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Research Papers: Design Theory and Methodology

J. Mech. Des. 2019;141(7):071101-071101-17. doi:10.1115/1.4042571.

Determining a suitable level of description, or granularity, for a product or process model is not straightforward, especially since granularity can manifest in multiple ways, but it is important to capture important elements in the model without building models that are too large to understand. This article investigates the implications of model granularity choices by simulating the design process of a diesel engine on different levels of detail, comparing the results and exploring ways to account for the differences. It uses two Design Structure Matrix (DSM) models for change prediction in a diesel engine at different levels of granularity to run simulations of the design process. Changes are a major source of rework and lead to frequent rescheduling of design tasks. The incremental nature of product development as well as design changes and their propagation complicate design process planning further. Process simulation may provide support in such contexts when it is based on an appropriate description of the product. The article shows that while coarse models can give an indication of likely process behavior, they miss potentially significant iteration loops.

Commentary by Dr. Valentin Fuster

Research Papers: Design Automation

J. Mech. Des. 2019;141(7):071401-071401-13. doi:10.1115/1.4042621.

This work presents a finite element analysis-based, topology optimization (TO) methodology for the combined magnetostatic and structural design of electrical machine cores. Our methodology uses the Bi-directional Evolutionary Structural Optimization (BESO) heuristics to remove inefficient elements from a meshed model based on elemental energies. The algorithm improves the average torque density while maintaining structural integrity. To the best of our knowledge, this work represents the first effort to address the structural-magnetostatic problem of electrical machine design using a free-form approach. Using a surface-mounted permanent magnet motor (PMM) as a case study, the methodology is first tested on linear and nonlinear two-dimensional problems whereby it is shown that the rapid convergence achieved makes the algorithm suitable for real-world applications. The proposed optimization scheme can be easily extended to three dimensions, and we propose that the resulting designs are suitable for manufacturing using selective laser melting, a 3D printing technology capable of producing fully dense high-silicon steel components with good soft magnetic properties. Three-dimensional TO results show that the weight of a PMM rotor can be slashed by 50% without affecting its rated torque profile when the actual magnetic permeability of the 3D-printed material is considered.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2019;141(7):071402-071402-13. doi:10.1115/1.4042617.

Periodic cellular structures with excellent mechanical properties widely exist in nature. A generative design and optimization method for triply periodic level surface (TPLS)-based functionally graded cellular structures is developed in this work. In the proposed method, by controlling the density distribution, the designed TPLS-based cellular structures can achieve better structural or thermal performances without increasing its weight. The proposed technique can be divided into four steps. First, the modified 3D implicit functions of the triply periodic minimal surfaces are developed to design different types of cellular structures parametrically and generate spatially graded cellular structures. Second, the numerical homogenization method is employed to calculate the elastic tensor and the thermal conductivity tensor of the cellular structures with different densities. Third, the optimal relative density distribution of the object is computed by the scaling laws of the TPLS-based cellular structures added optimization algorithm. Finally, the relative density of the numerical results of structure optimization is mapped into the modified parametric 3D implicit functions, which generates an optimum lightweight cellular structure. The optimized results are validated subjected to different design specifications. The effectiveness and robustness of the obtained structures is analyzed through finite element analysis and experiments. The results show that the functional gradient cellular structure is much stiffer and has better heat conductivity than the uniform cellular structure.

Commentary by Dr. Valentin Fuster
J. Mech. Des. 2019;141(7):071403-071403-9. doi:10.1115/1.4042616.

Topology optimization of macroperiodic structures is traditionally realized by imposing periodic constraints on the global structure, which needs to solve a fully linear system. Therefore, it usually requires a huge computational cost and massive storage requirements with the mesh refinement. This paper presents an efficient topology optimization method for periodic structures with substructuring such that a condensed linear system is to be solved. The macrostructure is identically partitioned into a number of scale-related substructures represented by the zero contour of a level set function (LSF). Only a representative substructure is optimized for the global periodic structures. To accelerate the finite element analysis (FEA) procedure of the periodic structures, static condensation is adopted for repeated common substructures. The macrostructure with reduced number of degree of freedoms (DOFs) is obtained by assembling all the condensed substructures together. Solving a fully linear system is divided into solving a condensed linear system and parallel recovery of substructural displacement fields. The design efficiency is therefore significantly improved. With this proposed method, people can design scale-related periodic structures with a sufficiently large number of unit cells. The structural performance at a specified scale can also be calculated without any approximations. What’s more, perfect connectivity between different optimized unit cells is guaranteed. Topology optimization of periodic, layerwise periodic, and graded layerwise periodic structures are investigated to verify the efficiency and effectiveness of the presented method.

Commentary by Dr. Valentin Fuster

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