In the paper the new paradigm for structural optimization without volume constraint is presented. Since the problem of stiffest design (compliance minimization) has no solution without additional assumptions, usually the volume of the material in the design domain is limited. The biomimetic approach, based on trabecular bone remodeling phenomenon is used to eliminate the volume constraint from the topology optimization procedure. Instead of the volume constraint, the Lagrange multiplier is assumed to have a constant value during the whole optimization procedure. Well known MATLAB topology based optimization code, developed by Ole Sigmund, was used as a tool for the new approach testing. The code was modified and the comparison of the original and the modified optimization algorithm is also presented. With the use of the new optimization paradigm, it is possible to minimize the compliance by obtaining different topologies for different materials. It is also possible to obtain different topologies for different load magnitudes. Both features of the presented approach are crucial for the design of lightweight structures, allowing the actual weight of the structure to be minimized. The final volume is not assumed at the beginning of the optimization process (no material volume constraint), but depends on the material’s properties and the forces acting upon the structure. The cantilever beam example, the classical problem in topology optimization is used to illustrate the presented approach.

Optimizing the aerodynamic structure of composite insulators can guarantee the safe operation of power systems. In this study, we construct a simulation model for composite insulator contaminant deposition using the COMSOL simulation software, and the rationality of the simulation model and method is verified through wind tunnel experiments. Taking the FXBW4-110/100 composite insulator as an example, we adopt a progressive optimization plan to explore the impacts of shed spacing s, and shed inclination angles α and β on its contaminant deposition characteristics under DC and AC voltages. Based on the numerical simulation results, we analyze the antifouling performance of insulators before and after structural optimization. The results indicate the following: 1) The contaminant deposition of the insulator under AC and DC voltages is negatively correlated with the shed spacing s, but positively correlated with the lower inclination angle β. 2) Under AC voltages, the contaminant deposition of the insulator increases with the upper inclination angle α, while under DC voltages, the contaminant deposition shows an uptrend first, then a downtrend and then an uptrend again with the increase of the upper inclination angle α. 3) Compared with the original model, the AC-optimized model ( α = 6°, β = 2° and s = 98 mm) with a larger shed spacing s, and smaller shed inclination angles α and β showed superior antifouling performance at wind speeds of no less than 2 m/s, and under the typical conditions ( v = 2.5 m/s, d = 20 μm, and ρ = 2 200 kg/m ³), its contaminant deposition is 15% less than that of the original model ( α = 10°, β = 2° and s = 80 mm).

The problem of optimal design of a steel plated girder according to the Eurocode 3 is considered. Code regulations admit the Finite Element Analysis (FEA) in designing plated structures with variable cross-sections. A technique of determining an approximate solution to the optimization problem is presented. It is determined a solution of a control theory optimization task, in which Eurocode requirements regarding the Ultimate Limit State (bearing capacity, local and global stability) as well as Serviceability Limit State (flexural rigidity) are used as appropriate inequality constraints. Static analysis is performed within the framework of linear elasticity and Bernoulli-Euler beam theory making an account for second-order effects due to prescribed imperfections. Obtained solutions, after regularization, may be used for direct verification with the use of FEA or as the first guess for iterative topology optimization algorithms. Code requirements governing the determination of optimal shape are visualized in the constraint activity diagram, which is a proposed tool for analysis of optimization process.