Structural Topology Optimization Research Articles

Adaptive scaled boundary finite element method for two/three-dimensional structural topology optimization based on dynamic responses

This paper presents an efficient solution for designing the topology of structures that can withstand dynamic loads. The method, called image/stereolithography (STL)-based adaptive scaled boundary finite element (SBFE), is a novel approach to topology optimization (TO) that is particularly effective for designing two/three-dimensional structures. The SBFE-based TO algorithm adopts a bi-evolutionary structural optimization (BESO) approach, which utilizes image/STL-based procedures to automatically adapt meshes and minimize mechanical compliance under varying volume fractions in the time domain. A key advantage of this approach is that it uses images of TO responses, rather than specific error functions, to guide the automatic adaptive mesh schemes. The method also incorporates a quadtree/octree mesh refinement to address the problem of hanging nodes, ensuring fast mesh convergence during the optimization process. Furthermore, a high-order implicit time integration technique provides a close approximation of equivalent static loads, allowing for the accurate mapping of displacement fields under actual dynamic responses at each time step. The effectiveness of this method is demonstrated through a variety of numerical examples and benchmarks.

Anisotropic Semicrystalline Homopolymer Dielectrics for High-temperature Capacitive Energy Storage.

High-temperature dielectric polymers are in high demand for powering applications in extreme environments. Here, we have developed high-temperature homopolymer dielectrics with anisotropy by leveraging the hierarchical structure in semicrystalline polymers. The lamellae have been aligned parallel to the surface in the dielectric films. This structural arrangement resembles the horizontal alignment of nanosheet fillers in polymer nanocomposites andnanosheet-like lamellae in block copolymers, which has been proven to provide the optimal topological structure for electrical energy storage. The unique ordering of lamellae in our dielectric films endue a significantly increased breakdown strength and a reduced leakage current compared to amorphous films. This novel approach of enhancing the capacitive energy storage properties by controlled orientation of lamellae in homopolymer offers a new perspective for the design of high-temperature polymer dielectrics.

Anisotropic Semicrystalline Homopolymer Dielectrics for High‐temperature Capacitive Energy Storage

High‐temperature dielectric polymers are in high demand for powering applications in extreme environments. Here, we have developed high‐temperature homopolymer dielectrics with anisotropy by leveraging the hierarchical structure in semicrystalline polymers. The lamellae have been aligned parallel to the surface in the dielectric films. This structural arrangement resembles the horizontal alignment of nanosheet fillers in polymer nanocomposites and nanosheet‐like lamellae in block copolymers, which has been proven to provide the optimal topological structure for electrical energy storage. The unique ordering of lamellae in our dielectric films endue a significantly increased breakdown strength and a reduced leakage current compared to amorphous films. This novel approach of enhancing the capacitive energy storage properties by controlled orientation of lamellae in homopolymer offers a new perspective for the design of high‐temperature polymer dielectrics.

Modified genetic algorithm for optimal design of truss structures

In this paper, topology and shape optimization of truss or frame structures is discussed. The optimization starts from a structure, into which a finite number of nodesare set; all the nodes are connected together by trusses in all possible variants. Unfit variants of the truss system are rejected. Two alternative ways of the optimization are compared: topology optimization starting from initial structure with a larger number of nodes, and topology optimization starting from initial structure with smaller number of nodes but with additional shape optimization of the obtained topology. The topology optimization is solved with original modified genetic algorithm, giving better results in comparison with classical genetic algorithm. Instead of further development of constraint system, the additional step is introduced into algorithm – purification of genotype, which allows complementary improvement of particular population individuals, and together for the optimization process retains more possibilities than stiffening of constraints. The shape optimization is solved by classical genetic algorithm. Both strategies effectively improve the solution, however the common topology/shape optimization requires less computer resources. All numerical examples are obtained with original software developed by the authors.

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

Multi-scale concurrent topology optimization of cellular structures with multiple microstructures for minimizing dynamic response in the time domain

This paper proposes a concurrent topology optimization method for optimizing the structures that are periodically filled with multiple microstructures excited by dynamic response in the time domain. At the macroscale, different microstructures are considered as different materials. To generate the various distribution of different microstructures, a multi-material interpolation approach based on the Solid Isotropic Material with Penalization (SIMP) is integrated. At the microscale, the energy-based homogenization method (EBHM) is employed to determine the macroscopic effective properties of the microstructures. All macroscale elements with identical material are represented by a distinct microstructure. For the proportional damping model, the HHT-α is implemented as a time integration technique to obtain the dynamic response of multi-scale and assumed multi-material structures. The objective function of the topology optimization problem is to minimize the mean dynamic compliance. Combined differentiate-then-discretize method with the adjoint variable method, the sensitivity analysis applies the gradient-based Zhang-Paulino-Ramos Jr. (ZPR) algorithm or Method of Moving Asymptotes (MMA) to update the design variables under multiple constraints in the time and space-discretized system. The proposed approach is numerically performed through 2D and 3D examples to demonstrate its effectiveness.

A New Strategy for Railway Bogie Frame Designing Combining Structural–Topological Optimization and Sensitivity Analysis

Rolling stock manufacturers are finding innovative structural solutions to improve the quality and reliability of railway vehicles components. Structural optimization processes represent an effective strategy for reducing manufacturing costs, resulting in geometries easier to design and produce. In this framework, the present paper proposes a new methodology to design a railway metro bogie frame, combining structural–topological optimization methods and sensitivity analysis. In addition, manufacturing constraints were included to make the component design suitable for production through sand-casting. A robust sensitivity analysis has highlighted the most critical load conditions acting on the bogie frame. Its effectiveness was verified by carrying out two different structural optimizations based on different loadings. Two equivalent designs were obtained. Computational times were positively reduced by about 57%. The maximum value of stress was reduced about 23%. This new methodology has shown encouraging results to streamline the design process of this complex mechanical system, allowing researchers to also include manufacturing requirements.

Multimaterial homologous topology optimization of large telescope structure under multiple elevation conditions

Multimaterial homologous topology optimization of large telescope structure under multiple elevation conditions

A T-splines-oriented isogeometric topology optimization for plate and shell structures with arbitrary geometries using Bézier extraction

Recently, the non-uniform rational B-splines (NURBS) have been considerably employed in modeling plate and shell structures, or developing the related size, shape or topology optimization methods for their design. However, the NURBS with the tensor product feature strongly hinders the effectiveness of the optimization on complex structures. The primary intention of the current research is to propose a new T-splines-oriented Isogeometric Topology Optimization (T-ITO) method and then address the critical design problem of plate and shell structures with arbitrary shapes in practical applications. Firstly, the Bézier extraction is utilized in the T-splines to map the geometrical model into a family of Bézier elements, each of which is presented by a local Density Distribution Function (DDF) for elementary topology. A global DDF is constructed by an assembly of all local DDFs with a natural connection to the present structural topology. Secondly, the T-splines-based IsoGeometric Analysis (T-IGA) formulation with the Bézier extraction for complex plate and shell structures is developed using the Kirchhoff-Love theory, where a universal numerical implementation framework is constructed, including the Rhino, MATLAB, export modules with all geometric information and import modules for the analysis. Thirdly, a mathematical formulation for plate and shell structures with arbitrary geometries is developed using the T-ITO method to improve structural loading-capability, and the sensitivity analysis with respect to design variables is rigorously derived in detail. Finally, several numerical examples of plate and shell structures with both regular and elaborate geometries are tested to demonstrate the validity, effectiveness, superiorities and indispensability of the T-ITO method.

Multi-scale design of composite material structures for maximizing fundamental natural frequency

This study deals with the topology optimization (TO) of linear elastic composite structures considering fundamental natural frequency maximization. The concept of functionally graded structures (FGS) is used for anisotropic composite material structure design to improve the structural dynamic performance. The rational approximation of material properties (RAMP) method was employed as an alternative to the solid isotropic material with penalization (SIMP) method to improve the convergence stability for eigen-frequency problem. In the SIMP method, the occurrence of local eigen-modes at low frequencies in the void region causes ill-convergence, whereas the RAMP method prevents local eigen-modes from occurring. The method of moving asymptotes is used as an optimizer. Numerical verification was performed for three structural types: cantilever beam, double-clamped beam, and four-pinned beam structure. In addition, for cantilever beam design, bi-objective optimization for maximizing fundamental natural frequency as well as minimizing structural compliance was performed using the adaptive weighting method that quantitatively reflects the designer's preference by adjusting the weight for each objective function at each iteration.

Body‐fitted topology optimization via integer linear programming using surface capturing techniques

AbstractRecent advancements in computational tools and additive manufacturing have expanded design possibilities on fluid devices and structures to also include aesthetics. However, traditional discrete density‐based topology optimization methods usually use square and cubic regular meshes, resulting in jagged contour patterns that require mesh refinement and post‐processing to numerical solution steps of complex physics problems. In this article, we propose a new isosurface boundary capture strategy for topology optimization in structural and fluid flow problems. The capture of smoothed boundaries is done via a simple strategy through element splitting and analysis domain remeshing. The smoothing procedure novelty lies on the optimizer regular mesh decomposition into smaller triangular or tetrahedral elements with a pseudo‐density nodal function that produces implicit geometry boundaries. We employ the TOBS‐GT (topology optimization of binary structures with geometry trimming) method to solve optimization problems for mean compliance and fluid flow energy dissipation, subject to a volume fraction constraint. Since, we perform discrete body‐fitted optimization, the material interpolation models are expressed in linear form without penalty factors. Our method produces a lower computational cost topology evolution with high resolution and mitigated sharp details, achieved via smooth edges and surfaces, as demonstrated through benchmark numerical examples in two‐ and three‐dimensional space. In addition, the proposed strategy facilitates the optimization of benchmark fluid flow examples for moderate Reynolds numbers.

Latent Diffusion Models for Structural Component Design

Recent advances in generative modeling, namely Diffusion models, have revolutionized generative modeling, enabling high-quality image generation tailored to user needs. This paper proposes a framework for the generative design of structural components. Specifically, we employ a Latent Diffusion model to generate potential designs of a component that can satisfy a set of problem-specific loading conditions. One of the distinct advantages our approach offers over other generative approaches is the editing of existing designs. We train our model using a dataset of geometries obtained from structural topology optimization utilizing the SIMP algorithm. Consequently, our framework generates inherently near-optimal designs. Our work presents quantitative results that support the structural performance of the generated designs and the variability in potential candidate designs. Furthermore, we provide evidence of the scalability of our framework by operating over voxel domains with resolutions varying from 323 to 1283. Our framework can be used as a starting point for generating novel near-optimal designs similar to topology-optimized designs.

Fail-safe topology optimization for a four-leg jacket structure of offshore wind turbines

Topology optimization (TO) has experienced substantial progress in both scholarly research and practical engineering applications. Recent years have witnessed extensive research on TO approaches incorporating the fail-safe concept, with a particular emphasis on potential failures. This paper proposes a TO methodology on the offshore wind turbine (OWT) jacket structure, focusing on the unexpected failure modes. The initial step involves constructing the formulation for maximum-minimization TO. A series of optimized structures can be generated by varying the sizes of individual damage populations and overall failure zones. A 5 MW OWT and jacket structure have been selected as the reference model. The external loads acting on the jacket structure are determined by given environmental conditions, as assessed using the DNV Bladed ™ package. The feasibility of an optimized structure is evaluated by comparing its static behaviors, such as maximum displacement and von Mises stress, to those of the reference structure. The investigation focuses on the fundamental frequencies of the optimized structure under various damage populations. The discovery demonstrates the superiority of the suggested methodology in the case of a potential failure.

An adaptive phase-field method for structural topology optimization

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the first-order optimality condition of the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.

Integrated topology and size optimization for frame structures considering displacement, stress, and stability constraints

Integrated topology and size optimization for frame structures considering displacement, stress, and stability constraints

Designing piezoelectric stretcher through multiphysics topology for enhanced photodynamic therapy in cancer treatment

This study presents an advancement in Photodynamic Therapy (PDT) by introducing piezoelectric stretchers designed to enhance tissue surface characteristics. With a focus on mitigating the impact of irregular tissue surfaces on light distribution, we propose a structural topology optimization method to design a stretcher that utilizes the piezoelectric effect for precise tissue stretching. The aim is to achieve uniform laser irradiance across treated tissue, thereby maximizing therapy efficiency. Our approach involves the formulation of finite element models that consider the piezoelectric effect and the elastic response in a multiphysics framework. Mesh convergence tests were conducted to strike a balance between accuracy and computational efficiency in evaluating the designed piezoelectric stretcher. The investigation into the application of piezoelectric stretchers for enhancing laser irradiance on non-uniform tissue reveals significant improvements in surface uniformity with increasing electric potential. Notably, the disparity between regions of high laser focusing and defocusing decreases as the stretcher expands, achieved through the application of higher voltages. The observed enhancement from no expansion to full expansion is quantified at 31 %. The implementation of electrically driven piezoelectric tissue expansion results in a more uniform tissue surface, leading to an augmentation of laser irradiance. In the absence of expansion, distinct areas of laser focus and near-zero irradiance are noted. Conversely, an increased potential yields a predominantly even surface, with 100 % extension achieving commendable laser irradiance uniformity.

Stress-based bi-directional evolutionary topology optimization for structures with multiple materials

Stress-based bi-directional evolutionary topology optimization for structures with multiple materials

Reformulation for stress topology optimization of continuum structures by floating projection

Stress topology optimization of continuum structures is an important topic for structural design and has been widely investigated. However, stress topology optimization itself is ill-conditioned and the resulting optimized designs highly depend on the used parameters, mesh size, and so on. In this paper, stress minimization and stress-constrained topology optimization problems are reformulated by introducing a global measure of an optimized design, the average solid stress. The floating projection topology optimization method is established with ε-relaxation and the p-norm function. Due to the modified problem formulations, the optimized design becomes insensitive to the selection of p in the p-norm function once p is large enough, such as p=16, to ensure the total elimination of stress concentration. Numerical results show the uniform stress distribution of optimized designs, demonstrating the effectiveness of the proposed method. Some findings on the elimination of stress concentration, mesh-independent optimized topology, equivalent smooth design, and impractical design are presented and discussed.

Finite element analysis and optimization design of large vibrating screen based on equivalent static load method

Vibrating screens have wide applications in various industries, ranging from agriculture to coal mining. In recent years, improvement in production have put forward higher requirements on the efficiency of vibrating screens. However, these large screens are prone to fatigue damage, particularly crack formation, over time. The emergence of substantial dynamic inertial forces can be attributed to the considerable body mass of a large vibrating screen. This study analyzed the structural strength of the HZXZ200x300 large vibrating screen, employing finite element simulation to identify the maximum equivalent stress and primary stress distribution. The main frame model of the vibrating screen box was constructed by integrating the equivalent static load and submodule methods. The model transitioned from dynamic response to static optimization under equivalent static and dynamic loads, significantly reducing calculation scale and enhancing optimization efficiency. Equivalent static sub-models were employed for topology optimization, determining the optimal structure for material performance distribution. This process yielded an optimal conceptual model for reconstructing the actual model. The structural strength was further improved by comparing three-dimensional and dynamic local stress relationships post-topological optimization, followed by reinforcing the vibrating screen structure and introducing reinforced bars for increased stability. The study showed that lightweight topology optimization significantly decreased the stress levels and improved the fatigue durability of beams. Local strengthening, accomplished via topology optimization, effectively reduced the maximum equivalent stress to 76.487 MPa, a decrease of 46.8%. The vibrating screen mass also decreased by 225 kg, a reduction of 14.9%. In summary, this study employed structural analysis, topology optimization, and local reinforcement to mitigate stress levels, enhance the fatigue life of a vibrating screen, and reduce its weight. This study offers an effective solution to the dynamic optimization challenges of complex structures.

Algorithms of isogeometric analysis for MIST-based structural topology optimization in MATLAB

Algorithms of isogeometric analysis for MIST-based structural topology optimization in MATLAB