Asymptotic analysis of shape functionals

By S. Nazarov, J. Sokołowski. 2003

186 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5d4aae2e9c7ae2fbd1e822d0578893a89cf5e79c

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Civil and Structural Engineering

1. Antonio André Novotny
2. Samuel Amstutz
3. E. A. Souza Neto
4. S. Nazarov
5. J. Sokołowski
6. Sebastian M. Giusti
7. Ole Sigmund
8. Emílio Carlos Nelli Silva

In Computational Theory and Mathematics

1. Antonio André Novotny
2. E. A. Souza Neto
3. Samuel Amstutz
4. J. Sokołowski
5. S. Nazarov
6. Sebastian M. Giusti
7. Emílio Carlos Nelli Silva
8. Luís Fernando Nogueira de Sá

In Mathematical Physics

1. Samuel Amstutz
2. Antonio André Novotny
3. S. Nazarov
4. J. Sokołowski

Citations in the corpus

• Topological derivative-based topology optimization of structures subject to Drucker–Prager stress constraints (2012, background): “Further theoretical developments are reported, among others, in [23, 4, 29].”
• Self–adjoint Extensions for the Neumann Laplacian and Applications (2006, methodology): “We refer the reader to [18–20], for further results on the asymptotic analysis of boundary value problems in singularly perturbed domains, and to [5] for applications to shape optimization.”
• Topological optimization of structures subject to Von Mises stress constraints (2010, background): “31) has some similarity with results proved in [30], where a theory is developed for a broad class of elliptic state equations and shape functionals in three space dimensions, then it is applied to the linear elasticity case.”
• Connections between topological sensitivity analysis and material interpolation schemes in topology optimization (2011, background): “(1999), and then developed by several authors, see, e.g., Amstutz (2006a, b), Guzina and Bonnet (2004), Nazarov and Sokooowski (2003) and Novotny et al. (2003).”
• Topological derivative for multi‐scale linear elasticity models applied to the synthesis of microstructures (2010, background): “It has proved extremely useful in the treatment of a wide range of problems, including the topology optimization of load-bearing structures [1, 4, 39], inverse analysis [5, 18, 27] and image processing [8, 28, 32], and is currently a subject of great interest in applied mathematics circles [3, 19, 3”