Structural Topology Optimization Research Articles

Isogeometric Topology Optimization of Multi-patch Shell Structures

Shell structures refer to structural elements that derive strength and load-bearing capacity from their thin and curved geometry. In practical applications, shell structures are commonly composed of multiple patches to represent intricate and diverse architectural configurations faithfully. Nevertheless, the design of multi-patch shell structures holds considerable promise. However, most of the previous work is devoted to the numerical analysis of multi-patch shell structures without further optimization design. The work proposes an inverse design framework, specifically focusing on multi-patch configurations based on Reissner–Mindlin theory. First, reparameterization and global refinement operations are employed on the provided multi-patch shell structures. Renumbering the indices of control points with shared degrees of freedom at the interface naturally ensures C0-continuity between patches. Subsequently, this study investigates the amalgamation of Isogeometric Analysis (IGA) and the Solid Isotropic Material with Penalization (SIMP) method for topology optimization of shell structures. The proposed approach is validated through numerical examples, emphasizing its capacity to enhance multi-patch shell structure design, showcasing robustness and efficiency.

Efficient strategy for topology optimization of stochastic viscoelastic damping structures

In this study, the dynamic topology optimization (TO) of stochastic viscoelastic damping structures (VDSs) is performed for the first time. However, the expensive computation cost seriously hinders the TO process. To address this problem, an efficient strategy is proposed. On the one hand, in the stochastic structural response analysis, a fully adaptive method based on direct probability integral method is presented to determine the number and locations of samples. Meanwhile, to improve the computational efficiency of structural response for each sample, a piecewise model-order reduction method based on Krylov subspace is adopted to generate the orthonormal basis and project the original large-scale system onto a low-order system. On the other hand, to overcome the optimization challenge arising from large number of design variables in the density-based topology method, a material-field series-expansion method is employed to describe the topology layout and significantly reduce the number of design variables. Moreover, the sensitivity of the optimization model is derived by the adjoint method and the method of moving asymptotes (MMA) is used to efficiently update the design variables. Some numerical examples comprehensively demonstrate the effectiveness and efficiency of the proposed strategy. The results indicate that the uncertainty of structural parameters greatly affect both the topology layout of VDS and vibration damping capacity.

Topology optimization of anisotropic structure for arbitrary objective functionals with exact free boundary representation

A new approach to performing sensitivity analysis of arbitrary objective functionals for anisotropic elasticity is proposed in this work. Three different objective functionals have been considered, and good agreement is achieved between derived topological derivatives and numerical ones. Following the verification of topological derivatives, structural topology optimizations for selected anisotropic problems are conducted. To efficiently achieve the exact free boundary representation, our Finite Element Method (FEM)-based optimization comprises two loops. In the initial loop, a fixed and coarse mesh is employed to solve the anisotropic problem and update the level-set function. Once this loop concludes, the second loop reconstructs the material domain, ensuring an exact boundary representation. The convergence of the second loop is facilitated by (1) utilizing topological derivatives instead of explicit derivatives of ϕ (similar to density derivatives) and (2) imposing the exact volume constraint on the Reaction-Diffusion Equation (RDE)-based level-set method. Moreover, we introduce a scheme to prevent structural breakdown, allowing for the standalone implementation of Loop 2 always with exact free boundary representation. The previously proposed algorithm for the exact volume constraint has been generalized to accommodate inequalities, resulting in an acceleration of the equivalent optimization process.

Topology optimization of incompressible structures subject to fluid–structure interaction

In this work, an algorithm for topology optimization of incompressible structures is proposed, in both small and finite strain assumptions and in which the loads come from the interaction with a surrounding fluid. The algorithm considers a classical block-iterative scheme, in which the solid and the fluid mechanics problems are solved sequentially to simulate the interaction between them. Several stabilized mixed finite element formulations based on the Variational Multi-Scale approach are considered to be capable of tackling the incompressible limit for the numerical approximation of the solid. The fluid is considered as an incompressible Newtonian fluid flow which is combined with an Arbitrary-Lagrangian Eulerian formulation to account for the moving part of the domain. Several numerical examples are presented and discussed to assess the robustness of the proposed algorithm and its applicability to the topology optimization of incompressible elastic solids subjected to Newtonian incompressible fluid loads.

Multi-feature parallel topology optimization of fiber-reinforced coated structures based on a dual variable scale filtering method

Due to their outstanding mechanical properties, fiber-reinforced polymer composite (FRPC) structures have become a prominent research topic. Yet, to surpass existing performance limits, their design potential should be expanded beyond conventional empirical methods. Moreover, because of the high manufacturing costs, the protection of FRPC structures should be considered in the design phase to extend their service life. In this paper, we introduce an innovative configuration wherein metal coatings are strategically applied to the surfaces of FRPC structures. This technique aims to protect the internal matrix and fiber materials, and to inhibit the interlaminar delamination of composite laminates. Then, a corresponding full-scale topology optimization framework is built based on a density-based method. The coating, matrix, and fiber materials are considered collectively, avoiding issues such as excessive computation, non-convex optimization, and fiber discontinuity. Furthermore, a dual variable scale filtering (DVSF) method and its simplified scheme are presented to optimize coating thickness based on the physical information obtained from finite element analysis. Meanwhile, the co-evolution of solid topology and fiber morphology, driven by algorithms, facilitates the parallel optimization of multiple geometric features. Several typical examples, including wing ribs, are provided to illustrate the effectiveness and superiority of our approach, highlighting its engineering relevance.

Structural Strength Analysis and Optimization of Commercial Aircraft Nose Landing Gear under Towing Taxi-Out Conditions Using Finite Element Simulation and Modal Testing

In the field of civil aviation, the nose landing gear is a critical component that is prone to damage during taxiing. With the advent of new technologies such as towing taxi-out and hub motors, the nose landing gear faces increasingly complex operational environments, thereby imposing higher performance demands. Ensuring the structural safety of the nose landing gear is fundamental for the successful application of these technologies. However, current research on aircraft nose landing gear under these new conditions is somewhat lacking, particularly in terms of reliable analysis models for real-world scenarios. This study focuses on a typical Class C aircraft, specifically the B-727 model, for which a finite element model of the nose landing gear is developed. Modal testing of the aircraft’s nose landing gear is conducted using the impact hammer method, and the results are compared with those from the simulations. The experimental data indicate that the error range for the first seven natural frequencies is between 0.23% and 9.27%, confirming the high accuracy of the developed landing gear model. Furthermore, with towing taxi-out as the primary scenario, a dynamic model of the aircraft towing system is established, and an analysis on the structural strength and topological optimization of the nose landing gear under various conditions, including high speeds and heavy loads, is performed. The results show that the developed model can effectively support the analysis and prediction of the mechanical behavior of the nose landing gear. Under high-speed, heavy-load conditions, the nose landing gear experiences significantly increased loads, with the maximum deformation primarily occurring at the lower section of the shock strut’s outer cylinder. However, no damage occurred. Additionally, under these conditions, an optimized structural design for the landing gear was identified, which, while ensuring structural strength, achieves a 22.32% reduction in the mass of the outer cylinder, also ensuring safety in towing taxi-out conditions.

A novel binomial strategy for simultaneous topology and size optimization of truss structures

The current work introduces a new probability-based regulatory mechanism for the simultaneous size and topology optimization of truss structures. The proposed mechanism, by leveraging the Boolean nature of the topological variables, attempts to forecast the behaviour of the search algorithm and emphasizes either topology or size actions to reduce the number of ineffective iterations. The importance of this task becomes more evident in further iterations since the optimal (or nearly optimal) structure topology is identified, and improper elimination of any member can result in infeasible mechanisms and lead to a waste of several iterations. To assess the effectiveness of the proposed auxiliary module, it is integrated with different optimization algorithms to solve distinct size and topology problems. The results demonstrate that this not only enhances the accuracy of the algorithms but also significantly reduces the required computational cost.

Anisotropic Semicrystalline Homopolymer Dielectrics for High‐Temperature Capacitive Energy Storage

AbstractHigh‐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.

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.

Robust topology optimization for multi-material structures considering material uncertainties

Multi-material structures have attracted more and more attention from scholars and engineers, because they usually have good composite performance. Uncertainty factors are ubiquitous in practice, especially for material uncertainties. Multi-material structures contain many materials with different properties, material uncertainties will affect the allocation of material usage, thereby affecting structural performance. Therefore, it is crucial to consider material uncertainties in the design of multi-material structures. This paper detailedly explores the impacts of elastic modulus uncertainty and Poisson's ratio uncertainty on the design of multi-material structures. The topology optimization is to minimize the compliance subjected to a mass constraint, where multiple materials can be freely allocated during the optimization. Floating projection topology optimization is adopted to search for the structural topologies, and robust sensitivity information is derived. For the quantification of material uncertainties, this paper introduces a non-intrusive polynomial chaos expansion (PCE) method to implicitly quantify them, the computational efficiency and accuracy in PCE is compared with the classical Monte Carlo method. Finally, topology optimization examples are provided to demonstrate the effects of elastic modulus uncertainty, Poisson's ratio uncertainty and hybrid uncertainty on the design of multi-material structures.

Topological optimization of ballistic protective structures through genetic algorithms in a vulnerability-driven environment

Reducing the vulnerability of a platform, i.e., the risk of being affected by hostile objects, is of paramount importance in the design process of vehicles, especially aircraft. A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats. However, this type of solution can lead to a significant increase in weight, affecting the performance of the aircraft. For this reason, it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight. One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures. Among the many optimization techniques available in the literature for this purpose, multi-objective genetic algorithms stand out as promising tools. In this context, this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms, aiming to simultaneously minimize the weight of protective structures and vulnerability. In addition to the use of the in-house software, which itself represents a novelty in the field of topology optimization of structures, the method incorporates a custom mutation function within the genetic algorithm, specifically developed using a graph-based approach to ensure the continuity of the generated structures. The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects, namely bullets and fragments from detonating objects. The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.

Linear and nonlinear topology optimization of origami structures based on crease pattern and axial rigidity

Linear and nonlinear topology optimization of origami structures based on crease pattern and axial rigidity

Isogeometric topology optimization of structures using the overweight approach

In this paper, a 2D isogeometric formulation of the material distribution for structural topology optimization considering minimum weight and local stress constraints using the overweight approach is proposed. The aim of this isogeometric formulation is to provide solutions with high spatial definition using a lower number of design variables in comparison with the formulations previously developed to define the material layout. Despite of this, an important number of local stress constraints has to be considered in the solution of the problem. For this purpose, an Overweight Constraint is used to consider all of them. The structural analysis is performed by means of the Isogeometric Analysis (IGA) and the distribution of material is modeled by means of quadratic B-splines. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP) that is driven by the information provided by a full first-order sensitivity analysis extension of the IGA formulation. Finally, the proposed formulation is tested by means of some benchmark problems, and the results show that the isogeometric formulation provides solutions with high spatial definition. A comparison with a Finite Element Method (FEM) topology optimization formulation is included.

Mapping structural topology optimization problems to quantum annealing

Mapping structural topology optimization problems to quantum annealing

Thermo-Mechanical Optimization of Die Casting Molds Using Topology Optimization and Numerical Simulations.

Conventional cooling channels used in die casting molds exhibit significant drawbacks, resulting in extended cooling times for cast parts. Issues such as the formation of dirt, limescale, and corrosion substantially diminish the thermal efficiency of these channels, leading to challenges in achieving uniform cooling and potential quality issues. In response to these challenges, this study proposes Topology Optimization as a novel approach. It involves designing cooling structures through Topology Optimization to replace traditional cooling channels, incorporating both Discrete and Gaussian boundary conditions to optimize thermal efficiency. Additionally, Structural Topology Optimization is employed to ensure structural integrity, preventing deformation or yielding under high loads during the die casting process. Numerical analysis revealed superior thermal performance compared to conventional channels, particularly when subjected to Discrete and Gaussian boundary conditions. Furthermore, the application of the latter establishes conformal cooling and minimizes temperature gradients in the casting, reducing casting defects such as shrinkage porosity. These findings highlight the efficacy of Topology Optimization in addressing the challenges of traditional cooling methods, with wide-ranging implications for manufacturing processes utilizing permanent molds for shaping materials.

Computational investigations for topology optimization of UAV and small-scale aircraft wings

This study was conducted under the 4R-UAV project. The project is funded by the Latvian Council of Science with the goal of creating an innovative, aerodynamically improved, environmentally friendly, zero waste, and zero emission UAV. For the Circular Aviation 4R (Reduce, Recycle, Reuse, Redesign) concept, this paper covers two Rs (Reduce and Redesign) aspects of the 4R-UAV project. Topology optimization of structures has gained enormous potential with the advances in additive manufacturing techniques. However, it is still challenging when it comes to conventional manufacturing. Aircraft/UAV wings are conventionally hollow structures and leave almost little or no space for further material removal. It becomes even more complicated when conventional manufacturing limitations are further imposed. Nevertheless, topology optimization is indeed an excellent way of reducing the mass of the structures by keeping the mechanical strength intact. This computational study attempts to implement topology optimization on a small-scale aircraft aluminum alloy wing as well as on a carbon composite UAV wing. In order to ensure the feasibility of not only additive manufacturing but also conventional manufacturing, controlled/limited topology optimization was applied only to the ribs of the wings. It was found that topology optimized wing ribs (aluminum and carbon composite) demonstrated a 20% mass reduction while up to 10% overall mass reduction of the wings was achieved. Moreover, after the topology optimization, the wings demonstrated improved mechanical characteristics and factor of safety. The knowledge learned from this study will be implemented for the topology optimization of the future small-scale 4R-UAV wings which will be mainly manufactured using additive manufacturing.

Multi-scale collaborative prediction of optimal configuration for carbon fiber woven composites based on deep learning neural networks

Since carbon fiber woven composite panels contain complex fiber bundle structures, the aim of this paper is to investigate the factors influencing the macro-equivalent properties and topological flexibility of composite panels resulting from variations in fiber bundle configuration. Firstly, the structural topology optimization design of carbon fiber composite plates was achieved using a multi-scale modeling approach with the variable density method. Nonlinear relationships between carbon fiber bundle configuration parameters and macroscopic equivalent properties, as well as macroscale topological flexibility, were determined using deep learning methods, respectively. The maximum error in the predicted values of the deep learning network model does not exceed 0.5% when compared with the results of the finite element calculations. In addition, utilizing deep learning networks to predict macro-equivalent properties of composites can significantly decrease computational time. The impact of varying the number of filaments in fiber bundles and the spacing of the fiber bundles on the flexibility of the topology was determined using a deep learning network. The optimal topological flexibility, along with its corresponding fiber bundle spacing and number of fiber bundle filaments, are globally searched within the design domain using an adaptive genetic algorithm. The study in this paper can provide a reference for designing fiber bundle configurations of composites for practical applications.

Robust topology optimization for transient dynamic response minimization

This paper presents a novel framework for topology optimization (TO) of structures subjected to uncertain transient loading. Random transient uncertain but bounded loading is modeled in the form of an ellipsoid convex model. A transformation matrix is defined with uncertainty in input parameters based on orientation and lengths of semi-major and semi-minor axes of the ellipsoid. Latin hypercube sampling is utilized to generate samples inside the normalized space. These samples are then converted to a physical space using a transformation matrix. The generalized-α method is employed to compute the dynamic response of the system subjected to time-dependent loading. A density-based TO formulation is used to minimize dynamic response. The robust topology optimization problem is defined as bi-criteria optimization to minimize both the mean and variance across all deterministic cases within the ellipsoidal bounds. The solid isotropic material with penalization method is employed for the interpolation of material stiffness. Helmholtz filter is used to stabilize the problem numerically. The optimality criteria method is used to update the design variables. The proposed scheme’s effectiveness and the efficiency of the optimized designs are checked using a set of numerical examples. For most of the cases, robust design exhibits a substantial reduction of approximately 70%–75% in standard deviation when compared with deterministic design. The results demonstrate the proposed framework’s ability to reduce structure transient response under uncertain but bounded regions.

Robust topology optimization of multi-material structures based on the material-field series-expansion method

The performance of composite structures can be dramatically improved through the synergy between different constituent materials. However, the topology optimization of multi-material structures poses a heavy computational burden, which becomes more significant when load uncertainty is considered. This article proposes an efficient method to address the problem of robust topology optimization of multi-material structures. Employing the property that the material-field series-expansion method can significantly reduce the number of design variables, the proposed method improves the computational efficiency of the robust optimization problem. Meanwhile, the modification of the original multi-material interpolation model improves the quality of the optimized designs. Monte Carlo simulation is used to treat the load uncertainty, but it is decoupled from the optimization process based on linear elasticity theory to reduce computation cost. The effectiveness of the proposed method is demonstrated by numerical examples, which show that robust design results can be efficiently generated by this method.

Topology optimization of gradient lattice structure filling with damping material under harmonic frequency band excitation

With the rapid development of 3D printing technology, lattice structures have been widely utilized in structural designs aimed at vibration resistance due to their excellent performance. In this study, considering the moderate improvement of vibration suppression property of existing graded lattice, we introduce high-damping material into the optimization framework and further enhance the vibration resistance ability of gradient lattices. This framework extends the existing framework of stiffness and mass distribution to incorporate the distribution of stiffness, mass, and damping, which allows us to consider the damping changes with the cell configuration. Initially, the lattice cells are assigned with two different constitutive materials, one with high stiffness and the other with excellent damping properties. Different from traditional lattice units, we can obtain a series of lattice units with adjustable stiffness , mass and damping in a certain range. Via the homogenization method on the frequency domain, the complex elastic matrices about distribution of these lattice cells controlled by three parameters are obtained. In the meantime, the loss factor of these lattice cells is also obtained. A polynomial-based interpolation technique is employed to characterize the graded lattice units, which is integrated into an optimization process aimed at minimizing the lattice structures’ vibration responses. Several numerical examples are presented to illustrate this framework’s effectiveness, and experimental tests on 3D printed specimens are conducted to validate the numerical results. It’s worth noting that under the condition that the total weight of the structure remains unchanged, this weakens the overall stiffness of the structure (the reduction of first-order natural frequency), but greatly increases the damping of the structure (with a widened resonance peak) to resist the vibration of the structure. For the lattice structures induced by damping materials, the average loss factor is 0.114, which is almost doubled to the average value of those not including the damping material. When comparing the results of the mean displacement amplitude with and without damping materials, the reduction of displacement amplitude of lattice structures is above 25 %. The methodology expands the scope of optimization design for lattice structures, moving beyond stiffness maximization to include vibration mitigation by determining the appropriate distribution of stiff and damping materials, showcasing the practical applicability of the presented methods in engineering practice.