A fast methodology for topology optimizations of electromagnetic devices

To alleviate the excessive computational burden involved in topology optimizations, an efficient methodology for topology optimization is proposed. In the proposed methodology, a multi-scale on/off method is designed to avoid using infinite number of decision parameters; and a stochastic approximation method is employed to minimize the computational costs when computing the sensitivity information. Numerical results are reported to showcase the merits of the proposed methodology.

A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclusions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

Permanent magnet synchronous motors (PMSM) are widely used in various fields of application of electric drives of industrial enterprises. For each application of the electric drive, it is necessary to accept technical requirements, such as the maximum torque of the electric motor and the fulfillment of the required conditions for the strength characteristics of the rotor and stator.PMSM has a number of advantages over other types of engines. Asynchronous motors have developed resource rational energy efficiency, while synchronous motors are more energy efficient without modifications. PMSM have smaller weight and size parameters, which allows them to be used in a wider field of application, for example, in household appliances, robots and many other drives.TARGET. The aim is to develop a methodology for topological complex optimization of the engine design, based on a genetic algorithm.METHODS. The genetic algorithm is more accurate than traditional analytical methods, the method used in the analysis of AC machines, takes less time than the usual trial and error design procedure based on the finite element method. The main optimization criterion is an increase in torque while maintaining the mass of the most expensive material (permanent magnets). This feature is important for the manufacture of a designed engine in production.RESULTS. A program has been written in Python, which made it possible to carry out a comprehensive topological optimization for the engine under consideration.CONCLUSION. Topological optimization based on the method of modifying the rotor design using a genetic algorithm with the additions necessary for correct operation with synchronous motors is presented.

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Power transformers are a critical component in transmission and distribution systems. To limit the temperature rise to extend the life-cycle while operating with enough reliability and controllability of a transformer, the design of the cooling system has attracted extensive research attention. In this paper, a topology optimization (TO) methodology is presented for designing the coolant flow paths in a prototype oil-natural air-natural (ONAN) power transformer to maximize the winding heat dissipation capacity without any compromise on the flow resistance. First, the thermal and fluid flow characteristics in both the winding and the radiator of the prototype transformer are numerically investigated through a fluidic-thermal coupled field approach. The preliminary cooling effectiveness of the oil circulation system is initialized. Second, a material-density-based TO scheme is employed to realize the optimal design of the oil baffle structures. In the TO optimization, artificial Darcy frictional forces are applied to the solidified cells to block their internal flows in the fluidic calculations, while the thermal conduction coefficients in those cells are enhanced to separate the baffles from the flowing oil in thermal analyses. Finally, the fluidic and thermal coupled fields of the prototype transformer winding region with structurally optimized oil baffles are numerically investigated to validate the TO effectiveness.

In this work, a novel three-dimensional (3D) topology optimization methodology for a flexible MBS undergoing both large overall motion and large deformation is proposed. Firstly, the flexible MBS of concern is accurately modeled via the 3D solid brick element of the absolute nodal coordinate formulation (ANCF), which utilizes positions of nodes and slopes as sets of generalized nodal coordinates. Secondly, to deal with the dynamic characteristics in the optimization process, the equivalent static load method is employed to transform the dynamic topology optimization problem into a static one. Last but not least, in order to reduce the computation time, the newly-developed moving morphable components (MMC) based topology optimization method is reevaluated to optimize the 3D flexible MBS. The MMC based framework incorporates more geometrical and mechanical information into the topology optimization directly and can optimize large-scale flexible MBS with high efficiency. Two numerical examples are presented to validate the accuracy of the solid element of ANCF and the effectiveness of the proposed optimization methodology, respectively.

The manufacturing of lattice structures has been greatly facilitated thanks to the advances in additive manufacturing. Functionally graded lattice (FGL) structures, a major class of such structures, developed using topology optimization (TO) are known to have superior mechanical characteristics such as high stiffness to weight ratio. A new design methodology using an integrated TO process is proposed for the development of FGL structures in this research. For that purpose, a material-penalization formula derived by the application of homogenization is integrated into the TO process. As a result, relative densities of the TO are mapped directly. This approach is more advantageous compared with the alternative techniques as there is no need to post-process the optimization results. Therefore, the degradation of the optimization results from post-processing is eliminated. Then, radial basis functions (RBFs) are used to create the geometry of the FGLs efficiently. The proposed methodology is demonstrated on a case study, where a cantilever beam with a desired bandgap characteristic is designed. Numerical results using the proposed method show that the first and second bending frequencies with the resulting optimized geometry are within 3% and 12% of the original TO design, whereas using method 1 the calculated relative errors are 24% and 74% and method 2 these errors are calculated as 8% and 34%, respectively. These comparative results indicate that the geometry created by the new method is superior to other design strategies as evidenced by the improved compatibility level between the bandgap performance results of the original unpenalized TO and structures generated using alternative techniques.

Free-mounted cooling plate multi-objective topology optimization method towards precision machine tool heat dissipation: An experimental and numerical study

Optimization in Simulation is an important problem often encountered in system behavior investigation; however, the existing methods such as response surface methodology and stochastic approximation method are inefficient. This paper presents a modification of a quasi‐Newton method, in which the parameters are determined from some numerical experiments. To demonstrate the validity of the devised method, two examples resembling the M/M/1 queueing problem are solved. The closeness of the converged solutions to the optimal solutions and a comparison with two stochastic approximation methods indicate that the modified quasi‐Newton method as devised in this paper is a robust and efficient method for solving optimization problems in simulation.

23 Stochastic approximation

ABSTRACTCultural heritage preservation requires a deeper understanding of their seismic response and imposes the use of effective strengthening methods. Fibre‐reinforced polymers (FRP) have emerged as an effective solution for strengthening masonry structural elements. The decision over the optimal configuration for a FRP‐based strengthening is a trade‐off between different objective functions such as strength, inelastic stiffness and cost. Although some studies have explored design alternatives and topology optimisation, experimental investigation remains limited, especially regarding the evaluation of seismic response. This study investigates the seismic capacity of unstrengthened and strengthened mortared–masonry arches through tilting table experiments and numerical simulations. The optimal strengthening arrangement is obtained through topology optimisation, and experimental results demonstrate its performance. A three‐dimensional numerical model, following a macro‐modelling approach through the so‐called concrete damage plasticity material model, is adopted. Numerical results are validated with existing literature and experimental data. A parametric study is conducted for full‐scale arches to evaluate the effect of dimensions and the embrace angle of masonry arches. The study reveals that the numerical model successfully replicates masonry arches' nonlinear behaviour and hinge mechanism. In addition, both experimental and numerical results highlight the effectiveness of optimised strengthening placement achieved through topology optimisation.

A domain evolution method to suppress the eigenfrequency and eigenmode errors caused by low-density elements in dynamic topology optimization

This paper is a continuation of our papers [9], [10] and [11] and is concerned with a Robbins-Monro type stochastic approximation method when a sequence of dependently distributed random vectors is given. The method of stochastic approximation has been first proposed by H. Robbins and S. Monro ([5]) and its modifications have been thereafter given by many authors. A typical one of them is as follows. Suppose that an RN-valued random vector Y„(x) can be observed at xERN and each instant n, and the expected value of Y n(X), denoted by E[Y„(x)]=1/17,(x), is unknown to us. Assuming that the equation itin(x)=0 has a solution x=8,, for each n=1, 2, • , it is desire to estimate 0,, for sufficiently large n on the basis of observed values Y1(X0), Y2(Xi), Y.+I(X,i), ••• at the points X„ Xi, •-• , X„, ••• which are produced by the following recurrence relation,

Thin perforated Steel Plate Shear Walls (SPSWs) are among the most common types of seismic energy dissipation systems to protect the main boundary components of SPSWs from fatal fractures in the high-risk zones. In this paper, the cyclic behavior of the different circular hole patterns under cyclic loading is reported. Based on the experimental results, it can be concluded that a change in the perforation pattern of the circular holes leads to a change in the locations of the fracture tendency over the web plate, especially at the plate-frame interactions. Accordingly, the cyclic responses of the tested specimens were simulated by finite element method using the ABAQUS package. Likewise, perforated shear panels with a new perforation pattern obtained by implementing Topology Optimization (TO) were proposed. It was found that the ultimate shear strength of the specimen with the proposed TO perforation pattern was higher than that of the other specimens. In addition, theoretical equations using the Plate-Frame Interaction (PFI) method were used to predict the shear strength and initial stiffness of the considered specimens. The theoretical results showed that the proposed reduced coefficients relationships cannot accurately predict the shear strength and initial stiffness of the considered perforated shear panels. Therefore, the reduced coefficients should be adopted in the theoretical equations based on the obtained experimental and numerical results. Finally, with the results of this study, the shear strength and initial stiffness of these types of perforated shear panels can be predicted by PFI method.

Design of patterned multilayer films with eigenstrains by topology optimization