Topology Optimization Methodology Research Articles

Voxel-based evolutionary topological optimization of connected structures for natural frequency optimization

AbstractThe topology optimization methodology is widely utilized in industrial engineering for designing lightweight and efficient components. In this framework, considering natural frequencies is crucial for adequately designing components and structures exposed to dynamic loads, as in aerospace or automotive applications. The scientific community has shown the efficiency of Bi-directional Evolutionary Structural Optimization (BESO), showcasing its ability to converge towards optimal solid-void or bi-material solutions for a wide range of frequency optimization problems in continuum structures. However, these methods show limits when the complexity of the domain volume increases; thus, they are well-suited for academic case studies but may fail when dealing with industrial applications that require more complex shapes. The connectivity of the structures resulting from the optimization also plays a fundamental role in choosing the best optimization approach, as some available commercial and open-source codes nowadays return unfeasible sparse structures. An improved voxel-based BESO algorithm has been developed in this work to cope with current limits in lightweight structure optimization. A significant case study has been developed to evaluate the performances of the new methodology and compare it with existing algorithms. In contrast to previous studies, the method we developed guarantees that the final structure respects constraints on the initial design volume and that the structure’s connection is preserved, thus enabling the manufacturing of the component with Additive Manufacturing technologies. The proposed approach can be complemented by smoothing algorithms to obtain a structure with externally appealing surfaces.

A level set based topology optimization for elastodynamic problems using BEM

The paper presents a topology optimization methodology for 2D elastodynamic problems using the boundary element method (BEM). The topological derivative is derived based on the variation method and the adjoint variable method. The level set method is employed for the representation of the material domain and voids within a specified design domain. Thus, the boundaries can easily be generated, following the zero isocontour of the level set function. Numerical implementation is carried out to demonstrate the effectiveness of the proposed topology optimization methodology in wave isolation and waveguide problems.

Adaptive Variable Design Algorithm for Improving Topology Optimization in Additive Manufacturing Guided Design

CAD-CAE software companies have introduced numerous tools aimed at facilitating topology optimization through Finite Element Simulation, thereby enhancing accessibility for designers via user-friendly interfaces. However, the imposition of intricate constraint conditions or additional restrictions during calculations may introduce instability into the resultant outcomes. In this paper, an algorithm for updating the design variables called Adaptive Variable Design is proposed to keep the final design space volume of the optimized part consistently under the target value while giving the main algorithm multiple chances to update the optimization parameters and search for a valid design. This algorithm aims to produce results that are more conducive to manufacturability and potentially more straightforward in interpretation. A comparison between several commercial software packages and the proposed algorithm, implemented in MATLAB R2023a, is carried out to prove the robustness of the latter. By simulating identical parts under similar conditions, we seek to generate comparable results and underscore the advantages stemming from the adoption and comprehension of the proposed topology optimization methodology. Our findings reveal that the integrated enhancements within MATLAB pertaining to the topology optimization process yield favourable outcomes with respect to discretization and the manufacturability of the resultant geometries. Furthermore, we assert that the methodology evaluated within MATLAB holds promise for potential integration into commercial packages, thereby enhancing the efficiency of topology optimization processes.

Topology optimization of the electrodes in dielectrophoresis-based devices

This paper aims for developing topology optimization methodology to design the shape of electrodes in Dielectrophoresis (DEP)-based devices. The DEP force is due to a non-uniform electric field induced by applied voltages to the electrodes. Shape of the electrodes has the principal effect on the direction and magnitude of the DEP force. In medical therapy microfluidic devices, DEP force is used for cell sorting and cell separation. While the direction and magnitude of the DEP force are desired to be determined and maximized respectively, the magnitude of the electric field should be minimized to avoid damaging cells. Approaching these goals is counter intuitive where the existing electrode designs are basic. Therefore, a detailed finite element model (FEM) is developed for DEP force and electric field to formulate an optimization problem to maximize the DEP force in a particular direction while there is a constraint on electric field's magnitude. Using the developed FEM, explicit formulations for sensitivity analysis are derived to implement a gradient-based topology optimization. The performance of developed methodology is assessed numerically to determine the direction of the DEP force and constraining the electric field and experimentally in a practical case study of particle trapping in a microfluidic channel.

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

A Multi-Objective Topology Optimization Methodology Using Deep Learning and Its Application to Electromagnetic Devices

Maximizing acoustic band gap in phononic crystals via topology optimization

Designing phononic crystals (PnCs) to exhibit the widest attainable band gap, or to encompass a designated frequency range, is imperative for the realization of PnCs tailored to specific functionalities. However, achieving a wide band gap of acoustic waves centered around a specified frequency remains a significant challenge. The challenge arises from the fact that the optimization objective function may be enhanced by disconnected air regions. Nonetheless, these disconnected regions obstruct the circulation of air, rendering PnCs devoid of practical engineering utility. In this study, we propose a topology optimization methodology aimed at crafting air/solid PnCs that maximize the band gap of acoustic waves at a specified central frequency. To ensure adequate air permeability within the PnCs, the optimization model incorporates the virtual temperature technique in conjunction with the minimum length scale technique. The topology of the PnC unit cell is represented with a low number of design variables through the material-field series expansion, and the Kriging-based optimization algorithm is used to solve the complicated optimization problem. Diverse optimized configurations are presented, and experimental findings compellingly underscore the efficacy of the proposed optimization approach in the design of phononic band gap crystals geared towards acoustic waves at the specified central frequency.

Evolutionary topology optimization approach to design multiphase soundproof systems with poroelastic media

SummaryWith the constant development of cities, noise sources have become increasingly present inside and outside living environments. Consequently, soundproof systems comprised of porous materials have been widely adopted as filling fabric of closed‐space structures, such as in the components of buildings, airplanes or automobiles. However, in many situations, simply filling spaces may not be the most effective approach. In that scenario, this work introduces a multiphase acoustic topology optimization methodology to design closed‐space structures for sound attenuation. Based on the Bi‐directional Evolutionary Structural Optimization (BESO) algorithm, the proposed approach combines Biot's poroelasticity equations, expressed in the mixed /p form, and the Unified Multiphase (UMP) technique to fully describe the multiphysics involved in the acoustic, poroelastic and elastic model relations. An objective function contemplating different combinations of structural, viscous and thermal dissipated powers is maximized over multiple frequencies. Volume constraints in each material phase and a novel material interpolation scheme are also considered. The resultant topologies present enhanced dissipated power levels and manufacturability, even when compared with various baseline configurations of similar volume fractions.

A novel interval dynamic topology optimization methodology of piezoelectric structures under reliable active control

In this paper, considering the influence of uncertainties in piezoelectric intelligent structures with active vibration control law, a robust topology optimization method to reduce the sensitivity of structural dynamic flexibility to uncertainty factors for piezoelectric intelligent structures is proposed. The effect of active control can be equivalent to the damping. Considering the influence of uncertainty, the structural dynamic response of the system will be within the interval range. Due to the monotonicity of the steady-state displacement response on uncertain parameters and the monotonicity of dynamic flexibility on uncertain parameters are both difficult to determine, a more accurate upper and lower limit is obtained using the collocation method. With the constraints of reliability and volume, the robustness index is defined based on the dynamic flexibility of the structure and defined as the objective function to establish the robust topology optimization model. In terms of optimization solution, the reliability index is transformed into the constraint translation distance. The sensitivity of constraint functions and objective functions to design variables is derived by employing the chain derivative method and the adjoint vector method. Finally, two examples are used to verify the effectiveness of the proposed method.

A discrete variable based methodology for topology optimization considering spatially uneven manufacturing errors

A discrete variable based methodology for topology optimization considering spatially uneven manufacturing errors

Designing MEMS accelerometer for enhanced sensitivity and reduced cross-sensitivity in landslide monitoring

MEMS accelerometers capable of detecting weak motions are required in measuring landslide movements. The sensor’s sensitivity and its independent readings of various acceleration modes are crucial factors in the design of these sensors. In addition, it is highly desired to fabricate these sensors with low-cost and flexible manufacturing technologies such as surface micromachining. This paper presents an advanced topology optimization approach to design the suspended structure for the maximum level of sensitivity and for a low cross-sensitivity in the reading of principal and lateral modes, while it is manufacturable with a low-cost surface micromachining process. The effect of inertial forces as a variable loading condition and mode switch prevention is applied using a meta-heuristic topology optimization method with simulated annealing. Considering the unique results of this topology optimization, PolyMUMPs surface micromachining is employed to manufacture the developed sensor. The fabricated sensor is subjected to measurement and subsequent comparison with analogous designs from the literature. The outcomes reveal a sensitivity of 0.3pF/g and cross-axis sensitivity of 0.048%, signifying a noteworthy advancement for surface micromachined accelerometers. Notably, this design, coupled with the devised topology optimization methodology, holds the potential for adoption by sensor manufacturers for diverse commercial applications.

All dielectric highly efficient achromatic meta-lens using inverse design optimization

This work presents a high-efficiency achromatic meta-lens based on inverse design with topology optimization methodology. The meta-lens design with high numerical aperture values (NA = 0.7, NA = 0.8, and NA = 0.9) optimized along wavelength range starts from 550 to 800 nm, then the direct solver along the full extended wavelength band from 400 to 800 nm that applied to the final optimized structures under the three conditions of the high numerical apertures have high focusing efficiency for the all conditions. The optimization problem is based on Kreisselmeier–Steinhauser (k-s) objective function, leading to approximately stable response over the broadband bandwidths of the three designs.

Topological Design Optimization Approach for Winding Oil Flow Paths in Oil-Natural Air-Natural Transformers Based on a Fluidic-Thermal Coupled Model

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.

Topology optimization of microstructures with perturbation analysis and penalty methods

Topology optimization at the continuum nano/microscale is of wide interest in designing and developing more efficient micro/nano electromechanical systems. This paper presents a new methodology for topology optimization of microstructures that is based on perturbation analysis and the penalty methods. The homogenized material coefficients are numerically computed based on perturbation analysis, and periodic boundary conditions are imposed by the penalty methods. The sensitivity analysis is implemented directly without the adjoint method. The extension of the proposed method to the design of components for multi-field analysis is straightforward. The capability and performance of the presented methodology are demonstrated through several numerical examples.

A Novel Derivative Free Methodology for Topology Optimization Based on Projective Transformations and Boolean Operations

Most existing methods for topology optimization update the material distribution iteratively based on the derivative information. However, the calculation of gradient is of low accuracy and even unavailable in some cases. Therefore, it is demanding to develop derivative methodology for the topology optimization (TO). Two typical types of derivative free methodologies for the TO, the evolutionary methods and the normalized Gaussian network based methods, still suffer from issues such as checkerboard pattern and heavy dependence on the initial topology. To this end, this paper proposes a novel derivative free methodology for the TO based on the projective transformations and Boolean operations. Specifically, the proposed method selects the basic structures to constitute a new topology. Projective transformations and Boolean operations are employed to represent the evolvement and the way of combinations of the basic structures. According to the comparison of numerical results with other methodologies, the proposed methodology is capable of effectively and efficiently enhancing the parameter performance without checkerboard pattern.

Topology Design and Optimization of Modular Soft Robots Capable of Homogenous and Heterogenous Reconfiguration

Abstract The deformability of soft material robots provides them with the ability to transform between complex shapes and forms. This unique ability facilitates Modular Soft Robots (MSoRos) to assemble and reconfigure into different configurations, e.g., planar and spherical. These topologies display widely different locomotion modes that are desirable to navigate different environments, e.g., crawling or rolling for these cases. This research presents topology design and optimization methodology of MSoRos capable of both homogeneous and heterogeneous reconfiguration in spherical and planar configurations. Homogeneous reconfiguration refers to the scenario when all the modules are identical, while the heterogeneous contains nonidentical modules. The sequential design approach uses a polyhedron (Archimedean or Platonic) as the base solid to define module characteristics. As the design processes involve nonlinear projections, the base polyhedron also dictates the type of reconfiguration—heterogeneous (Archimedean) or homogeneous (Platonic). Thereafter, it applies the polyhedron vertex alignment principle to ensure geometric alignment of the modules during reconfiguration. Planar and spherical distortion metrics are defined to quantify distortions due to reconfiguration. Subsequently, the optimal topology is obtained by minimizing a cost function that is a weighted sum of the two distortion metrics. The result is a set of MSoRos capable of distinct 1D and 2D planar configurations (both heterogeneous and homogeneous) and multiple 3D spherical configurations of varying radii (both heterogeneous and homogeneous). The methodology is validated on a MSoRo system based on the combination of a cuboctahedron (Archimedean solid) and a cube and an octahedron (Platonic solids).

Functionally graded structure design for magnetic field applications

This study presents topology optimization methodology of anisotropic magnetic composites, which consist of two ferromagnetic materials with low and high reluctivity values, considering the nonlinear magnetic saturation effect. Instead of employing the asymptotic homogenization theory, the representative volume element method combined with the machine learning is used to build the continuous function model and it is applied to obtain the material property according to the design variable change. Finally, the micro-scale functionally graded structure composed of two ferromagnetic materials with the macro-scale topological morphology is simultaneously designed to improve the magnetic performance of actuators. Numerical examples for symmetric and asymmetric magnetic actuator models are provided to validate the effectiveness of proposed design process. In the numerical results, optimized configurations and objective values obtained with the nonlinear magnetic composite material, which depend on the intensity of the magnetic flux density, are compared with those of the linear magnetic composite material.

A novel design of the offshore wind turbine tripod structure using topology optimization methodology

To achieve a design with the desired stiffness, strength, and durability at the component level, topology optimization has been practiced and was effective in the design of sustainable products, by autumnally allocating the available material within the design domain to form the shortest loading path. In the conceptual phase, this paper proposed a design methodology using topology optimization technique for lightweight design of a tripod structure - a typical form of foundation for offshore wind turbines (OWTs). The minimum compliance subject to prescribed volume percentage is formulated and an innovative tripod structure is generated by interoperating the optimized structure. To facilitate comparison, a tripod structure of a 5 MW OWT is referenced. The system performances are comprehensively and synthetically assessed, encompassing the natural frequency, maximum von Mises stress in ultimate load cases and cumulative fatigue damage. It is discovered that the total mass of the novel design is substantially less than that of the reference structure. In contrast, the fatigue resistance has been significantly enhanced. These finding reveal conclusively that the proposed topology optimization approach is capable of generating novel designs, reducing weight and alleviating fatigue damage.

Topology optimization for dynamic flexible multibody systems using the Flexible Natural Coordinates Formulation

This work proposes a fully-coupled topology optimization methodology to optimize the structural components of flexible multibody systems. It employs the Adjoint Variable Method (AVM) and the Flexible Natural Coordinates Formulation (FNCF) to achieve constant Jacobians in the reduced mass, stiffness, and damping matrix when computing the sensitivity information. Although a fully-coupled approach is inherently computationally more expensive than a method based on equivalent static load, the use of FNCF can reduce the computational time of a fully-coupled approach by only computing these terms once per design iteration, as opposed to for each timestep. The methodology is demonstrated through two optimization cases on a slider-crank multibody system and compared with the commonly used equivalent static load approach. The second case showcases the inter-component and system-level optimization capabilities of the fully-coupled approach by minimizing the deformation energy of two flexible bodies while only optimizing one body’s structural design.

Topology optimization for additive manufacturing with strength constraints considering anisotropy

Abstract Combining topology optimization and additive manufacturing (AM) is a promising approach to breaking through the limitations of conventional design and developing innovative structures with high performance. However, the unique manufacturing constraints in AM should be considered when developing the topology optimization algorithms for AM. Material anisotropy is one of the common characteristics of AM materials due to the layer-by-layer manufacturing techniques. This work proposes a topology optimization approach for AM with strength constraints considering anisotropy. The Hoffman failure criterion is adopted to represent the anisotropic strength behaviors of AM materials. Based on the Hoffman failure criteria and the p-norm measure aggregation function, a global strength constraint formulation is established. Under the framework of solid isotropic material with penalization, we develop a topology optimization methodology to minimize the structural weight or volume fraction subject to structural stiffness and strength constraints. Several two-dimensional (2D) or 3D numerical test cases are performed to validate the effectiveness and performance of the developed method. The results indicated that the proposed method could make full use of material properties by considering anisotropic strength. Besides, the topological optimization considering strength anisotropy could be combined with build direction optimization to further reduce the structural weight.