Topology Optimization Approach Research Articles

A novel binomial-based fuzzy type-2 approach for topology and size optimization of skeletal structures

The current work introduces a new probability-based fuzzy type-2 decision mechanism to adjust the optimization process during the simultaneous size and topology optimization of the Skeletal structural systems. For the probabilistic part a binomial module is developed that feeds the fuzzy mechanism by forecasting success probability for future topological actions. The proposed fuzzy decision mechanism permanently monitors the optimization process and attends to dynamically tune the balance between size and topology actions. The presented strategy, by reducing the number of ineffective iterations, significantly enhances the efficiency of the optimization process. Since the proposed decision mechanism is designed as an auxiliary separate module it can be integrated with different optimization methods. Accordingly, in this study, it is integrated with four different optimization algorithms and applied to solve distinct size and topology problems. To comprehensively evaluate the effect of the proposed strategy a new performance index is defined and employed. The acquired results demonstrate that the proposed decision mechanism considerably enhances the search performance of the algorithms on handling the structural size and topology optimization problems.

Enhancing sports mouthguards with PLA + and PC: stress reduction, energy absorption, and topology optimization.

The objective of this paper was to compare the effectiveness of different materials for mouthguards in preventing oral and maxillofacial injuries during sports activities. The present study compares the stress-reduction and energy absorption capabilities of two other fused filament materials - poly(lactic-acid plus) (PLA+) and polycarbonate (PC), with Ethylene-vinyl acetate (EVA), which is the most commonly used material for mouthguard fabrication. Two human skulls were modelled, and a boxing glove simulated punches along the x, y, and z-axes with 5mm displacement with 1 kN force. Firstly, the maximum principal stress curve in the skull was compared for forces along the three perpendicular directions. Furthermore, the present study examines materials energy absorption properties, including their specific energy absorption characteristics and initial peak von Mises stresses. Additionally, a topology optimization approach is used to create an alternative design for a mouthguard to improve specific energy absorption. The model without a mouthguard showed the highest stress concentration of 32.298MPa in the teeth, followed by the EVA material, which resulted in a maximum principal stress of 28.525MPa. Fused filament 3D materials, such as PLA + and PC, on the other hand, showed better mechanical effectiveness in both lower jaw dislocation and lower maximum principal stress by 30.82% and 51.25% in the mandibular and maxillary teeth. Though EVA comparatively shows better specific energy absorption capability at 2.24kJ/kg post-optimization than PLA + and PC, the peak principal stress experienced in the mandibular region was comparatively higher. The topology optimization, however, improved the energy-absorbing capabilities of PLA + by 4.5 times, reaching 1.37kJ/kg and PC from 0.165kJ/kg to 0.38kJ/kg. This study demonstrates that PLA + and PC have better stress reduction capabilities than EVA and could be promising materials for the fabrication of mouthguards in sports activities. This study highlights the importance of topology optimization in dental materials science and engineering to develop safer and more effective mouthguard designs.

Isogeometric proportional topology optimization (IGA-PTO) for multi-material problems

This study addresses the multi-material optimization problem by the effective and robust isogeometric proportional topology optimization (IGA-PTO) approach. Non-uniform rational B-spline basis functions are used for descriptions of geometry, displacement field, and density fields of material phases. The alternating active-phase algorithm is employed to convert the optimization problem with multiple constraints into a series of sub-problems of single constraint. Several examples are exhibited, and intensive comparisons with the gradient-based optimality criteria (OC) algorithm are presented to highlight the superior performance of the proposed PTO algorithm. Finally, the optimized topologies are prototyped using 3D printing technology to evidence the manufacturing feasibility.

Design and optimization of acoustic reflector for uniform diffusion

Sound diffusion performance is considered as an important issue in building acoustics. A well-diffused sound field can effectively enhance the human listening experience. To this end, we have investigated several optimization strategies to design a sub-wavelength acoustic metasurface that can achieve broadband uniform diffuse reflections. These designs are based on Fresnel lens surface, groove-like structure, level-set method, topology optimization approach, respectively. Meanwhile, a strategy combining Monte-Carlo searches and other derivative-free algorithms has been analyzed and used to ensure, as far as possible, a global optimum for the objective function when dealing with the multi-peak problem encountered in complex sound fields. Numerical simulations show that the resulting metasurfaces with the best diffusion performance have similar configurations between different design methods. The simulated sound pressure field was also verified by experimental measurements. From a general perspective, the proposed optimization strategy and simulation framework can provide a greater degree of freedom for geometric configuration and benefit the design of interior components in building acoustics.

Topology optimisation of fibre-reinforced composites accounting for buckling resistance and manufacturability

A topology optimisation approach that accounts for buckling resistance and manufacturability using fibre-reinforced composites is presented. This approach combines topology optimisation and fibre orientation optimisation to achieve a design with maximum buckling resistance. To ensure the optimal designs can be manufactured using 3D printing, constraints based on the continuity of fibre orientation and fibre path generation are applied. A compressed column, a stubby cantilever and an MBB beam are designed to demonstrate the response of the topology and fibre orientation when accounting for buckling resistance, as well as the compromise due to the inclusion of manufacturing constraints. The results show that the presented approach successfully guarantees manufacturability with a significant increase in buckling resistance.

Discrete level set method enhanced by conformal mapping: an efficient approach for topology optimization of piezoelectric energy harvesters

Discrete level set method enhanced by conformal mapping: an efficient approach for topology optimization of piezoelectric energy harvesters

Level-set topology optimization with PDE generated conformal meshes

This paper presents a level-set topology optimization approach that uses conformal meshes for the analysis of the displacement field. The structure’s boundary is represented by the iso-contour of a level-set field discretized on a fixed background design mesh. The conformal mesh is updated for each design iteration via a PDE based mesh morphing process that identifies the set of facets in the background mesh that are homeomorphic to the boundary and relaxes the homeomorphic mesh to conform to the structure’s boundary and ensure high element quality. The conformal mesh allows for a more accurate computation of the response versus density and some level-set based methods which interpolate material properties using the volume fraction. Numerical examples illustrate the proposed approach by optimizing linear-elastic two- and three-dimensional structures, wherein insight into the performance of the mesh morphing process is provided. The examples also highlight the scalability of the approach.

A simultaneous shape and topology optimization approach of shell structures based on isogeometric analysis and density distribution field

This paper presents a novel simultaneous shape and topology optimization approach of shell structures based on isogeometric analysis and density distribution field. In the optimization approach, Non-Uniform Rational B-Splines (NURBS) technology is utilized to describe the geometry and material distribution of the shell structures. The coordinates and densities of the NURBS control points are utilized as design variables to simultaneously optimize the shape and topology of shell structures. The proposed approach offers significant advantages, including ease of implementation, seamless integration with CAD models, high efficiency, and smooth, clear boundaries. Two representative examples are performed to demonstrate the effectiveness of the proposed approach. The optimized configurations are compared with other works and commercial software results.

Enhancing topology optimization with colored body-fitted mesh using adaptive filter, dual re-meshing strategy, and OOP programming paradigm

This study introduces a novel topology optimization approach by employing power law-based material interpolation and adaptive filtering in the framework of the unstructured grids. As an extension of the established Solid Isotropic Material with Penalization (SIMP) method that utilizes the fixed structured mesh, the proposed Colored Body-Fitted Optimization (CBFO) method adopts the body-fitted grids to enhance efficiency, accuracy, and adaptability for diverse engineering applications. Notably, incorporating body-fitted meshes with intermediate density profiles enables improved flexibility in the numerical simulations and eliminates the need for re-meshing in each iteration. The dual re-meshing strategy drastically reduces computational costs, with only two re-meshing procedures required throughout the optimization process. This approach facilitates the generation of dense mesh regions around critical boundaries to augment solution accuracy while enabling sparse mesh configurations in the low-sensitivity regions, thereby boosting computational efficiency without compromising performance. The effectiveness, robustness, and efficiency of the CBFO method are validated through testing on multiple standard minimum compliance and compliant mechanism problems. The proposed optimization method can converge in dozens of iterations, obtain better objective function values, and save computational costs by up to 69 % compared to the previous method using the body-fitted mesh. Additionally, a concise MATLAB script implementing the proposed method using an Object-Oriented Programming (OOP) paradigm is provided in the appendix and the supplementary material, complete with annotations.

Topology optimization design of multi-modal resonators for metamaterial panels with maximized broadband vibroacoustic attenuation

Resonant metamaterial panels can achieve exceptional vibroacoustic attenuation by subwavelength local resonators attached to a host structure. While single-mode resonators provide improvements only in a narrow band, recent advancements propose multi-modal resonators for broadband attenuation. However, existing designs utilize only a limited number of modes, and effective methodologies are lacking to systematically design resonator layouts that achieve an appropriate amount of resonances across the target frequency range, with an adequate participating mass. In this study, we tackle this challenge by developing a dedicated topology optimization method for multi-modal resonator design in metamaterial panels. The method leverages effective thin plate modelling, i.e. a homogenized metamaterial representation through an effective mass density, which provides accurate and very efficient vibroacoustic predictions. The optimization objective is to maximize the broadband diffuse field sound transmission loss (STL) of the metamaterial panel while constraining mass. The optimization problem is solved by gradient-based mathematical programming, for which the necessary (adjoint) sensitivities of objective and constraints are derived. The efficacy of the proposed topology optimization approach is demonstrated by targeting the suppression of coincidence dips in orthotropic host plates. For narrowband coincidence dips, the optimized resonator exhibits maximized mass participation in one single mode of interest. For broadband coincidence dips, the method effectively generates multi-modal resonators with up to 6 resonances distributed across the target frequency range. It is finally demonstrated that the topology-optimized designs surpass the performance of simpler, parametrically optimized multi-modal resonator layouts, as well as of conventional treatments by a damping layer of rubber.

CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

3D Printed Metamaterials for Energy Absorption in Motorsport Applications

In this study, various 3D printed metamaterials are investigated for application in energy absorbing structures in motorsports. Impact attenuating structures are used to decelerate vehicles and protect drivers in the event of a crash. Additive manufacturing enables complex plastic structures which can facilitate improved angular resistance and reduced weight and cost compared with traditional approaches. Metamaterials were 3D printed from PLA using commercially available equipment and include gyroid structures, a novel reinforced gyroid design and a lattice designed using finite-element analysis-based topology optimization. Compression testing was used to measure stress–strain response, compressive modulus, and energy absorption. This demonstrated gyroids and reinforced gyroids have ideal compressive behavior for high energy absorption under impact. The topology optimized metamaterial was found unsuitable for this application due to its high stiffness, revealing a weakness in traditional topology optimization approaches which are not catered to maximize energy absorption. The reinforced gyroid demonstrated the highest specific energy absorption and was used to manufacture an impact attenuator which demonstrated the potential to safely stop a hypothetical 300 kg vehicle crash. This work supports that gyroid-based structures can reduce weight, volume and cost over current materials in all motorsport categories, with improved safety from oblique crashes.

The Bisection Method and the Accelerated Dynamical Mean Value Optimization Method in Comparison of Different Topology Optimization Approaches

The Bisection Method and the Accelerated Dynamical Mean Value Optimization Method in Comparison of Different Topology Optimization Approaches

A microstructural topology optimization approach for vibro-acoustic interaction systems based on the piecewise constant level set method

A microstructural topology optimization approach for vibro-acoustic interaction systems based on the piecewise constant level set method

Topology optimization for fatigue reserve factors

This paper describes a topology optimization approach that applies the common fatigue analysis practices of rainflow cycle counting and critical plane searches to cover both proportional and non-proportional fatigue loading conditions of metals. The existing literature on topology optimization has so far mainly considered fatigue damage under proportional loading conditions and typically uses continuous damage models to avoid the discontinuous nature of fatigue rainflow cycle counting and critical plane searches. Furthermore, previous publications often introduced heuristic schemes to scale the fatigue damage and set the move limits for the design variables rather low to avoid oscillations in the design variables and damage responses during the optimization iterations, because fatigue damage is typically highly localized. Therefore, these approaches cause many optimization iterations. Contrarily, our present approach applies the fatigue reserve factor (FRF) directly in the optimization formulation instead of the fatigue damage where FRF is a fatigue reserve factor for infinite fatigue life. The inverse FRF scales nearly linearly with the stresses. Therefore, the present approach needs no heuristic scaling for the fatigue topology optimization. The numerical implementation applies the semi-analytic adjoint sensitivity method for multiple load cases. Numerically, FRF shows more stable optimization convergence using less optimization iterations. Different FRF topology-optimized designs for a variety of fatigue damage types are validated and compared. Additionally, the optimized FRF designs are compared to both strictly stiffness optimized designs and stress strength optimized designs.

Adaptive topology optimization for enhancing resistance to brittle fracture using the phase field model

Computational cost is one of the challenges in the field of fracture resistance topology optimization. An efficient topology optimization approach is proposed for enhancing resistance to structural fracture based on the adaptive isogeometric–meshfree method. The mesh can be adaptively refined in the computational and design domains simultaneously to capture the fracture and structural boundary delicately, which significantly reduces the degree of freedom and improves the efficiency of the topology optimization problems related to crack propagation. The proposed approach naturally inherits the advantages of both the computer-aided design and continuity of the higher-order basis functions, where the geometry and the analysis models in the process of topology optimization are integrated. The problem is formulated to maximize the absorbed energy throughout the crack process using the solid isotropic material with penalization method under volume constraints. The phase field method is used for modeling crack propagation, thereby eliminating the need of an explicit representation of the crack surface and complex tracking procedures, while a delicate mesh is still required. With this approach, the external work required during the fracture process is maximized, and the crack growth is delayed remarkably. Several representative examples are demonstrated to verify the effectiveness of the present approach in fracture-resistance-enhanced topology optimization, and the computational cost shows remarkable improvement.

A smooth maximum regularization approach for robust topology optimization in the ground structure setting

A smooth maximum regularization approach for robust topology optimization in the ground structure setting

Additively manufactured conformal cooling channels through topology optimization

Cooling channels play a critical role in various casting and molding processes, impacting both the cycle time and quality of the product. As additive manufacturing technologies become increasingly prevalent, conventional straight-drilled channels are being progressively substituted by intricate cooling lines that conform to the contours of the fabricated part. This transition can lead to a significant reduction of the solidification time and temperature gradients, consequently lowering the occurrence of part defects. However, designing such channels becomes challenging as geometric complexity and manufacturing constraints increase. In this work, we present a density-based topology optimization approach to generate conformal cooling channels in molds and dies inserts. To mitigate temperature variations, the objective function is penalized using the temperature standard deviation of the insert cavity surface. A density-gradient-based constraint is further utilized to reduce the generation of overhanging structures and promote manufacturability. In particular, the use of this constraint leads to the generation of channels characterized by a teardrop-shaped cross section. The cooling efficiency of a selected optimized design is confirmed through computations using a body-fitted solver. The geometry is subsequently manufactured by Laser Powder Bed Fusion (LPBF) and experiments are conducted to compare its performance in comparison to a design featuring straight-drilled channels. The results demonstrate that the optimized geometry significantly enhances the heat extraction rate and further leads to a 43% reduction of the cavity temperature standard deviation.

Topological design of soft substrate acoustic metamaterial for mechanical tuning of sound propagation

The design of tunable acoustic waves is crucial in phononic crystals (PnCs), as acoustic waves exhibit continuous variation across diverse frequency ranges in practical applications. While there have been research efforts on tunable PnCs, existing design strategies predominantly rely on predetermined topology and scatterer shapes based on empirical experience. This reliance poses challenges in ensuring customized and reversible tuning of the bandgap. In this work, we present a customized tunable PnC design model and solution strategy based on soft substrates, which enables reversible tuning of a specific frequency/order bandgap. The designed structure consists of a soft substrate and crystalline columns dispersed in the soft substrate and air. The relative positions of the scatterers in the air are changed by stretching the substrate, thereby realizing the modulation of sound propagation. Since soft materials have both material nonlinearities and complex geometrical variations that are difficult to obtain design sensitivity information, the material-field series expansion topology optimization approach is employed to achieve custom tunable design of the bandgap. The paper presents simulation-based analyses and experimental verification of the customized bandgap opening and closing. The results demonstrate a close alignment between theoretical predictions of propagation curves and experimental findings. This concurrence serves as evidence that the soft-substrate PnC, derived through topology optimization, effectively facilitates the adjustment of bandgaps of arbitrary orders and enables switching between various acoustic functions.

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.