@misc{12643,
  abstract     = {{Optimization of fiber-reinforced composite structures with nonlinear load-bearing behavior is a complex task that is becoming increasingly relevant in practice. Therefore, it is desirable to automatically determine essential influences on the structural behavior of fiber composite shells and stability-relevant objective functions and constraints in the context of structural optimization. This work deals with a variational approach for the derivation and computation of design sensitivities of elastic solid shell structures, as described in [1], and the extension to anisotropic layered composite structures. Design sensitivities concerning fiber angles and layer thicknesses are derived and quantitatively determined in the context of the finite ele-ment method (FEM). The anisotropic analysis model is founded on [2], in which a sophisti-cated solid-shell formulation based on reduced integration, as described in [3], is extended to discretize the composite with only one element over the whole thickness by means of mul-tiple integration points. This can be understood as a special case of equivalent-single-layer theories (ESLT). Examination of global stiffness and sensitivity matrices using methods from principal component analysis (PCA), such as singular value decomposition (SVD), are used to identify crucial design changes corresponding to major changes in the structural behavior of the composite. Results are discussed by referecne to a chosen numerical example.}},
  author       = {{Liedmann, Jan and Barthold, Franz-Joseph and Gerzen, Nikolai}},
  booktitle    = {{93rd Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2023}},
  issn         = {{1617-7061}},
  location     = {{Dresden}},
  number       = {{3}},
  publisher    = {{Wiley}},
  title        = {{{Gradient-based determination of principal design influences on composite structures}}},
  doi          = {{https://doi.org/10.1002/pamm.202300177}},
  volume       = {{23}},
  year         = {{2023}},
}

@misc{12801,
  abstract     = {{The present contribution derives a theoretical framework for constructing novel geometrical constraints in the context of density-based topology optimization. Principally, the predefined geometrical dimensionality is enforced locally on the components of the optimized structures. These constraints are defined using the principal values (singular values) from a singular value decomposition of points clouds represented by elemental centroids and the corresponding relative density design variables. The proposed approach is numerically implemented for demonstrating the designing of lattice or membrane-like structures. Several numerical examples confirm the validity of the derived theoretical framework for geometric dimensionality control.}},
  author       = {{Gerzen, Nikolai and Mertins, Thorsten and Pedersen, Claus B. W.}},
  booktitle    = {{Structural and Multidisciplinary Optimization}},
  issn         = {{1615-147X}},
  keywords     = {{Manufacturing constraints, Topology optimization, Geometric constraints, Gradient based structural optimization, Lattice designing, Additive manufacturing}},
  number       = {{5}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Geometric dimensionality control of structural components in topology optimization}}},
  doi          = {{10.1007/s00158-022-03252-7}},
  volume       = {{65}},
  year         = {{2022}},
}

@inbook{12615,
  author       = {{Materna, Daniel and Gerzen, Nikolai}},
  booktitle    = {{Digitalisierung im Bauwesen - Ausbildungsinhalte nordrhein-westfälischer Hochschulen}},
  pages        = {{84--85}},
  title        = {{{Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik}}},
  year         = {{2021}},
}

@inbook{12616,
  author       = {{Materna, Daniel and Gerzen, Nikolai}},
  booktitle    = {{Digitalisierung im Bauwesen - Forschungsinhalte nordrhein-westfälischer Hochschule}},
  pages        = {{73--74}},
  title        = {{{Bauingenieurwesen: Digitales Bauen, Mathematik und Bauinformatik}}},
  year         = {{2021}},
}

@inbook{2282,
  author       = {{Barthold, Franz-Joseph and Gerzen, Nikolai and Kijanski, Wojciech and Materna, Daniel}},
  booktitle    = {{Mathematical Modeling and Optimization of Complex Structures}},
  editor       = {{Neittaanmäki, Pekka and Repin, Sergey and Tuovinen, Tero}},
  isbn         = {{978-3-319-23563-9}},
  pages        = {{229--257}},
  publisher    = {{Springer-Verlag}},
  title        = {{{Efficient Variational Design Sensitivity Analysis}}},
  year         = {{2016}},
}

@article{2315,
  author       = {{Gerzen, Nikolai and Barthold, Franz-Joseph and Klinkel, S. and Wagner, W. and Materna, Daniel}},
  journal      = {{International Journal for Numerical Methods in Engineering}},
  number       = {{1}},
  pages        = {{29--42}},
  title        = {{{Variational sensitivity analysis of a non-linear solid shell element}}},
  doi          = {{10.1002/nme.4545}},
  volume       = {{96}},
  year         = {{2013}},
}

@article{2316,
  author       = {{Gerzen, Nikolai and Materna, Daniel and Barthold, Franz-Joseph}},
  journal      = {{Computational Mechanics}},
  number       = {{3}},
  pages        = {{379--396}},
  title        = {{{The inner structure of sensitivities in nodal based shape optimisation}}},
  volume       = {{49}},
  year         = {{2012}},
}