accuracy and versatility have been presented in [5,6]. The focus of our current work is on the further improvement of its stability and robustness.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A non-invasive node-based form finding approach with discretization-independent target configuration

Caspari

Landkammer

Steinmann

2018

Adv. Model. and Simul. in Eng. Sci.

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Form finding is used to optimize the shape of a semi-finished product, i.e. the material configuration in a forming process. The geometry of the semi-finished product is adapted so that the computed spatial configuration corresponds to a prescribed target spatial configuration. Differences between these two configurations are iteratively minimized. The algorithm works non-invasively, thus there is a strict separation between the form update and the finite element (FE) forming simulation. This separation allows the use of arbitrary commercial FE-solvers. In particular, there is no need for a modification of the FE forming simulation, only the material configuration is iteratively updated. A new method is introduced to calculate the difference between the target and the computed spatial configuration. Thereby the target mesh is separated from the mesh for the FE forming simulation, which enables a more accurate and independent representation of the target configuration. In addition, the possibility of taking into account manufacturing constraints in the optimization process is presented. The procedure is illustrated for the example of the first stage of a novel two-stage sheet-bulk metal forming process.

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Section: Description Of An Update Stepmentioning

confidence: 99%

Section: Description Of An Update Stepmentioning

confidence: 99%

Section: Description Of An Update Stepmentioning

confidence: 99%

Section: Description Of An Update Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A non-invasive node-based form finding approach with discretization-independent target configuration

Caspari

Landkammer

Steinmann

2018

Adv. Model. and Simul. in Eng. Sci.

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A global damping factor for a non‐invasive form finding algorithm

Landkammer

Steinmann

2015

Proc Appl Math and Mech

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Inverse form finding based on the finite element method (FEM) aims in determining the optimal material (undeformed) configuration when knowing the target spatial (deformed) configuration in a discretized setting. The strategy is to iteratively update the material coordinates and recompute the spatial configuration by a FEM simulation until the computed spatial nodal positions are close enough to a priori given spatial nodal positions. A form finding algorithm is utilized, which is purely based on geometrical considerations and can be coupled with arbitrary external FEM software via subroutines in a non-invasive fashion. At large deformations degenerated elements can occur when updating the material coordinates. Evaluating the mesh quality of the updated material configuration and adjusting a global damping factor before recomputing the next spatial configuration helps to avoid mesh distortions.

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