Structural Topology Optimization Research Articles

Topology Analysis and Structural Optimization of Air Suspension Mechanical-Vibration-Reduction Wheels

This paper designs a kind of air suspension mechanical-vibration-reduction wheel for mining engineering vehicles; the research work on topology analysis and the structural optimization of the inner and outer rims are carried out with this wheel as the research object. Using Workbench finite-element analysis software, taking the results of static analysis and modal analysis of the two as constraints, a variety of structural improvement styles are obtained through a topology analysis method and compared and verified, and a more reasonable improvement result is selected and assembled into a whole wheel for final analysis and verification. The results show that the optimization results of the wheel still meet the design’s load-bearing requirements, and the weight is lighter; the topology analysis results are ideal.

TOP2DFVT: An Efficient Matlab Implementation for Topology Optimization based on the Finite-Volume Theory

The finite-volume theory has shown to be numerically efficient and stable for topology optimization of continuum elastic structures. The significant features of this numerical technique are the local satisfaction of equilibrium equations and the employment of compatibility conditions along edges in a surface-averaged sense. These are essential properties to adequately mitigate some numerical instabilities in the gradient version of topology optimization algorithms, such as checkerboard, mesh dependence, and local minima issues. Several computational tools have been proposed for topology optimization employing analysis domains discretized with essential features for finite-element approaches. However, this is the first contribution to offer a platform to generate optimized topologies by employing a Matlab code based on the finite-volume theory for compliance minimization problems. The Top2DFVT provides a platform to perform 2D topology optimization of structures in Matlab, from domain initialization for structured meshes to data post-processing. This contribution represents a significant advancement over earlier publications on topology optimization based on the finite-volume theory, which needed more efficient computational tools. Moreover, the Top2DFVT algorithm incorporates SIMP and RAMP material interpolation schemes alongside sensitivity and density filtering techniques, culminating in a notably enhanced optimization tool. The application of this algorithm to various illustrative cases confirms its efficacy and underscores its potential for advancing the field of structural optimization.

Concurrent Topology Optimization of Curved-Plate Structures with Double-Sided Stiffeners

Due to their high specific stiffness, particularly in bending, along with their strong design capabilities, stiffened plates have become a prevalent structural solution in aerospace and various other fields. In pursuit of optimizing such structures, a topology optimization method named Heaviside-function-based directional growth topology parameterization (H-DGTP) was proposed in our previous work. However, this approach is limited to designing planar, single-sided stiffened structures. Thus, this paper extends the scope of this method to encompass double-sided, curved, stiffened panels, presenting a topology optimization technique tailored for such configurations. Specifically, considering the position, shape of the curved panels, and the arrangement and height of the stiffeners as design variables, while prioritizing structural stiffness as the objective, a topology optimization model for double-sided curved stiffened plate structures is established, and the corresponding sensitivities of the objective with respect to the design variables are analytically derived. Numerical examples illustrate that simultaneously optimizing the position and shape of the plate, as well as the layout and height of the stiffeners on both sides of the curved plate, results in greater stiffness compared to optimizing only part of these variables, validating the necessity and effectiveness of the proposed method.

Advancements in diabetic foot insoles: a comprehensive review of design, manufacturing, and performance evaluation.

The escalating prevalence of diabetes has accentuated the significance of addressing the associated diabetic foot problem as a major public health concern. Effectively offloading plantar pressure stands out as a crucial factor in preventing diabetic foot complications. This review comprehensively examines the design, manufacturing, and evaluation strategies employed in the development of diabetic foot insoles. Furthermore, it offers innovative insights and guidance for enhancing their performance and facilitating clinical applications. Insoles designed with total contact customization, utilizing softer and highly absorbent materials, as well as incorporating elliptical porous structures or triply periodic minimal surface structures, prove to be more adept at preventing diabetic foot complications. Fused Deposition Modeling is commonly employed for manufacturing; however, due to limitations in printing complex structures, Selective Laser Sintering is recommended for intricate insole designs. Preceding clinical implementation, in silico and in vitro testing methodologies play a crucial role in thoroughly evaluating the pressure-offloading efficacy of these insoles. Future research directions include advancing inverse design through machine learning, exploring topology optimization for lightweight solutions, integrating flexible sensor configurations, and innovating new skin-like materials tailored for diabetic foot insoles. These endeavors aim to further propel the development and effectiveness of diabetic foot management strategies. Future research avenues should explore inverse design methodologies based on machine learning, topology optimization for lightweight structures, the integration of flexible sensors, and the development of novel skin-like materials specifically tailored for diabetic foot insoles. Advancements in these areas hold promise for further enhancing the effectiveness and applicability of diabetic foot prevention measures.

Non-probabilistic reliability-based multi-scale topology optimization of thermo-mechanical continuum structures with stress constraints

A reliability-based non-probabilistic multiscale topology optimization (NRBMTO) method with stress constraints is proposed for thermo-mechanical continuous structures with uncontrollable stresses. The physical parameters, external loads and temperature values at the macro scale, are regarded as non-probabilistic uncertain parameters in the optimization of structural topologies with complex physical fields at multi-scale. The homogenization-based finite element method is employed to quantify thermo-mechanical structures with multi-scale uncertain parameters in the established multi-scale topology model. The ellipsoid model is applied to describe the uncertainty of non-probabilistic random variables, and the non-probabilistic reliability index is obtained by estimating the failure probability based on the first-order reliability method (FORM). The unit stresses are aggregated to the global maximum stresses with the normalized p-norm function, taking into account the mechanical and thermal stresses. The sensitivity information of the compliance and stress constraint to the macro- and micro-design variables and uncertain variables are derived simultaneously. The macro- and micro- design variables are solved by the method of moving asymptotes (MMA), respectively. Several numerical examples are given to verify the effectiveness and feasibility of the proposed NRBMTO method. The results demonstrate that the optimized structure based on the NRBMTO method provides better security with reliability index β=3 and minimum compliance (244.39) while stress is controlled below 235 MPa compared to the classical deterministic multiscale topology optimization (DMTO) method.

Size and topology optimization of truss-like structures under seismic excitations incorporating probabilistic aspects

Size and topology optimization of truss-like structures under seismic excitations incorporating probabilistic aspects

The path-engulfment method for topology optimization of structures

To address the challenge of establishing and solving mathematical models for engineering structural optimization, a new topological optimization method that integrates load-transfer path theory with the engulfment algorithm is presented in this paper. The presented method applies the load-transfer path theory to identify the main load-bearing areas of the structure and utilizes the principle of concentrating more materials in relatively high-stress regions and fewer materials in relatively low-stress regions. An engulfment algorithm is introduced to optimize the material distribution. A comparative analysis between the presented and variable-density methods revealed that the path-engulfment method enhances the structural stiffness and strength while reducing its mass, confirming its precision and efficacy in structural optimization. The path-engulfment method was implemented on a truck crane frame, resulting in an optimized structure with increased stiffness and strength and reduced mass compared to the original design. Furthermore, this method eliminates the need for establishing and solving complex mathematical models while addressing issues related to checkerboards and gray-scale elements. A smooth boundary approach was introduced by leveraging the engulfment algorithm, enabling the direct application of the optimized structure for manufacturing purposes, particularly in engineering applications.

Substructure-based topology optimization design method for passive constrained damping structures

Abstract This work presents a generalized substructure-based topology optimization method for passive constrained layer damping (PCLD) structures. Here, the model of PCLD structure is obtained by the Kirchhoff–Love thin plate formulation, and the whole structure is assumed to be composed of substructures with different yet connected scales and artificial lattice geometry features. Each substructure is condensed into a super-element to obtain the associated density-related matrices under the different geometry feature parameters, and the surrogate model for the stiffness and mass matrix of PCLD substructures with different densities has been particularly built. Using cubic spline interpolation, the derivatives of super-element matrices to the associated densities can be evaluated efficiently and accurately. The modal loss factor is defined as objective functions and topology optimization for the PCLD structures is formulated based on the model for PCLD plates that are described by combining the condensed substructures. Numerical examples under two lattice patterns of substructures and their corresponding physical tests show that the correctness and superiority of this substructure-based topology optimization approach for PCLD plates are verified.

Concurrent multiscale topology optimization for size-dependent structures incorporating multiple-phase materials

The significant progress in additive manufacturing has resulted in the development of well-engineered microstructures with innovative topological configurations, showcasing exceptional performance across diverse fields. Topology optimization is widely recognized as an advanced design tool that provides engineers with new insights for creating lightweight structures. As integration devices continue to trend towards miniaturization, the size effect in small-scale structures remains a persistent challenge. The absence of characteristic parameters to describe this size effect hinders proper explanation through traditional multiscale topology optimization based on classical mechanics. Therefore, we propose a size-dependent topology optimization framework for concurrent multiscale design involving multiple-phase materials. The modified couple stress theory is proposed to account for the size effect in small-scale structures. The numerical findings suggest that the size effect is significantly influenced by the ratio of elastic modulus, volume fraction, and width-to-length ratio of the representative volume element as its characteristic size approaches the length of the material. These results highlight the importance of considering size-dependent effects in topology optimization for multiscale design and provide valuable insights for engineers and researchers in this field.

Concurrent level set topology and fiber orientation optimization of fiber-reinforced composite structures

Concurrent level set topology and fiber orientation optimization of fiber-reinforced composite structures

MQ quasi-interpolation-based level set method for structural topology optimization

MQ quasi-interpolation-based level set method for structural topology optimization

Data-driven and physics-based methods to optimize structures against delamination

Composite materials and multi-material components often fail at their internal interfaces/adhesive joints, and hence special attention should be given to such catastrophic delamination events to guarantee the system’s functional requirements. So far, however, the majority of structural topology optimization problems have focused on optimal distribution of the bulk materials by considering interfaces as perfectly bonded. This motivates the introduction of optimization methods that explicitly take into account the role of the material interfaces to optimize structures against delamination. In this work, we propose a data-driven heuristic optimization approach for the identification of optimal cohesive interfaces with linearly graded fracture properties to increase the ability of the composite structure to withstand peeling. Moreover, for given cohesive interface properties, we investigate the applicability of the physics-based Solid Isotropic Material with Penalty (SIMP) topology optimization approach to optimize the internal structure of a substrate in problems where the stress field is affected by interface delamination.

Topology optimization of an elliptical parabolic shell structure: effect of penalty factor and load type

Topology optimization of an elliptical parabolic shell structure: effect of penalty factor and load type

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Topology optimization of truss structure considering kinematic stability based on mixed-integer programming approach

Topology Optimization of Motorbike Footsteps Using Finite Element Method

Footsteps are a foothold for motorbike riders and passengers; they also play a role in maintaining stability when driving. Footsteps must have a solid and lightweight material to support the load from the feet and body of the rider and passengers. In this study, the footstep with the material made from the waste drum brake shoe varied by reducing mass through the static structural simulation process and topology optimization process using Ansys Workbench to get optimal mass, total deformation, equivalent stress, maximum principal stress, and safety factor from each variation. The footstep geometry will be subjected to a load of 1000N and provided with the necessary support. Based on the data obtained during this study, the initial footstep geometry produces data in the form of total deformation (1.383 mm), equivalent stress (21.013 MPa), and safety factor (1.227). The 10% variation produces data in the form of total deformation (1.4368 mm), equivalent stress (20,564 MPa), ,and safety factor ( 1.2538). The 20% variation yields data in the form of total deformation (0.98037 mm), equivalent stress (18.111 MPa), maximum principal stress (18.41 MPa), and safety factor (yield strength: 1.4236,. At the same time, the 25% variation produces data in the form of total deformation (1.3058 mm), equivalent stress (22.27 MPa), and safety factor (1.1577).

A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method

A truly meshless approach to structural topology optimization based on the Direct Meshless Local Petrov–Galerkin (DMLPG) method

Research on Lightweight Rail Vehicle Body Based on Sensitivity Analysis

In view of the development trend of rail vehicles towards higher operating speed and low power consumption, a scheme for a lightweight rail vehicle body is proposed, based on sensitivity analysis. Using topology optimization of the vehicle body section structure, finite element models of the vehicle body section structure under single working conditions and multiple working conditions were established, respectively, and the force transmission path of the vehicle body structure under different working conditions was obtained under different working conditions. The topology of the cross-sectional structure of the vehicle body was optimized by the compromise planning method with weights. Then, a reconstruction and performance analysis of the car body section was carried out based on the optimization results and finally the finite difference method was used to analyze the sensitivity of the vehicle body structure and the vehicle body size was optimized based on the sensitivity analysis results. The results showed that the weight reduction rate of the railway vehicle body section stiffened plate was 4.47% compared to the optimization period and the modal performance analysis results of the optimized structure met the requirements. The weight reduction ratio of the optimized body structure was 21.6%

Development of optimization method for truss structure by quantum annealing

In this study, we developed a new method of topology optimization for truss structures by quantum annealing. To perform quantum annealing analysis with real variables, representation of real numbers as a sum of random number combinations is employed. The nodal displacement is expressed with binary variables. The Hamiltonian H is formulated on the basis of the elastic strain energy and position energy of a truss structure. It is confirmed that truss deformation analysis is possible by quantum annealing. For the analysis of the optimization method for the truss structure, the cross-sectional area of the truss is expressed with binary variables. The iterative calculation for the changes in displacement and cross-sectional area leads to the optimal structure under the prescribed boundary conditions.

A [formula omitted] continuous multi-patch framework for adaptive isogeometric topology optimization of plate structures

This study proposes a novel computationally efficient methodology to perform topology optimization (TO) of fourth-order plate structures within the framework of multi-patch isogeometric analysis. This is realized by taking the multifold benefits of isogeometric PHT-Splines to (1) discretize the C1 continuous weak form of plate structures, (2) develop a C0 continuous density field for the material distribution in TO and inherently remove the need for filters, and (3) provide a hierarchical tree structure for the structural mesh to effortlessly implement an adaptive mesh refinement (AMR) strategy. Moreover, to ensure continuity between isogeometric patches, we adopt a strong C1 coupling between the boundaries. This is established by constructing new basis functions, defined as a linear combination of existing C0 functions at the patch interfaces. The density field in TO is further enhanced with a first-neighbourhood smoothening algorithm based on the Shepard function to generate printable topologies and alleviate the post-processing stages after optimization. An element-centre density, based on the control point densities of the isogeometric mesh, is used as the marking scheme for the AMR to determine the subdomains to be refined. Utilizing the Geometry Independent Field approximaTion, the design and adaptive analysis-optimization stages were independently discretized respectively through NURBS and PHT-Splines, allowing easy transfer of multi-patch geometries from industry-standard packages. Multiple numerical examples illustrate the stability of the multi-patch algorithm in optimizing the geometries effectively. The results also show considerable advantages in terms of solution accuracy such as precise field, smooth topology and computational efficiency.

Dynamic topology optimization of two-phase viscoelastic composite structures considering frequency- and temperature-dependent properties under random excitation

This article proposes an efficient optimum design method of constrained layer damping (CLD) plates characterized by non-proportional damping subjected to random excitation. Considering frequency and temperature dependence, a two-phase viscoelastic composite material composed of stiffness-phase and damping-phase materials is used as the damping layer. The pseudo excitation and hybrid expansion methods are adopted to compute the random responses at the specified frequency intervals as the objective functions. The sensitivity analysis is performed through the adjoint vector method. The similarity index is defined to distinguish the various optimal layouts quantitatively. Several numerical examples clearly demonstrate the robustness and effectiveness of the proposed method, highlighting a remarkable improvement of over 60% in computational efficiency. Furthermore, it is proved that, when subjected to broadband random excitation, the damping materials' temperature- and frequency-dependent properties are critical factors in obtaining accurate vibration responses and desirable optimal layouts. The effects of the layer thicknesses and volume fractions of composite structures on topology optimization are also discussed. The results indicate that both layer thickness and volume fraction can change the mechanical properties of the composite structure and further affect the distribution characteristics of the damping material.