Structural Topology Optimization Research Articles

Anti-fatigue optimization of the twisting force arm of landing gear based on Kriging approximate sequential optimization method

ABSTRACT The twisting force arm (TFA) is an important part of the pillar landing gear, anti-fatigue optimization on its structure can improve the reliability of the landing gear. However, the optimization accuracy of the conventional optimization method is limited by the basic topological structure from the views of topological theory. Besides that, the optimization efficiency of the conventional method is also relatively low because of the high computational cost of the fatigue life estimation. In this paper, an anti-fatigue optimization method of the TFA was developed to improve the optimization accuracy and efficiency by using the approximate sequential optimization method after an optimal basic topological structure was obtained. To verify its effectiveness, the proposed method was introduced to the anti-fatigue optimization of a pillar landing gear TFA. The results show that the optimization accuracy of the proposed method is higher than the conventional method, and the computational cost can be reduced 82.35%. This indicates that the proposed method can improve the optimization accuracy and efficiency of the anti-fatigue optimization.

Research on the spatial structure of environmental art design based on topology optimization and morphology optimization

Abstract In this paper, firstly, a mathematical model of spatial structure topology optimization is constructed, and sensitivity analysis, approximate model fitting and optimization finding strategy for topology optimization in environmental art design are carried out. Secondly, morphological optimization is carried out from the morphological model of spatial structure and the urban thermal environment through urban environmental art design and morphological optimization. Finally, the optimization of structural morphology is explored under static multiple working conditions and single-objective optimization, considering the dynamic frequency of the structure. The results show that as the optimization proceeds, the total strain energy, axial strain energy and bending strain energy of the space structure increase to 0.45, 0.52 and 0.5 of the initial structure, respectively. At the 9th iteration of optimization, the performance is at its peak. The load-carrying capacity is 1.59 times that of the 35th step and 1.5 times that of the initial structure. The research results of this paper can provide references and guidance for structural design and optimization in the fields of environmental art design and urban planning.

Topology optimization of periodic structures for crash and static load cases using the evolutionary level set method

Assembly complexity and manufacturing costs of engineering structures can be significantly reduced by using periodic mechanical components, which are defined by combining multiple identical unit cells into a global topology. Additionally, the superior energy-absorbing properties of lattice-based periodic structures can potentially enhance the overall performance in crash-related applications. Recent research developments in periodic topology optimization (PTO) have shown its efficacy for tackling new design problems and finding advanced novel structures. However, most of these methods rely on gradient information in the optimization process, which poses difficulties for crash problems where analytical sensitivities are usually not directly applicable. In this paper, we present an effective periodic evolutionary level set method (P-EA-LSM) for the optimization of periodic structures. P-EA-LSM uses a low-dimensional level-set representation based on moving morphable components to parametrize a single unit cell, which is replicated in the design domain according to a predefined pattern. The unit cell is optimized using an evolutionary algorithm and the structural responses are calculated for the entire system. We initially assess the performance of P-EA-LSM using three 2D minimum compliance test cases with varying periodicities. Our results demonstrate that our approach produces solutions comparable to other state-of-the-art methods for PTO while keeping a low dimensionality of the optimization problem. Subsequently, we effectively evaluate the capabilities of P-EA-LSM in a crashworthiness scenario. This particular application highlights the significant potential of the method, which does not rely on analytical sensitivities.

Visualization analysis of research hotspots on structural topology optimization based on CiteSpace

Structural topology optimization has gained widespread attention due to more possibilities of innovative structural design. The current research focus/hotspots, application areas, main research scholars, institutions and the countries involved in structural topology optimization are visually presented through clustering and visual analysis based on CiteSpace. The four metric dimensions of the literatures in this paper are as follows: annual quantity of papers and core countries, core authors and co-authors’ institutions, hotspots and burst terms, and the highly co-cited papers. The results show the research hotspots in this field are concentrated on keywords such as "level set method", "sensitivity analysis", "homogenization", "genetic algorithm", etc. Regarding the research frontier, “moving morphable component (MMC)”, “additive manufacturing (AM)” and “deep learning” are hot topics. In addition, Y. Sui, Z. Kang and O. Sigmund, etc. have high publications. M. Bendsøe and O. Sigmund have high citations. Dalian University of Technology, Technical University of Denmark, etc. are prominent institutions. Moreover, China accounts for more than 34% in the terms of original WOS literatures following by the USA and Australia. This paper could identify structural topology optimization development patterns for the scholars concerned with this field, especially novices, to quickly focus and track the research priorities.

Topology optimization of multi-material structures considering anisotropic yield strengths

Multi-material structures offer the superior performance and broader designable freedom, and have gained increasing interest benefitting from the advances in additive manufacturing (AM) technique. However, the effect of anisotropic yield strength of these AM-fabricated parts on topology optimization of multi-material structures has so far received little attention. In the current work, an anisotropic strength-based topology optimization method for multi-material structures is developed for maximizing strength performance under total mass constraint, which allows for the consideration of directional dependence and tension-compression asymmetry of yield strengths based on the Tsai-Wu yield criterion. Another challenge for multi-material structures design is that the possible permutations of numerous candidate materials are unlimited, it is impossible that all combinations of multiple candidate materials are tested for the optimal strength performance of multi-material structures. To solve this problem, we propose a preselection method for the inclusion or exclusion of candidate materials based on their elastic properties, yield strengths and densities before optimization. Afterwards, our topology optimization method can automatically find the optimal combination of volume fractions of different candidate materials. Several 2D and 3D numerical examples are investigated for minimizing the maximum of failure indexes of strength for fixed total mass. The advantages of multi-material structures are verified by comparing to single-material designs. The effectiveness of the preselection method of candidate materials is also verified.

EMsFEM based concurrent topology optimization method for hierarchical structure with multiple substructures

An efficient concurrent topology optimization method based on the Extended Multiscale Finite Element Method (EMsFEM) is proposed to design the hierarchical structure with multiple substructures in this paper. Firstly, the mathematical description model for the topology of hierarchical structures and the interpolation model for material are established at both the macro and substructural levels. Then the concurrent topology optimization formulation for hierarchical structures is proposed based on EMsFEM. After that, the sensitivity analysis scheme of the objective function and constraint functions is given, based on which the Method of Moving Asymptotes (MMA) is employed to update design variables. The assumption of separation of length scales is not required in the proposed method, which avoids the disconnection between adjacent substructures. Besides, without limiting the topology and spatial distribution of substructures in advance, the concurrent topology optimization for hierarchical structures with multiple substructures can be realized using this method. The provided numerical examples verify the correctness and effectiveness of the proposed sensitivity analysis method as well as the feasibility, effectiveness and scalability of the proposed concurrent topology optimization method for hierarchical structures. Finally, the influence of the initial substructure configurations and the number of substructure types on the final configuration and mechanical performance of hierarchical structures are explored with a series of numerical examples.

Effective thermal conductivity estimation using a convolutional neural network and its application in topology optimization

Topology optimization of heterogeneous structures can find significant use in a wide range of applications, and its fabrication has been made possible by recent advances in additive manufacturing. However, the optimization procedure is computationally expensive, as each structural update requires the re-evaluation of the properties. The computational time is the major limiting factor in large-scale and complex structural optimization. In this study, a convolutional neural network (CNN) model for predicting effective thermal conductivity inspired by the VGG networks is proposed. Trained using 130,000 unique binary images, the model achieves high predictive accuracy. Specifically, it shows a mean absolute percent error (MAPE) of 0.35% in testing when the thermal conductivity of the solid is ten times larger than the fluid, and when the thermal conductivities assigned are that of aluminum and water, the MAPE is 2.35%. The prediction time is 15 ms for a single image with 128 × 128 pixels, which is 3 to 5 orders of magnitude faster than a finite volume simulation. When employed in topology optimization, the CNN retains a MAPE between 0.67% and 11.8% for different cases. The CNN model correctly predicts trends in effective thermal conductivity and improves the structure to close proximity of a theoretical maximum in all cases.

Topology optimization of truss structure under load uncertainty with gradient‑free proportional topology optimization method

This study proposes a method for truss topology optimization (TO) that incorporates uncertain static and dynamic loads based on the efficient gradient‑free proportional topology optimization (PTO) method. The uncertain loads are modeled using probabilistic parameters and the objective function is constructed as the mean structural compliance with the constraint is imposed to the structural material volume. The univariate dimension reduction method and Gauss-type (UDRG) quadrature are used to quantify and propagate the load uncertainty to estimate the objective function. By the UDRG method, the TO of truss structures under uncertain loads can be transformed into a simple deterministic problem. To obviate the necessity for sensitivity analysis, the PTO method with comparable accuracy and efficiency as the gradient-based method is used. The proposed methodology is corroborated through multiple illustrative examples, which also serve to elucidate the ramifications of load uncertainty on optimized truss designs.

Thermoelastic topology optimization for structures with temperature-dependent material properties

Thermoelastic topology optimization for structures with temperature-dependent material properties

Strength constrained topology optimization of hyperealstic structures with large deformation-induced frictionless contact

This paper developed a strength constrained topology optimization method for hyperelastic structures with large deformation-induced frictionless contact. The Neo-Hookean hyperelastic constitutive equation is adopted as the material model that incorporates both material and geometric nonlinearity. The large deforming contact is described by the node-to-segment algorithm. The topology optimization model is developed under the SIMP framework. Given the SIMP-related fictitious domain, we develop a nodal variable-based interpolation scheme to build smooth correlation between the contact force and nodal density variables, thus enabling the smooth transition and variation of contact conditions. Moreover, to guarantee the structure strength, local strain energy constraints are formulated and aggregated by the P-norm function. The details of sensitivity analysis are explicitly explained. At last, several benchmark examples are conducted that validate the proposed method.

Reliability-based topology optimization of fractionally-damped structures under nonstationary random excitation

This contribution proposes an effective reliability-based topology optimization (RBTO) framework for the layout of viscoelastic dampers of energy-dissipating structures under nonstationary seismic excitation, in which the constitutive behavior of viscoelastic damper is described by the novel fractional derivative models. To formulate the RBTO problem, the installation number of fractional viscoelastic dampers is minimized under the constraints of dynamic reliability, and the design variables are chosen as the damper parameters and the existence variables of the potential fractional viscoelastic dampers. The explicit responses are first established for the fractionally-damped structure, and the explicit response sensitivities with respect to the design variables are further derived through the adjoint variable method (AVM). On this basis, an explicit time-domain method (ETDM) is developed for explicit formulation of the statistical moments of responses and the moment sensitivities of the fractionally-damped structure, which are further employed to analytically derive the first-passage dynamic reliabilities and the reliability sensitivities of the structure based on the classical level-crossing process theory. Finally, the RBTO problem for the layout of fractional viscoelastic dampers is solved with the gradient-based method of moving asymptotes (MMA), in which the existence variables of fractional viscoelastic dampers can be driven to binary solutions by the solid isotropic material with penalization (SIMP) technique. An engineering application involving a building frame structure installed with fractional viscoelastic dampers is presented to validate the feasibility of the proposed ETDM-based RBTO framework.

Topology optimization of self-contacting structures

Inclusion of contact in mechanical designs opens a large range of design possibilities, this includes classical designs with contact, such as gears, couplings, switches, clamps etc. However, incorporation of contact in topology optimization is challenging, as classical contact models are not readily applicable when the boundaries are not defined. This paper aims to address the limitations of contact in topology optimization by extending the third medium contact method for topology optimization problems with internal contact. When the objective is to maximize a given contact load for a specified displacement, instabilities may arise as an optimum is approached. In order to alleviate stability problems as well as provide robustness of the optimized designs, a tangent stiffness requirement is introduced to the design objective. To avoid a non-physical exploitation of the third medium in optimized designs, small features are penalized by evaluating the volume constraint on a dilated design. The present work incorporates well-established methods in topology optimization including Helmholtz PDE filtering, threshold projection, Solid Isotropic Material Interpolation with Penalization, and the Method of Moving Asymptotes. Three examples are used to illustrate how the approach exploits internal contact in the topology optimization of structures subjected to large deformations.

Robust topology optimization of truss-like continuum structures under uncertain loads based on cloud model

The traditional structural performance may be seriously degraded due to applied indeterministic cases. A novel framework for robust topology optimization of truss-like continuum considering uncertain loads is presented. The robust optimization formula is constructed as minimizing the weighted sum of expectancy and standard variance of structural compliance with volume constraints. In this framework, both the magnitude and direction of applied loads are uncertain and independent. Truss-like continuum provides the topology optimal structure theoretically. Based on the classic truss-like optimization method, the statistical moments of compliance are accurately evaluated utilizing a bivariate cloud model tool. An effective strategy based on linear decoupling is reported to largely reduce the total number of finite element analysis. The optimization is achieved with gradient-based mathematic programming. Several numerical examples demonstrate a better structural robust performance obtained by the proposed algorithm than the traditional one.

BNSL GOBNILP algorithm in application to damage intensity prognostic system to RC multistorey residential buildings subjected to negative impacts of the industrial environment of mines

Paper presents a method of predicting the damage intensity of multifamily prefabricated RC buildings located in the range of impacts of the industrial environment of mines. The research studied the effects of mining impacts in the form of large-scale continuous ground deformation and mining tremors. For this purpose, in-situ data collected in the database was used. Additional information in the database included: structural and material features, quality of maintenance and durability of the analysed buildings. Finally, a predictive model represented by an optimal Bayesian network structure was created. To obtain the optimal topology of the DAG network structure, a Bayesian network learning algorithm from data GOBNILP was adapted. According to this algorithm, the optimisation process was carried out through Gurobi Optimizer. Thus, the conducted analyses represent the first time the above-mentioned approach has been applied in the interdisciplinary field of civil and environmental engineering. As part of the analyses, the available metric scores were verified and multiple network structures were examined according to their complexity. This made it possible to select the best Bayesian network in terms of generalizing the knowledge acquired while learning its structure. The possibility of using the obtained model for issues of diagnosis of damage causes and their prediction was also presented.

Structural topology optimization considering geometrical and load nonlinearities

The pressure loads are always perpendicular to the deformed surface. Under the large deformation, the pressure loads will lead to load nonlinearity because of the direction change. This paper proposes a topology optimization method considering both geometrical and load nonlinearities. The geometrically nonlinear finite element formulation is described to consider the pressure loads. A topology optimization model is constructed with the external work as objective function and volume fraction as constraint. The sensitivity information is derived by the adjoint method. Numerical examples demonstrate the effectiveness of the proposed method.

A novel numerical manifold method and its application in parameterized LSM-based structural topology optimization

In this paper, a high-efficiency structural topology optimization framework based on combination of numerical manifold method (NMM) and parameterized level set method (PLSM) is established. The NMM uses two cover systems to discretize the model, which can accurately represent the complex boundary of the design domain. A new numerical manifold element has been derived for the application of NMM in PLSM-based optimization. To obtain enhanced accuracy for structural analysis, a multilevel subdivision technique for numerical manifold element generation is presented, and the related numerical integration scheme coupled with the interpolation point selection strategy is provided. For the proposed topology optimization, the new update method of element stiffness matrix is exclusively formulated as well as the calculation method of volume fraction. Some representative structural optimization problems demonstrate that the proposed structural topology optimization method is very effective for two-dimensional (2D) and three-dimensional (3D) structural topology optimization problems.

Structural topology optimisation based on a multi-agent model

In this study, we propose to equip the basic vector-based multi-agent system with global structural awareness by introducing strain energy density gradient vectors to achieve structural topology optimisation. This multi-agent based topology optimisation method can conveniently generate diverse and competitive structural designs with different parameters of the agent swarm behavior rules (separation, alignment and cohesion). Several numerical examples are introduced to explore the relationship between parameters and resulting design diversities. It is demonstrated that the proposed method can produce a variety of designs that possess not only high structural performance but also distinctly different topologies. Taking advantages of the computational multi-agent system, this method has potential to be easily integrated with agent system algorithms in other research fields to generate diverse designs with high structural performance, elegant geometries and interesting features for architects, engineers and other designers.

TopSTO: a 115-line code for topology optimization of structures under stationary stochastic dynamic loading

TopSTO: a 115-line code for topology optimization of structures under stationary stochastic dynamic loading

Исследование свойств регулярных структур, полученных аддитивными технологиями в сочетании с методами порошковой металлургии

Despite significant amount of research and applied works in the additive technologies, problems of the topological optimization of structures obtained by combining 3D printing and the powder metallurgy methods remain insufficiently studied both theoretically and experimentally. Results of simulating regular structures made of plastics and studying their destruction processes could be effectively used as a starting approach in developing technology for production of the composite materials based on the titanium alloys with the increased level of strength properties. Based on numerical experiments and full-scale tests, the most preferred types of structures were determined. They include honeycomb structures based on PLA with the following strength properties: elastic modulus — 342.3 MPa; ultimate compressive strength — 20.4 MPa; specific strength — 81 MPa cm3/g. 3D models realized on plastics were used in manufacture of the metal composites using technology combining selective laser melting and powder metallurgy. In addition to increasing density and eliminating porosity of structures made from the titanium alloy powders, the strength properties level also increases after infiltration with the lower-melting alloys, since redistribution of stresses arising in the titanium frame under load is ensured. Bending strength alters in the range of 1140...1560 MPa and elastic modulus - in the range of 49 500...54 000 MPa depending on the composite composition and selective laser melting modes. Rockwell hardness increases from 35 to 45 HRC, and Brinell hardness — from 340 to 410 HB, which is by 20...25 % higher than hardness of the rolled products from the VT6 alloy. The increased strength values could be explained by the material composite structure formed by combination of the two mutually penetrating frames. Results of testing samples for strength are another argument in favor of the proposed infiltration method implying combined additive and powder metallurgy methods.

Compliance Prediction for Structural Topology Optimization on the Basis of Moment Invariants and a Generalized Regression Neural Network.

Topology optimization techniques are essential for manufacturing industries, such as designing fiber-reinforced polymer composites (FRPCs) and structures with outstanding strength-to-weight ratios and light weights. In the SIMP approach, artificial intelligence algorithms are commonly utilized to enhance traditional FEM-based compliance minimization procedures. Based on an effective generalized regression neural network (GRNN), a new deep learning algorithm of compliance prediction for structural topology optimization is proposed. The algorithm learns the structural information using a fourth-order moment invariant analysis of the structural topology obtained from FEA at different iterations of classical topology optimization. A cantilever and a simply supported beam problem are used as ground-truth datasets, and the moment invariants are used as independent variables for input features. By comparing it with the well-known convolutional neural network (CNN) and deep neural network (DNN) models, the proposed GRNN model achieves a high prediction accuracy (R2 > 0.97) and drastically shortens the training and prediction cost. Furthermore, the GRNN algorithm exhibits excellent generalization ability on the prediction performance of the optimized topology with rotations and varied material volume fractions. This algorithm is promising for the replacement of the FEA calculation in the SIMP method, and can be applied to real-time optimization for advanced FRPC structure design.