Aug 2026· Mathematics and mechanics of solids· 0 citations· 24 references
Abstract
We present a numerical method for eigenfrequency optimization in two-dimensional and three-dimensional linearized elasticity, based on necessary optimality conditions where the optimal stiffness tensor saturates the upper Hashin–Shtrikman bound. The approach, grounded in the homogenization method, exploits recently derived explicit Hashin–Shtrikman bounds and corresponding optimal microstructures in three space dimensions for mixtures of two non-void elastic phases, enabling an efficient computational realization of the optimality criteria framework. It is capable of identifying global optimizers in most cases. Benchmark examples, including cantilever and bridge problems, demonstrate that true composite designs are obtained as optimal. A penalization procedure is then applied to recover mostly classical designs, with only a slight decrease in the objective functional. Finally, the proposed method is compared with the solid isotropic material with penalization method and is shown to yield improved performance.
This work presents the development and implementation of a second-order optimization algorithm based on a relaxed Newton method for the minimization of nonlinear scalar objective functions with multiple design variables. The proposed strategy combines a modified Newton scheme with a customized backtracking formulation,...
A. Gallo, Enrico Armentani, M. Ferraiuolo et al.· Frattura ed Integrità Strutt...· 0 citations
Gradient-based optimization (GBO) of problems constrained by partial differential equations is central to parameter identification and structural design in solid mechanics. Lattice Boltzmann method (LBM) schemes for linear elastic solids have only recently been derived. Combined with automatically generated discrete ad...
Johannes L. Grafen, Florian Kaiser, Stephan Simonis et al.· 0 citations
Abstract This study presents a global three-dimensional multi-objective optimization of a non-axisymmetric exhaust volute in a centrifugal compressor, aiming to enhance efficiency across a wide operating range using a global gas dynamics optimization approach. A three-dimensional parameterization method for the volute...
Lu Liang, Wuqi Gong, Ya Li et al.· International Journal of Tur...· 0 citations
The transmission eigenvalue problem plays an increasingly important role in inverse scattering theory. Although significant progress has been made in developing efficient numerical methods for the problem over the last two decades, its numerical treatment for curved domains in $\mathbb{R}^d$ ($d=2,3$) remains challengi...
This work presents a comparative analysis of Reduced-Order Models (ROMs) applied to incompressible fluid dynamics within geometrically parametrized domains. Two distinct reduced-order solution strategies are investigated and compared: a monolithic coupled solver and a segregated SIMPLE-based algorithm. Their performanc...
Andrea Buffolini, Davide Oberto, G. Rozza· 0 citations
