Material Topology Optimization Research Articles

Topology optimization framework for thermoelastic multiphase materials under vibration and stress constraints using extended solid isotropic material penalization

This paper proposes a multiphase material topology optimization (MMTO) method for thermal–mechanical structures that takes into account the effect of the temperature field under stress and frequency constraints. Thermoelastic coupling occurs when an engineering structure is concurrently subjected to thermal and mechanical loads. This work focuses on the following: (1) the derivation of three interpolation schemes that use stress, dynamic, and thermal loads based on the extended solid isotropic material penalization (SIMP) method; (2) the incorporation of stress and dynamic constraints of multi-material thermal-elastic structural designs; and (3) the effective control of the impact of thermal loads on structures based on stress and frequency levels. Numerical experiments show that a clear distinction exists in the final topologies for mechanical and thermal loads among materials. Coupled and uncoupled mechanical and thermal behaviors can be predicted using finite element models based on materials’ coefficients of thermal expansion. We see this method is capable of optimizing a structure’s strength and stability while solving the issue of a thermal environment. In addition, it allows for the precise management of stress and vibration levels when structures are not exposed to a thermal environment.

Strength-to-Weight Optimization of Driver Shafts: A Comparative Analysis of Material Selection, Manufacturing Methods, Generative Design, and Topology Optimization using Fusion 360

This study presents a comprehensive comparative analysis of strategies for optimizing the strength-to-weight ratio of driver shafts in automobile applications. The research focuses on four key areas: material selection, manufacturing methods, generative design, and topology optimization. Firstly, a range of materials commonly used in driver shaft manufacturing is evaluated, considering factors such as strength, weight, durability.. Various manufacturing methods, including traditional techniques and advanced processes like additive manufacturing, are assessed for their impact on shaft performance. The study also delves into the application of generative design and topology optimization techniques. Generative design algorithms are employed to explore innovative shaft geometries that enhance structural integrity while minimizing weight. Topology optimization algorithms are utilized to optimize material distribution within the shaft, further improving strength-to-weight characteristics. The findings highlight the potential benefits of integrating advanced design methodologies with appropriate material selection and manufacturing processes. This research contributes valuable insights for optimizing driver shafts, enhancing automobile performance, and achieving efficient utilization of materials in automotive engineering. Key Words: Driver Shaft design, Strength and weight optimization, Generative Design, Topology Optimization, Material and manufacturing Consideration.

Design of the multiphase material structures with mass, stiffness, stress, and dynamic criteria via a modified ordered SIMP topology optimization

This paper, a multi-material topology optimization method (MMTO) is presented for two-dimensional structures using modified ordered solid isotropic material with penalization (SIMP) under multiple constraints such as mass, stiffness, frequency, and stress. The element density is obtained by a density filtering and the Heaviside approximation, which are combined to avoid gray elements and numerical issues of stress. Effective improvement of multiphase material topology optimization was performed including the criteria for stiffness, stress, and free vibration. P-norm stress aggregation is employed to calculate the maximum von Mises stress and sensitivity of von Mises stress is formulated by the adjoint method. The natural frequency and stress constraints are solved simultaneously to enhance the stability and reduce the stress concentration of the optimized structures, which are not much covered in the literature. The multi-mode phenomenon in the eigenfrequency problem is treated by the simply proposed technique. Results indicate that the multi-material designs with multi-constraints can be illustrated and optimized effectively. The optimized topologies, for stress minimization, indicate that the maximum stress can be significantly reduced compared with compliance minimization. The maximum von Mises stress of the topological results considering the maximum stiffness with natural frequency and mass constraints is higher than that maximum stiffness with only mass constraints, which indicates that the optimized structure created considering the eigenvalues is safer. The proposed approach can obtain a reasonable result that effectively controls the stress level and reduces the stress concentration at the high stress regions of multi-phase material structures with multi-constraints. Benchmark numerical examples are presented to confirm the effectiveness of the presented method.

A Note on Redesign Material Substitution and Topology Optimization in a Lightweight Robotic Gripper

The gripper is required because it is the portion of the robot that makes direct contact with the object being grasped. It should weigh as little as possible without compromising functionality or its performance. This study aims to reconsider the construction of a lightweight robotic gripper by modifying the gripper's materials and topology. Using the finite element (FE) method, several types of gripper materials were evaluated for static stress. On the basis of the results of the FE analysis, the optimal material candidate was chosen using the weighted objective method. Using the Fusion 360 software, the topology of the selected material was then optimized in an effort to achieve the 40% weight reduction’s objective. In addition, the suggested optimized geometry is then fine-tuned so that it can be manufactured as efficiently as possible. The final step in the validation of the robotic gripper's design was stress static analysis. The revised gripper design has a mass of 0.08 kg, a reduction of 94% from the original mass, and a safety factor of 3.67%, which satisfies the desired level of performance for the robotic gripper. Utilizing different materials and optimizing the gripper's topology can significantly reduce the overall mass of a robotic gripper.

Biomimetic Design and Topology Optimization of Discontinuous Carbon Fiber-Reinforced Composite Lattice Structures

The ever-increasing requirements for structural performance drive the research and development of lighter, stronger, tougher, and multifunctional composite materials, especially, the lattice structures, heterogeneities, or hybrid compositions have attracted great interest from the materials research community. If it is pushed to the extreme, these concepts can consist of highly controlled lattice structures subject to biomimetic material design and topology optimization (TO). However, the strong coupling among the composition and the topology of the porous microstructure hinders the conventional trial-and-error approaches. In this work, discontinuous carbon fiber-reinforced polymer matrix composite materials were adopted for structural design. A three-dimensional (3D) periodic lattice block inspired by cuttlefish bone combined with computer modeling-based topology optimization was proposed. Through computer modeling, complex 3D periodic lattice blocks with various porosities were topologically optimized and realized, and the mechanical properties of the topology-optimized lattice structures were characterized by computer modeling. The results of this work were compared with other similar designs and experiments to validate the effectiveness of the proposed method. The proposed approach provides a design tool for more affordable and higher-performance structural materials.

A generalized discrete fiber angle optimization method for composite structures: Bipartite interpolation optimization

AbstractThis paper proposes a novel fiber angle optimization method for composite, termed bipartite interpolation optimization (BIO), to address high‐dimensional design variables and inefficient fiber orientation optimization. The weighting functions of BIO are constructed with the help of multiphase material topology optimization approach. Various permutations and combinations of n design variables are utilized to represent 2n discrete candidate angles. Since the weighting functions of the way automatically satisfy the sum constraint, it is unnecessary to address the sum constraints during the optimization process. Compared with the traditional discrete material optimization strategy and solid isotropic material with penalization scheme, the BIO method reduces the dimension of the mathematical model for optimizing fiber angles. Compared to the shape functions with penalization scheme, the BIO method can be extended to the optimization problem of 2n candidates. Numerical examples of different types demonstrate that the proposed method has higher solution efficiency in the optimization problem of fiber orientation selection and is suitable for three‐dimensional shell optimization problems. It provides a new technical means for the structural optimization design of composite laminates.

Multi material topology and stacking sequence optimization of composite laminated plates

Multi material topology and stacking sequence optimization of composite laminated plates

Modular-topology optimization of structures and mechanisms with free material design and clustering

Topology optimization of modular structures and mechanisms enables balancing the performance of automatically-generated individualized designs, as required by Industry 4.0, with enhanced sustainability by means of component reuse. For optimal modular design, two key questions must be answered: (i) what should the topology of individual modules be like and (ii) how should modules be arranged at the product scale? We address these challenges by proposing a bi-level sequential strategy that combines free material design, clustering techniques, and topology optimization. First, using free material optimization enhanced with checkerboard suppression, we determine the distribution of elasticity tensors at the product scale. To extract the sought-after modular arrangement, we partition the obtained elasticity tensors with a novel deterministic clustering algorithm and interpret its outputs within Wang tiling formalism. Finally, we design interiors of individual modules by solving a single-scale topology optimization problem with the design space reduced by modular mapping, conveniently starting from an initial guess provided by free material optimization. We illustrate these developments with three benchmarks first, covering compliance minimization of modular structures, and, for the first time, the design of non-periodic compliant modular mechanisms. Furthermore, we design a set of modules reusable in an inverter and in gripper mechanisms, which ultimately pave the way towards the rational design of modular architectured (meta)materials.

Study on two-phase material topology optimization for transient heat conduction

Study on two-phase material topology optimization for transient heat conduction

Functionally Graded Materials Beams Subjected to Bilateral Constraints: Structural Instability and Material Topology

In recent years, the study of Functionally graded materials (FGM) opened exciting new venues for the control and manipulation of engineered materials and structures. In this study, we investigate bilaterally constrained FGM beams with programmable material functions. The FGM beams are fabricated using 3D printing techniques, and tested t understand the behavior of structural instability (i.e., postbuckling) under the bilateral confinements. Theoretical and numerical models are developed to investigate the postbuckling response, and the results are compared to experimental observations with satisfactory agreements. Material topology optimization is then carried out to investigate the influences of the material functions on the release of the stored energy during the bucking mode transitions in the FGM beams. It is found that stored energy variations can be used to optimize the material functions, which allows for the guided design of bi-walled FGM beams with well-defined controllability over the structural instability. The reported bilaterally constrained FGM beams with optimized material functions can be used in a multitud of different applications.

Multi-phase Material Topology Optimization Design of Heat Dissipation Structures Considering Topology-dependent Heat Sources

Multi-phase Material Topology Optimization Design of Heat Dissipation Structures Considering Topology-dependent Heat Sources

An incremental form interpolation model together with the Smolyak method for multi-material topology optimization

An incremental form interpolation model integrated with the anisotropic Smolyak method and the Non-Uniform Rational B-Spline (NURBS) method is proposed for multiple material topology optimization. Only a single category of design variables is exploited to characterize the material properties for any number of material types and the Smolyak method embedded within the NURBS method is devised to represent the topology density field while keeping the number of polynomials to a minimum, leading to a significant reduction in the number of design variables. An arbitrary number of volume and/or mass constraints can be implemented with the introduction of the characterization function to indicate the existence information for each material. Finally, the effectiveness of the proposed methodology is illustrated by three numerical examples.

Topology optimization of the microstructure of solid oxide fuel cell cathodes

Thermal mismatch significantly influences the stress state and lifetime of solid oxide fuel cells (SOFCs). The microstructure of the LSM–YSZ cathode is optimized by using the asymptotic homogenization method and three-phase material topology optimization to improve thermal mismatch. Two orthogonal microstructures are obtained by taking minimum thermal mismatch as the object with some constraints. The microstructures constitute a cathode in the form of periodic fiber bundles. Results show that the coefficients of the thermal expansion of the microstructures are almost equal to those of the electrolyte layer at different temperatures, thus eliminating thermal mismatch. The microstructures have higher effective ion conductivity than typical cathodes. The optimization results are helpful for the design of future electrodes.

Multiphase material topology optimization of Mindlin-Reissner plate with nonlinear variable thickness and Winkler foundation

In typical, structural topology optimization plays a significant role to both increase stiffness and save mass of structures in the resulting design. This study contributes to a new numerical approach of topologically optimal design of Mindlin-Reissner plates considering Winkler foundation and mathematical formulations of multi-directional variable thickness of the plate by using multi-materials. While achieving optimal multi-material topologies of the plate with multi-directional variable thickness, the weight information of structures in terms of effective utilization of the material at the appropriate thickness location may be provided for engineers and designers of structures. Besides, numerical techniques of the well-established mixed interpolation of tensorial components 4 element (MITC4) is utilized to overcome a well-known shear locking problem occurring to thin plate models. The well-founded mathematical formulation of topology optimization problem with variable thickness Mindlin-Reissner plate structures by using multiple materials is derived in detail as one of main achievements of this article. Numerical examples verify that variable thickness Mindlin-Reissner plates on Winkler foundation have a significant effect on topologically optimal multi-material design results.

Integrated design of structure and anisotropic material based on the BESO method

An Integrated structural and material topology optimization method considering optimal material orientation is presented based the on bi-direction evolutionary structural optimization (BESO) method. It is assumed that the macrostructure is composed of uniform cellular material but with different orientation. The homogenization method is used to calculate the effective material properties which builds a connection between material and structure. The continuous material orientation design variables and the discrete topology design variables are treated hierarchically in an iteration. The principal stress method is adopted and embedded to determine the optimal material orientation, meanwhile the topologies of the macrostructure and its material microstructure are concurrently optimized by using the BESO method. Numerical examples are conducted to demonstrate the effectiveness of the proposed optimization algorithm.

Topological Optimal Material Design of Structures with Moved and Regularized Heaviside Function

This study presents a new regularized penalty form to carry out material topology optimization of structures. In general, the regularization form of typical SIMP has been used to reduce material discontinuity of densities which describe boundaries of finite elements and finally provide numerical stability in sensitivity analysis of optimization procedures and the problem of 0–1 formulation. However, optimal solutions of the regularized SIMP depend on penalty parameters such as typical SIMP, since penalty relation of Young’s modulus and density of regularized SIMP is similar to that of typical SIMP in spite of regularization. In this paper, the penalty relationship between Young’s modulus and material density of typical SIMP becomes extended by multiplying it with a moved and regularized form of a material indication function, i.e., Heaviside function. The new penalization method does not depend on filter methods for free-checkerboards; therefore, computational savings can be obtained. Numerical examples demonstrate that the incorporation of moved and regularized Heaviside function in the SIMP leads to convergent solutions with clear boundaries between materials and no materials and without checkerboard patterns.

Damping material distribution analysis for structural-acoustic optimization

The damping material topology optimization problem of structural-acoustic radiation is discussed. According to the artificial material hypothesis, a novel optimization approach of the damping materials distribution method is introduced. The mathematical formulation about damping material topology optimization is established. Finally, a hexahedral box structures for example, the distribution topology optimization method is illustrated. With topology optimization, material conversion between damping and artificial materials is achieved. Numerical results indicate that the proposed artificial material hypothesis for topology optimization is effective and feasible.

A novel artificial dual-phase microstructure generator based on topology optimization

The mechanical properties of dual-phase (DP) steel are mostly derived from its microstructure, e.g., volume fraction, size, distribution and morphology of each constituent phase. An artificial microstructure generator with an enhanced novel phase assignment algorithm based on material topology optimization is proposed to investigate the mechanical properties of DP steel. With this algorithm, phase assignment process is performed on a modified Voronoï tessellation to achieve the targeted representative volume element (RVE) with a good convergence. This method also includes a proper orthogonal decomposition (POD) reduction of flow curves (snapshots) to identify the optimal controlling parameters for DP steel. This numerical method significantly improves the representation of the generated RVE with low computational cost. The proposed method is verified using a DP590 steel which indicates a good agreement with experimental material behavior and RVE predictions based on real microstructures. Predictions of plastic strain patterns including shear bands using the artificial microstructure closely resemble the actual material behavior under similar loading conditions. Robustness of this approach provides a new dimension for RVE development based on artificial microstructure which can effectively be implemented in material characterization.

Evaluation of Optimized Topology Design of Cross-Formed Structures with a Negative Poisson’s Ratio

This study presents an application of the material topology optimization approach using Gauss point density as a design variable in order to mechanically investigate and then design material possessing structures constructed by materials with a negative Poisson’s ratio. Materials with a positive Poisson’s ratio are commonly utilized for structures. However, the materials are more fragile than those of negative Poisson’s ratio with respect to impact resistance or tolerance. The topological optimal results provide basic and mechanical information to develop the materials with a negative Poisson’s ratio. Numerical examples of cross-formed structures such as beam-to-column connections demonstrate the efficiency of topology optimization tool in order to analyze materials with positive and negative Poisson’s ratios.

Simultaneous parametric material and topology optimization with constrained material grading

We consider the problem of parametric material and simultaneous topology optimization of an elastic continuum. To ensure existence of solutions to the proposed optimization problem and to enable the imposition of a deliberate maximal material grading, two approaches are adopted and combined. The first imposes pointwise bounds on design variable gradients, whilst the second applies a filtering technique based on a convolution product. For the topology optimization, the parametrized material is multiplied with a penalized continuous density variable. We suggest a finite element discretization of the problem and provide a proof of convergence for the finite element solutions to solutions of the continuous problem. The convergence proof also implies the absence of checkerboards. The concepts are demonstrated by means of numerical examples using a number of different material parametrizations and comparing the results to global lower bounds.