Yet another parameter-free shape optimization method

Swartz, Kenneth E.; Mittal, Ketan; Schmidt, Mathias; Barrera, Jorge-Luis; Watts, Seth; Tortorelli, Daniel A.

doi:10.1007/s00158-023-03684-9

Cited by 6 publications

(3 citation statements)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 1. Furthermore, the shape optimization method parameterizes the topology, preserving shape changes as described in [55]. Note that despite this manuscript focusing on LC phases, the design parameterization can be formulated such that it appropriately simulates cholesteric (i.e., chiral nematic) or blue (double twist cylinders packed in cubic lattices) phases.…”

Section: Design Parameterizationmentioning

confidence: 99%

“…To formulate a well-posed optimization problem, the design fields are filtered to prevent highly oscillatory orientations and complex shapes [55,56]. Thus, we optimize the parameters p, but we model the structure using the filtered parameters p that define the filtered orientation ñ and shape perturbations ∆X.…”

Section: Design Parameterizationmentioning

confidence: 99%

“…Here , Γ ∆X D represents the surface where the Dirichlet conditions are applied for the shape parameters. For shape optimization, ∆X is interpolated from the nodal values via the usual Lagrangian finite element basis functions [55]. For LC orientation, α and α are parameterized to be piecewise uniform over the elements, i.e., α, α ∈ L 2 .…”

Section: Filter Analysismentioning

confidence: 99%

See 2 more Smart Citations

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Barrera,

Cook,

Lee

et al. 2024

Polymers

View full text Add to dashboard Cite

Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.

show abstract

Section: Design Parameterizationmentioning

confidence: 99%

Section: Design Parameterizationmentioning

confidence: 99%

Section: Filter Analysismentioning

confidence: 99%

See 1 more Smart Citation

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Barrera,

Cook,

Lee

et al. 2024

Polymers

View full text Add to dashboard Cite

show abstract

Level-set topology optimization with PDE generated conformal meshes

Schmidt,

Barrera,

Mittal

et al. 2024

Struct Multidisc Optim

View full text Add to dashboard Cite

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

show abstract

Discretization-independent node-based shape optimization with the Vertex Morphing method using design variable scaling

Geiser,

Schmölz,

Baumgärtner

et al. 2024

Struct Multidisc Optim

View full text Add to dashboard Cite

The Vertex Morphing method is a node-based shape parameterization that uses an explicit filtering approach to regularize the optimization problem and generate smooth shapes. It has been successfully applied to shape optimization problems of industrial size in recent years. This work investigates in detail how irregular discretizations, design surface boundaries, and complex geometries can influence the progress of a gradient-based optimization using the standard Vertex Morphing formulation. A sensitivity weighting approach based on the available shape morphing functions is presented, which eliminates all of the aforementioned influences. Subsequently, a design variable scaling strategy is developed that transforms the optimization problem into an alternative design space and allows the use of arbitrary, even highly irregular surface discretizations in combination with black-box optimization algorithms for shape optimization with the Vertex Morphing method. Illustrative academic examples and an application case of an additively manufactured part are presented to support the work.

show abstract

Yet another parameter-free shape optimization method

Cited by 6 publications

References 48 publications

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

Level-set topology optimization with PDE generated conformal meshes

Discretization-independent node-based shape optimization with the Vertex Morphing method using design variable scaling

Contact Info

Product

Resources

About