Integrated optimal topology design and shape optimization using neural networks

This paper presents a performance index for topology and shape optimization of plate bending problems with displacement constraints. The performance index is developed based on the scaling design approach. This performance index is used in the Performance-Based Optimization (PBO) method for plates in bending to keep track of the performance history when inefficient material is gradually removed from the design and to identify optimal topologies and shapes from the optimization process. Several examples are provided to illustrate the validity and effectiveness of the proposed performance index for topology and shape optimization of bending plates with single and multiple displacement constraints under various loading conditions. The topology optimization and shape optimization are undertaken for the same plate in bending, and the results are evaluated by using the performance index. The proposed performance index is also employed to compare the efficiency of topologies and shapes produced by different optimization methods. It is demonstrated that the performance index developed is an effective indicator of material efficiency for bending plates. From the manufacturing and efficient point of view, the shape optimization technique is recommended for the optimization of plates in bending.

The gradient based topological optimization tools introduced during the last ten years tend naturally to modify the topology of a domain by creating small holes inside the domain. Once these holes have been created, they usually remain unchanged, at least during the topological phase of the optimization algorithm. In this paper, a new asymptotic expansion is introduced which allows to decide whether an existing hole must be removed or not for improving the cost function. Then, two numerical examples are presented: the first one compares topological optimization with standard shape optimization, and the second one, issued from a lake oxygenation problem, illustrates the use of the new asymptotic expansion.

This paper presents a progressive type of variational principle for topological shape optimization. The principle makes it possible to derive a finite element method (FEM) for searching structural shapes with minimal weight and high strength in the optimization operation. The principle is based on that of minimum potential energy. In the formulation of this principle, we first assume both a search domain and an optimum one. The search domain includes the optimum one. Then, the search domain is locally eliminated according to the information of minimum strain energy in the domain. When a maximum equivalent stress in the search domain reaches the yield stress as a constraint condition, it is evaluated that the search domain agrees with the optimum one. Therefore, we obtain the variational principle for the topological optimization. Next, we derive the FEM based on this principle. Finally, we obtain the optimum topological shapes of two-dimensional finite element models using the FEM. Hence, the validity of the variational principle is confirmed from the numerical solutions of the models.

The structure optimization design of bridge crane based on HyperWorks is studied in this paper. The girder structure of the bridge crane can affect the performance of the bridge crane to certain extent. Based on the structure optimization technology of HyperWorks, the topological optimization, shape optimization and size optimization for one 50t bridge crane have been researched. The analysis results show that the weight of the optimized girder of the bridge crane has been significantly reduced than before, and the performance has been improved.

The optimal topology of a two dimensional linear elastic body can be computed by regarding the body as a domain of the plane with a high density of material. Such an optimal topology can then be used as the basis for a shape optimization method that computes the optimal form of the boundary curves of the body. This results in an efficient and reliable design tool, which can be implemented via common FEM mesh generator and CAD input-output facilities.

This paper presents the optimum load-speed diagram evaluation for a linear micromotor, including multitude cantilever piezoelectric bimorphs, briefly. Each microbeam in the mechanism can be actuated in both axial and flexural modes simultaneously. For this design, we consider quasi-static and linear conditions, and a relatively new numerical method called the smoothed finite element method (S-FEM) is introduced here. For this purpose, after finding an optimum volume fraction for piezoelectric layers through a standard numerical method such as quadratic finite element method, the relevant load-speed curves of the optimized micromotor are examined and compared by deterministic topology optimization (DTO) design. In this regard, to avoid the overly stiff behavior in FEM modeling, a numerical method known as the cell-based smoothed finite element method (CS-FEM, as a branch of S-FEM) is applied for our DTO problem. The topology optimization procedure to find the optimal design is implemented using a solid isotropic material with a penalization (SIMP) approximation and a method of moving asymptotes (MMA) optimizer. Because of the higher efficiency and accuracy of S-FEMs with respect to standard FEMs, the main micromotor characteristics of our final DTO design using a softer CS-FEM are substantially improved.

A shape design sensitivity analysis and optimization procedure is proposed using a meshfree method. A CAD tool connection is established to facilitate the seamless integration of structural modeling, simulation, and design optimization. A new CAD-based method for design velocity computation is proposed, applicable to both the meshfree method and the finite element method. A shape design variable can be chosen among the geometric parameters defined in the CAD model in order to support a concurrent engineering environment. A new CAD-based method for updating the discrete model is proposed, such that the meshfree model is automatically updated in a continuous and consistent way during design optimization. The proposed method is applied to 2D and 3D linear elastic problems, as well as to a large deformation hyperelastic problem.

To study the design method of openings on the web of an I-beam, three I-beams with different circular holes were designed using the traditional truss mechanism, and the circular holes were reinforced by ring stirrups. A shear test was performed to study the failure modes of the I-beams and efficiency of the ring stirrups. A new method for establishing the truss mechanism was proposed, which used the windowed evolutionary structural optimization method to calculate the topology optimization solution of the I-beam. From the topology optimization results, the strut-and-tie model (STM) was established, which revealed the stress mechanism of the I-beam. Via the STM, the optimal shape and location for the opening of the I-beam under shear load states were presented. The quantity of reinforcing bars, porosity and ultimate load of the I-beam designed by the STM were, respectively, 0.67, 5.5 and 1.2 times those of the experimental model.

In this paper, a topological optimum design for the shape of a groove in a dry gas seal is described. Dry gas seals are widely used in high speed and high pressure rotating machinery such as gas turbines, compressors, and so on because of their high reliability compared to other types of seals. However, recent requirements for reducing emission with further control of leakage are in order. With this background, we propose applying topological optimization to the groove shape in a dry gas seal to reduce its leakage while keeping its stiffness for safe operation. First, the method of topological optimum design as applied to the groove of a dry gas seal is explained via numerical analysis. Next, results of the topological optimization are shown via categorizing an optimum shape map. Finally, the mechanism of reducing the gas leakage with an optimized seal is discussed based on the prediction of the flow field using a CFD analysis.

Topology design and structural optimization of Co-Cr frameworks for implant-supported prostheses.

This paper reviews the recent developments of design optimization methods for electromagnetic devices, with a focus on machine learning methods. First, the recent advances in multi-objective, multidisciplinary, multilevel, topology, fuzzy, and robust design optimization of electromagnetic devices are overviewed. Second, a review is presented to the performance prediction and design optimization of electromagnetic devices based on the machine learning algorithms, including artificial neural network, support vector machine, extreme learning machine, random forest, and deep learning. Last, to meet modern requirements of high manufacturing/production quality and lifetime reliability, several promising topics, including the application of cloud services and digital twin, are discussed as future directions for design optimization of electromagnetic devices.

Shape optimization (with topological changes) has become a de facto standard approach for synthesizing new designs. Current approaches heavily rely on voxelized modifications of the initial domain, followed by heuristic reconstruction procedures that result in a detailed shape design. The initial domain is almost always conservatively estimated so that the design space spans a sufficiently large set of possible solutions. We propose a novel approach to shape optimization that exploits the geometric and topologic properties of medial zones and a new shape modification paradigm to synthesize shapes with topological guarantees. The medial zone is a ‘thick skeleton’ of the domain induced by prescribed boundary conditions, and represents an initial solution that is topologically valid. We modify such an initial solution by adding or subtracting ‘bubbles’ of material defined via prescribed shape functions. The proposed approach has many advantages in terms of topological guarantees, shape control, and computational cost, supports parametric optimization of free-form geometry, and can be implemented in any geometric representation that supports distance computations.

In this chapter, a topology optimization algorithm based on the topological derivative concept combined with a level-set domain representation method is presented. The model problem is governed by the elasticity system into two spatial dimensions. The topological asymptotic expansion of a tracking-type shape functional, associated with the nucleation of a small circular inclusion endowed with different material property from the background, is rigorously derived. Finally, the obtained theoretical result is used as a steepest-descent direction in the optimization process, which is applied in the context of compliance structural topology optimization and topology design of compliant mechanisms.

We shall extend the homogenization design method for the global stiffness maximization of an elastic structure to the optimization problem related to eigenvalues for free vibration such as maximization of a specified set of eigenvalues, maximization of the distance of the two specified eigenvalues, and identification of a structure that possesses a set of specified eigenvalues. To this end, the basic mathematical formulation and a solution method are proposed as well as various numerical examples of obtaining the optimum layout of both plane plate, and three-dimensional shell structures.

Technological progress is leading to the incorporation of digital twinning and artificial intelligence, causing engineering design and scientific procedures to transition into an AI-driven age. Digital twinning and modeling have been increasingly included into engineering design optimization, particularly via processes like topology optimization and generative design, to provide modern design solutions efficiently. The integration of topology optimization with additive manufacturing is revolutionizing the design optimization process in the automotive industry, where there is a pressing demand for lightweight design and improving production efficiency. A design optimization methodology has been developed to optimize an Automotive Seatbelt Bracket subjected to dynamic load and fatigue. The innovative design is lighter and consolidates the entire assembly into a single body that can be manufactured using additive manufacturing.