Topology Optimization Approach Research Articles

ToRoS: A Topology Optimization Approach for Designing Robotic Skins

Soft robotics offers unique advantages in manipulating fragile or deformable objects, human-robot interaction, and exploring inaccessible terrain. However, designing soft robots that produce large, targeted deformations is challenging. In this paper, we propose a new methodology for designing soft robots that combines optimization-based design with a simple and cost-efficient manufacturing process. Our approach is centered around the concept of robotic skins---thin fabrics with 3D-printed reinforcement patterns that augment and control plain silicone actuators. By decoupling shape control and actuation, our approach enables a simpler and cost-efficient manufacturing process. Unlike previous methods that rely on empirical design heuristics for generating desired deformations, our approach automatically discovers complex reinforcement patterns without any need for domain knowledge or human intervention. This is achieved by casting reinforcement design as a nonlinear constrained optimization problem and using a novel, three-field topology optimization approach tailored to fabrics with 3D-printed reinforcements. We demonstrate the potential of our approach by designing soft robotic actuators capable of various motions such as bending, contraction, twist, and combinations thereof. We also demonstrate applications of our robotic skins to robotic grasping with a soft three-finger gripper and locomotion tasks for a soft quadrupedal robot.

Design of effective heat transfer structures for performance maximization of a closed thermochemical energy storage reactor through topology optimization

This study addresses the need for heat transfer intensification in closed thermochemical energy storage reactors using topology optimization as a design approach. We introduce a novel topology optimization framework to simultaneously optimize fins geometry and amount of enhancer material while meeting specific discharge time, bed size, and bed porosity requirements. The proposed topology optimization framework is thoroughly tested by optimally designing innovative fin structures in a reference thermochemical storage reactor aimed at heat storage in industrial applications and operated with Strontium Bromide in the range 150-250 °C. The generated designs show performance improvement up to +286% compared to state-of-the-art designs. Our findings also indicate that the optimal amount of enhancer material varies significantly; large bed sizes with high packing factors maximize reactor energy density while highly packed reactive beds provide a larger amount of energy in fixed discharge times compared to less packed reactive beds. Finally, the benefits and limitations of the proposed topological optimization approach, as well as the extent to which the optimal designs found are generally applicable are thoroughly discussed to provide guidelines for configuring high-performing closed system thermochemical energy storage reactors.

Electromagnetic and Mechanical Topology Optimization for SynRM Rotors Considering High Dimensional Constraints

The knowledge-based parametric design process of the rotor topology of the synchronous reluctance motor (SynRM) requires a tedious parameter definition, selection, and searching process until an optimal design can be obtained. This research proposes a topology optimization approach based on solid isotropic material with penalization method for the SynRM rotor topology design. The aim is to pursue a more intelligent and automatic design process. Specifically, the proposed method aims to generate the SynRM rotor design of high output torque profile. Meanwhile, the mechanical constraints including structural compliance and stress etc. are also considered for promising the structural reliability of the rotor. Considering the high dimensional constraints caused by the multi-physics performances, the augmented Lagrangian method based optimization framework is developed to solve the minimization problem in a compact scheme. To prove the effectiveness of the developed method, simulations and analysis on the topology optimization of SynRMs are performed in this research. Prototyping and experiment are also conducted for verifying the performance of the optimized structure.

Stress-based topology optimization approach using binary variables and geometry trimming

Stress-based topology optimization approach using binary variables and geometry trimming

Machine learning powered sketch aided design via topology optimization

Structural topology optimization is an important design tool in the conceptual design phase of a product. However, the current topology optimization design is mostly driven strictly based on mathematical and mechanical models. Although the innovative design can be automated, it mostly lacks effective manual experience guidance. To improve the efficiency of computer-aided structural design models, this work proposes a sketch-guided topology optimization approach based on machine learning. Using neural network-based style transfer techniques, computer-digitized/hand-drawn sketches are explicitly incorporated into topology optimization in the form of constraint functions. The obtained optimization results not only satisfy the requirements of optimal mechanical properties, but also fully demonstrate the design intention and requirements of designers. Numerical examples show that the proposed approach can effectively compensate for the lack of manual experience guidance for topology optimization.

Topology optimization for energy absorption of quasi-brittle structures undergoing dynamic fractures

In this paper, we introduce a topology optimization approach aimed at improving the energy absorption of quasi-brittle structures under impact loading. Our method focuses on incorporating dynamic fracture behavior throughout the impact process to maximize the energy acting on the structure. To achieve this, we integrate a dynamic phase field method into density-based topology optimization, enabling us to simulate the initiation and propagation of complex dynamic fractures. The optimization formulation aims to maximize the absorbed energy over a specified period while adhering to material volume and compliance constraints. Sensitivity analysis was originally provided to accelerate computations and optimization. Several numerical examples show that the incorporation of dynamic fracture effects leads to superior energy absorption of the optimized structure compared to static strategies or neglecting the fracture process. Moreover, the proposed scheme facilitates tailored designs for different impact loading rates.

Optimizing structural topology design through consideration of fatigue crack propagation

This paper presents an advanced approach for structural topology optimization by incorporating fatigue crack propagation analysis. The extended finite element method (X-FEM) is employed to model initial crack propagation, while the Paris model serves as the basis for simulating fatigue crack growth. The proposed methodology aims to optimize the structural design by minimizing compliance while considering volume and fatigue constraints. The proposed method employs the developed bi-directional evolutionary structural optimization (BESO) algorithm. The accuracy of the proposed technique is validated through the solution of benchmark problem and is further demonstrated in its effectiveness and robustness by examining several numerical examples. The optimization process considers various crack conditions, including the absence of cracks, horizontal and vertical cracks of different lengths. The optimized topologies obtained through the proposed algorithm clearly demonstrate the impact of crack presence, crack direction, and crack length on the material distribution. Furthermore, the convergence histories of the objective function, represented by mean compliance, highlight the influence of crack length on the stiffness and converged compliance of the structure. The results demonstrate its ability to adapt the material distribution based on fatigue cracks propagation conditions and achieve optimal topologies that balance structural integrity and performance.

Kirigami pattern design for buckling-induced assembly 3D structures via topology optimization

Complex three-dimensional (3D) mesostructures are attracting an increasing interest due to their wide applications in microelectronics, biomedicine and other fields. A buckling-induced 3D structure can be assembled by buckling of a 2D plane precursor rapidly and precisely at low cost. However, the inverse design problem of finding 2D precursor configurations corresponding to the predetermined 3D mesostructures has not been well solved yet. In the present work, an inverse method is developed for buckling-induced assembly 3D structure design. Unlike the existing methods, the Moving Morphable Void (MMV) -based topology optimization approach is adopted for driving the inverse design. The voids in MMV are defined as kirigami cuts on the 2D precursor with explicit geometry parameters to generate complex buckling deformation. To cope with the costly non-linear optimization, the Equivalent Static Loads (ESL) method is incorporated, with which the non-linear optimization process can be transformed into a linear static optimization process. Therefore, the layout of the pattern of cuts is sought on the 2D precursor with linear sensitivity calculation. Some self-assembly numerical examples demonstrate the effectiveness and efficiency of the proposed approach.

Structural topology optimization of three-dimensional multi-material composite structures with finite deformation

In this work, an explicit three-dimensional (3D) topology optimization approach is presented for multi-material composite structures accounting the finite deformation effect. The proposed method employs different sets of 3D Moving Morphable Voids (MMVs) to identify each phase material, resulting in explicit geometric descriptions of the optimized composite structures and a reduction in the number of design variables. The decoupling between the topology description and finite element analysis of composite structures enables the removal of redundant degrees of freedom, thereby mitigating the convergence issue of finite deformation analysis caused by low-density elements and leading to significant computational savings. Numerical experiments of composite structures with two- and three-phase materials are optimized to validate the accuracy and efficiency of the proposed method. The results demonstrate that, under finite deformation, the distribution of each phase material in optimized 3D composite structures is significantly affected by the amplitude of external loads, and the optimized layout could be quite different from its counterpart under small deformation assumption.

Augmented Lagrangian approach for multi-objective topology optimization of energy storage flywheels with local stress constraints

Augmented Lagrangian approach for multi-objective topology optimization of energy storage flywheels with local stress constraints

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.

XFEM\\GFEM based approach for topology optimization of extruded beams with enhanced buckling resistance

In this paper, an efficient formulation for the topology optimization of extruded beams is developed considering linearized buckling, displacement, and stress constraints. The proposed method relies on a computationally efficient extended\\generalized finite element (XFEM\\GFEM) formulation for the forward problem, recently developed for the analysis of beams. In this method, a coarse 3D finite element (FE) mesh is enhanced with global enrichment functions, enabling a substantial reduction in the number of degrees of freedom with comparable accuracy to a traditional 3D FE fine mesh. The material distribution at the cross-section is optimized utilizing the material density approach with the Solid Isotropic Material with Penalization (SIMP) method.Our objective is to minimize the total weight of the beam, subject to performance constraints including buckling, displacement, and stress. The forward problem enables the application of general loading and boundary conditions. Thus, both buckling and lateral–torsional buckling are automatically considered. The optimization problem is solved using a gradient-based optimization approach, with analytical gradients derived by using the adjoint variable method. Several numerical examples are presented to investigate the accuracy and efficiency of the proposed formulation. A parametric study showed that the optimized cross-section is strongly dependent on the length and permissible buckling load. In addition, it is shown that a simultaneous formulation leads to significantly different designs, with different structural behavior, compared to results obtained by considering only a subset of the performance constraints. Finally, we verify the model on a beam warping problem under pure torsion, in which the cross-section optimization converges to a known analytical solution. Compared with traditional FEM, two orders of magnitude in terms of execution time are reported in favor of the proposed XFEM\\GFEM approach.

Three-Dimensional Material Mask Overlay Topology Optimization Approach With Truncated Octahedron Elements

Abstract This paper presents a 3D material mask overlay topology optimization approach using truncated octahedron elements and spheroidal masks. Truncated octahedron elements provide face connectivity between two juxtaposed elements, thus eliminating singular solutions inherently. A novel meshing scheme with Tetra-Kai-Decaheral or TKD (generic case of truncated octahedron) elements is proposed. The scheme is extended to parameterized generic-shaped domains. Various benefits of implementing the elements are also highlighted, and the corresponding finite element is introduced. Spheroidal negative masks are employed to determine the material within the elements. Seven design variables define each mask. A material density formulation is proposed, and sensitivity analysis for gradient-based optimization is developed. fminconmatlab function is used for the optimization. The efficacy and success of the approach are demonstrated by solving structures and compliant mechanism design problems. Compliance is minimized for the former, whereas a multi-criteria arising due to flexibility and stiffness measures is extremized for optimizing the mechanisms. Convergence of the optimization is smooth. The volume constraint is satisfied and remains active at the end of the optimization.

Eklemeli imal edilmiş gözenekli topolojilerin ısıl performansı üzerine deneysel incelemeler

Additive manufacturing enables researchers to form unique and unconventional topologies satisfying design compactness, improved efficiency, and lower cost. Design freedom introduced by the additive manufacturing reveals the idea of implementing the topology optimization approach into thermal systems. In this study, changes in thermal performance of three types of topologies: gyroid, hexagon (honeycomb), and rectilinear are experimentally investigated. In addition, porosity level of each topology is varied in between 25%, 50% and 75% to improve the impact of the study. The experimental results indicate that gyroid structures are thermally more efficient (up to 15.6%) than the remaining topologies. Furthermore, thermal diffusivities of the rectilinear and gyroid topologies with 25% porosity level are measured as the extremes, and it is detected that these structures propagate heat 1.1 times greater than the hexagon structure.

Inverse design of mechanical springs with tailored nonlinear elastic response utilizing internal contact

This work employs a contact-aware topology optimization approach for the design of nonlinear springs with a broad range of prescribed load–displacement responses in both tension and compression. By leveraging the third medium contact approach to model internal contact, this method enables the utilization of collision between parts to achieve the desired load–displacement response while minimizing material consumption. The effectiveness of the proposed computational design approach is demonstrated using axially loaded springs as a benchmark, but the proposed method is also applicable to more general cases, including the design of periodic nonlinear material microstructures and metamaterials.

STO-DAMV: Sequential topology optimization and dynamical accelerated mean value for reliability-based topology optimization of continuous structures

In deterministic topology optimization (TO), due to not taking into account the uncertainties of the structural system, explicitly, resulting optimal layouts may conclude in low reliable levels or unreliable optimum design conditions. The objective of reliability-based topology optimization (RBTO) is to integrate the reliability concept into topology optimization, finding the optimized structures priori by the designer through a mathematical framework guaranteeing that the least reliability level is achieved. In the present investigation under a constant volume fraction, the bisection algorithm is implemented for approximating the optimal feature of the structure in the TO framework by applying the moving iso-surface threshold (MIST) topology optimization approach. The results from the previous step are employed to consider uncertainties by a reliability analysis algorithm. A reliability analytical method based on dynamical accelerated formulation is combined with the TO-based bisection algorithm as a novel sequential topology optimization and reliability analysis (STORA) for RBTO. The descent condition is guaranteed in the dynamical accelerated mean value method to search the most probable point which is applied in TO for finding optimum layouts of continuous structure problems. A dynamical step factor in the reliability loop of the STORA and the MIST integration are applied to find the optimum layouts in the optimization loop. Illustrative examples are presented for validation and to maintain the capability of the proposed sequential topology optimization and dynamical accelerated mean value (STO-DAMV). Based on the results, it is demonstrated that the application of reliability analysis with the integration of bisection in topology optimization can produce a robust reliability analysis with stable results in RBTO which facilitates a more reliable design than that acquired by TO. It is also concluded that, under identical accuracy, STO-DAMV for STORA is improved in view of computational robustness.

Topology optimization approach for functionally graded metamaterial components based on homogenization of mechanical variables

The micron resolutions that 3D printers are reaching allow for a change of paradigm in the design of components, optimizing not only the topology of the component, but also the microstructure of the material, which can adopt different objectives at different locations in the component, reaching different mechanical properties and different optimal microstructures at those locations. This constitutes a flip in the design objectives to focus on tailored material work, aimed either at local objectives or at component-wide ones, instead of pursuing homogeneous material properties for global objectives. For this new concurrent structure-material design leading to optimized components made of functionally graded (FG) metamaterials, new topology optimization (TO) procedures are needed in which the objective is to obtain component-wise mechanical variables or distributions of these variables, rather than global component objectives as compliance, which is a typical objective of classical TO approaches.In this work we present a new TO approach aimed at FG metamaterial design pursuing homogeneous mechanical variables. We focus on homogenization of deformation level along the component by minimizing its standard deviation across the domain. The proposed formulation can be naturally generalized to anisotropy, nonlinear behavior, and other optimization objectives. Convergence to a suitable optimized solution, with a distribution of material properties resulting in a homogeneously deformed component, is obtained. These FG material properties may be obtained from local metamaterial design. Classical material/void configurations may also be obtained following our procedure, and results for such cases can be compared qualitatively to the Solid Isotropic Material with Penalization (SIMP) approach.

Improving the performance of a multi-material topology optimization model involving stress and dynamic constraints

In this study, an approach for multi-material topology optimization (MMTO) that addresses several distinct matters is proposed. The proposed formulation, which is based on the alternating active-phase algorithm (AAPA) and the Jacobi approach, can firstly deal with dynamic topology optimization. As a second execution, the method is used to resolve the strength-enhancing, globally applicable von Mises stress limitations. In addition, stress constraints are applied concurrently to the dynamic issues. As a result, the stability and strength of the structures are both improved at the same time. Thirdly, the eigenvalues shift approach and the modified interpolation scheme are proposed to prevent the mode switching and pseudo modes in the MMTO problem, respectively. Multi-material architectures with and without stress limitations reveal different optimum results for each frequency constraint. The design variables are required the method of moving asymptotes (MMA) for updating new design variables after main loop. Extensive numerical examples are given, and the authors highlight outstanding questions that are the focus of current studies.

Concurrent topology optimization of parts and their supports for additive manufacturing with thermal deformation constraint

A typical manufacturing failure in powder bed additive manufacturing (AM) is caused by the collision between the already printed structure and the powder recoater due to large thermal deformation. This paper presents a density-based topology optimization (TO) approach to concurrently design parts and their supports that are not susceptible to such a manufacturing failure. The thermal deformation during the layer-by-layer AM process is predicted based on an inherent strain method, and the top surfaces' upward deformations are constrained below the powder layer thickness to avoid recoater collision. To increase the design freedom of TO, the parts and their supports are composed of lattice unit cells with different volume fractions, whose effective stiffness matrixes are predicted by the numerical homogenization and surrogate models. Besides, an overhang constraint and a two-field-based length scale control formulation are also utilized, ensuring overall manufacturability. With the proposed approach, lightweight structures with optimized mechanical properties and controllable manufacturing qualities can be obtained. Numerical examples are given to demonstrate the effectiveness of the proposed approach.

Topology optimization of porous structures by considering acoustic and mechanical characteristics

Porous structures are widely found in nature and have been extensively studied due to their high stiffness-to-weight ratio, excellent sound absorption, and robustness regarding loading variation. This paper proposes a new topology optimization approach for the design of porous acoustic-mechanical structures based on the three-field floating projection topology optimization (FPTO) method. In order to capture the change of ambiguous structural boundary during topology optimization, the mixed displacement/pressure (u/p) finite element formulation with the linear material interpolation scheme is adopted. The artificial porous features of the structures are generated by imposing the local volume constraint defined by a constant or adaptive filter radius. The 0/1 constraints of the design variables are simulated by the floating projection constraint so that the final design has a clear topology. To verify the effectiveness of the proposed method, some interesting 2D and 3D numerical examples considering their mechanical and acoustic characteristics simultaneously are presented to achieve porous structures by minimizing dynamic compliance, possibly with an additional acoustic constraint. The results also show that the resulting porous features are useful in improving the acoustic performance of the optimized designs.