Eigenvalue problems play a fundamental role in structural dynamics and engineering design, with topology optimization offering powerful tools for achieving superior performance. While most research has focused on eigenvalue maximization, only a few studies have explored eigenvalue assignment or reduction. This work investigates the challenges associated with eigenfrequency minimization in level-set topology optimization, highlighting the risk of infeasible or fragmented designs. To overcome these issues, we propose a formulation that integrates connectivity constraints to preserve structural integrity, thereby addressing an inherent limitation of eigenfrequency reduction. A comparative analysis of eigenfrequency minimization and maximization is presented, emphasizing the role of the ersatz material interpolation scheme and the impact of constraint enforcement. The proposed methodology is demonstrated through numerical examples, illustrating its effectiveness in achieving feasible layouts and highlighting its potential applications across a wide class of structural dynamics problems. • Tackles the challenge of minimizing and reducing specific eigenfrequencies. • Highlights key differences from eigenfrequencies maximization. • Proposes connectivity constraints to preserve structural integrity.

This paper introduces a novel automated framework for the optimal design of steel truss structures, incorporating plastic deformations through the complementary strain energy of residual forces while minimizing weight. The presented methodology is equally applicable to purely elastic scenarios, ensuring zero plastic deformations and further reducing material usage. To achieve this, a nonlinear finite element (FE) program was developed, capable of accounting for large deformations and initial geometric imperfections. A genetic algorithm (GA) was integrated to iteratively optimize the objective function, enabling a fully automated design process. The efficiency and versatility of the framework were validated through four numerical examples. The first two comprise benchmark cases: a 9-bar planar truss and a 25-bar space truss. The remaining two examples were selected to be more representative of practical applications, involving a prestressed arched truss and a double-layer space truss. Analyses of various configurations were performed to demonstrate the robustness of the approach. Using the proposed methodology, significant improvements in plastic performance and material efficiency were achieved, underscoring its potential, adaptability, and effectiveness in advancing truss design techniques.