Topology, Size, and Shape Optimization in Civil Engineering Structures: A Review

The optimization of civil engineering structures is critical for enhancing structural performance and material efficiency in engineering applications.Structural optimization approaches seek to determine the optimal design,by considering material performance,cost,and structural safety.The design approaches aim to reduce the built environment’s energy use and carbon emissions.This comprehensive review examines optimization techniques,including size,shape,topology,and multi-objective approaches,by integrating these methodologies.The trends and advancements that contribute to developing more efficient,cost-effective,and reliable structural designs were identified.The review also discusses emerging technologies,such as machine learning applications with different optimization techniques.Optimization of truss,frame,tensegrity,reinforced concrete,origami,pantographic,and adaptive structures are covered and discussed.Optimization techniques are explained,including metaheuristics,genetic algorithm,particle swarm,ant-colony,harmony search algorithm,and their applications with mentioned structure types.Linear and non-linear structures,including geometric and material nonlinearity,are distinguished.The role of optimization in active structures,structural design,seismic design,form-finding,and structural control is taken into account,and the most recent techniques and advancements are mentioned.

Quantile-based optimization under uncertainties for complex engineering structures using an active learning basis-adaptive PC-Kriging model

The Reliability-Based Design Optimization(RBDO)of complex engineering structures considering uncertainties has problems of being high-dimensional,highly nonlinear,and timeconsuming,which requires a significant amount of sampling simulation computation.In this paper,a basis-adaptive Polynomial Chaos(PC)-Kriging surrogate model is proposed,in order to relieve the computational burden and enhance the predictive accuracy of a metamodel.The active learning basis-adaptive PC-Kriging model is combined with a quantile-based RBDO framework.Finally,five engineering cases have been implemented,including a benchmark RBDO problem,three high-dimensional explicit problems,and a high-dimensional implicit problem.Compared with Support Vector Regression(SVR),Kriging,and polynomial chaos expansion models,results show that the proposed basis-adaptive PC-Kriging model is more accurate and efficient for RBDO problems of complex engineering structures.

Web Layout Design of Large Cavity Structures Based on Topology Optimization

Large cavity structures are widely employed in aerospace engineering, such as thin-walled cylinders, blades andwings. Enhancing performance of aerial vehicles while reducing manufacturing costs and fuel consumptionhas become a focal point for contemporary researchers. Therefore, this paper aims to investigate the topologyoptimization of large cavity structures as a means to enhance their performance, safety, and efficiency. By usingthe variable density method, lightweight design is achieved without compromising structural strength. Theoptimization model considers both concentrated and distributed loads, and utilizes techniques like sensitivityfiltering and projection to obtain a robust optimized configuration. The mechanical properties are checked bycomparing the stress distribution and displacement of the unoptimized and optimized structures under the sameload. The results confirm that the optimized structures exhibit improved mechanical properties, thus offering keyinsights for engineering lightweight, high-strength large cavity structures.

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials.The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass,as well as the local volume fraction of all phases.The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function,avoiding the parameter dependence in the conventional aggregation process.Furthermore,the local volume percentage can be precisely satisfied.The effects including the globalmass bound,the influence radius and local volume percentage on final designs are exploited through numerical examples.The numerical results also reveal that porous structures keep a balance between the bulk design and periodic design in terms of the resulting compliance.All results,including those for irregular structures andmultiple volume fraction constraints,demonstrate that the proposedmethod can provide an efficient solution for multiple material infill 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,multiobjective 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.

Concurrent Two-Scale Topology Optimization of Thermoelastic Structures Using a M-VCUT Level Set Based Model of Microstructures

By analyzing the results of compliance minimization of thermoelastic structures,we observed that microstructures play an important role in this optimization problem.Then,we propose to use a multiple variable cutting(M-VCUT)level set-based model of microstructures to solve the concurrent two-scale topology optimization of thermoelastic structures.A microstructure is obtained by combining multiple virtual microstructures that are derived respectively from multiple microstructure prototypes,thus giving more diversity of microstructure and more flexibility in design optimization.The effective mechanical properties of microstructures are computed in an off-line phase by using the homogenization method,and then a mapping relationship between the design variables and the effective properties is established,which gives a data-driven model of microstructure.In the online phase,the data-driven model is used in the finite element analysis to improve the computational efficiency.The compliance minimization problem is considered,and the results of numerical examples prove that the proposed method is effective.

A stepwise optimization method for topology structure of fluid machinery network

The circulating water system is widely used as the cooling system in the process industry,which has the characteristics of high water and power consumption,and its energy consumption level has an important impact on the economic performance of the whole system.Pump network and water turbine network constitute the work network of the circulating water system,that is,the fluid machinery network.Based on the previous studies,this paper proposes a stepwise method to optimize the fluid machinery network,that is,to optimize the network structure by using the recoverable pressure-head curve of the branch,and consider the recovery of adjustable resistance at the valve of each branch,so as to further reduce energy consumption and water consumption.The calculation result of the case shows that the topology structure optimization can further reduce the operation cost and the annual capital cost on the basis of the fixed structure optimization,and the total annualized cost can be reduced by 30.04%.The optimization result of different flow shows that both the pump network and the water turbine network tend to series structure at a low flow rate whereas to parallel structure at a high flow rate.

A Hybrid Level Set Optimization Design Method of Functionally Graded Cellular Structures Considering Connectivity

With the continuous advancement in topology optimization and additive manufacturing(AM)technology,the capability to fabricate functionally graded materials and intricate cellular structures with spatially varying microstructures has grown significantly.However,a critical challenge is encountered in the design of these structures–the absence of robust interface connections between adjacent microstructures,potentially resulting in diminished efficiency or macroscopic failure.A Hybrid Level Set Method(HLSM)is proposed,specifically designed to enhance connectivity among non-uniform microstructures,contributing to the design of functionally graded cellular structures.The HLSM introduces a pioneering algorithm for effectively blending heterogeneous microstructure interfaces.Initially,an interpolation algorithm is presented to construct transition microstructures seamlessly connected on both sides.Subsequently,the algorithm enables the morphing of non-uniform unit cells to seamlessly adapt to interconnected adjacent microstructures.The method,seamlessly integrated into a multi-scale topology optimization framework using the level set method,exhibits its efficacy through numerical examples,showcasing its prowess in optimizing 2D and 3D functionally graded materials(FGM)and multi-scale topology optimization.In essence,the pressing issue of interface connections in complex structure design is not only addressed but also a robust methodology is introduced,substantiated by numerical evidence,advancing optimization capabilities in the realm of functionally graded materials and cellular structures.

Full-Scale Isogeometric Topology Optimization of Cellular Structures Based on Kirchhoff-Love Shells

Cellular thin-shell structures are widely applied in ultralightweight designs due to their high bearing capacity and strength-to-weight ratio.In this paper,a full-scale isogeometric topology optimization(ITO)method based on Kirchhoff-Love shells for designing cellular tshin-shell structures with excellent damage tolerance ability is proposed.This method utilizes high-order continuous nonuniform rational B-splines(NURBS)as basis functions for Kirchhoff-Love shell elements.The geometric and analysis models of thin shells are unified by isogeometric analysis(IGA)to avoid geometric approximation error and improve computational accuracy.The topological configurations of thin-shell structures are described by constructing the effective density field on the controlmesh.Local volume constraints are imposed in the proximity of each control point to obtain bone-like cellular structures.To facilitate numerical implementation,the p-norm function is used to aggregate local volume constraints into an equivalent global constraint.Several numerical examples are provided to demonstrate the effectiveness of the proposed method.After simulation and comparative analysis,the results indicate that the cellular thin-shell structures optimized by the proposed method exhibit great load-carrying behavior and high damage robustness.

Multi-Scale Design and Optimization of Composite Material Structure for Heavy-Duty Truck Protection Device

In this paper,to present a lightweight-developed front underrun protection device(FUPD)for heavy-duty trucks,plain weave carbon fiber reinforced plastic(CFRP)is used instead of the original high-strength steel.First,the mechanical and structural properties of plain carbon fiber composite anti-collision beams are comparatively analyzed from a multi-scale perspective.For studying the design capability of carbon fiber composite materials,we investigate the effects of TC-33 carbon fiber diameter(D),fiber yarn width(W)and height(H),and fiber yarn density(N)on the front underrun protective beam of carbon fiber compositematerials.Based on the investigation,a material-structure matching strategy suitable for the front underrun protective beam of heavy-duty trucks is proposed.Next,the composite material structure is optimized by applying size optimization and stack sequence optimization methods to obtain the higher performance carbon fiber composite front underrun protection beam of commercial vehicles.The results show that the fiber yarn height(H)has the greatest influence on the protective beam,and theH1matching scheme for the front underrun protective beamwith a carbon fiber composite structure exhibits superior performance.The proposed method achieves a weight reduction of 55.21% while still meeting regulatory requirements,which demonstrates its remarkable weight reduction effect.

Identification of time-varying system and energy-based optimization of adaptive control in seismically excited structure

The combination of structural health monitoring and vibration control is of great importance to provide components of smart structures.While synthetic algorithms have been proposed,adaptive control that is compatible with changing conditions still needs to be used,and time-varying systems are required to be simultaneously estimated with the application of adaptive control.In this research,the identification of structural time-varying dynamic characteristics and optimized simple adaptive control are integrated.First,reduced variations of physical parameters are estimated online using the multiple forgetting factor recursive least squares(MFRLS)method.Then,the energy from the structural vibration is simultaneously specified to optimize the control force with the identified parameters to be operational.Optimization is also performed based on the probability density function of the energy under the seismic excitation at any time.Finally,the optimal control force is obtained by the simple adaptive control(SAC)algorithm and energy coefficient.A numerical example and benchmark structure are employed to investigate the efficiency of the proposed approach.The simulation results revealed the effectiveness of the integrated online identification and optimal adaptive control in systems.

Effect of Property Tax on Optimization and Upgrading of Industrial Structure

China's economic growth and economic development has entered a new stage,and the optimization and upgrading of industrial structure is the core driving force for China to achieve high-quality economic development during the"14 th Five-Year Plan"period.Property tax has a conductive effect on the upgrading of industrial structure.Therefore,from the perspective of property tax and industrial structure adjustment and the relationship between them,this study summarizes the relevant research of domestic and foreign scholars.On the basis of the research,the paper puts forward some relevant policy suggestions on improving China's property tax and promoting the optimization and upgrading of China's industrial structure.

Optimal Insurance with Background Risk under the Ambiguity and Belief Heterogeneity Structure

In this paper, we discuss the optimal insurance in the presence of background risk while the insured is ambiguity averse and there exists belief heterogeneity between the insured and the insurer. We give the optimal insurance contract when maxing the insured’s expected utility of his/her remaining wealth under the smooth ambiguity model and the heterogeneous belief form satisfying the MHR condition. We calculate the insurance premium by using generalized Wang’s premium and also introduce a series of stochastic orders proposed by [1] to describe the relationships among the insurable risk, background risk and ambiguity parameter. We obtain the deductible insurance is the optimal insurance while they meet specific dependence structures.

Cost-optimization based target reliabilities for design of structures exposed to fire

Adequacy of structural fire design in uncommon structures is conceptually ensured through cost-benefit analysis where the future costs are balanced against the benefits of safety investment.Cost-benefit analyses,however,are complicated and computationally challenging,and hence impractical for application to individual projects.To address this issue,design guidance proposes target reliability indices for normal design conditions,but no target reliability indices are defined for structural fire design.We revisit the background of the cost-optimization based approach underlying normal design target reliability indices then we extend this approach for the case of fire design of structures.We also propose a modified objective function for cost-optimization which simplifies the evaluation of target reliability indices and reduces the number of assumptions.The optimum safety level is expressed as a function of a new dimensionless variable named“Damage-to-investment indicator”(DII).The cost optimization approach is validated for the target reliability indices for normal design condition.The method is then applied for evaluating DII and the associated optimum reliability indices for fire-exposed structures.Two case studies are presented:(i)a one-way loaded reinforced concrete slab and(ii)a steel column under axial loading.This study thus provides a framework for deriving optimum(target)reliability index for structural fire design which can support the development of rational provisions in codes and standards.

A novel robust design method for improving stability of optimized structures

It is known that structural optimization may lead to designs of structures having low stability and sometimes even kinematically unstable designs. This paper presents a robust design method for improving the stability of opti mized structures. A new approach is proposed, in which cer tain perturbation loads are introduced and the corresponding compliance is added to the objective function as a penaliza tion. The stability of the optimized structures can thus be improved substantially by considering structural responses to the original and the introduced loads. Numerical exam ples show the simplicity and effectiveness of the proposed method.

Optimized body structure and packaging for car ODB impact performance

Front bumper, crash box and side rail are key body structural parts in front crash. Deformation space is affected by compartment packaging. The improvement suggestions are proposed to solve the problems existed in the current vehicle struc- ture and compartment packaging based on the areas that influence performance of automobile offset deformable barrier impact, such as the side rail, mounting, storage battery packaging,etc. It is proved that dO % offset crash simulation result of one certain car is well-correlated with the physical test. Optimization cases meet the crash performance requirements. The objec- tive of the analysis is to guide structural design and improves a car＇ s crash safety performance.

An Optimized Structure Design of the HT-7U Vacuum Vessel

The vacuum vessel of the HT-7U superconducting tokamak will be a fully-welded structure with a double-wall. The space between the double-wall will be filled with borated water for neutron shielding. Non-circular cross-section is designed for plasma elongating. Horizontal and vertical ports are designed for diagnosing, vacuum pumping, plasma heating and plasma current driving, etc. The vacuum vessel consists of 16 segments. It will be baked out at 250℃ to obtain a clean wall. When the machine is in operation, both the hot wall (the wall temperature is around 100℃) and the cold wall (wall temperature is in normal equilibrium) are considered. The stress caused by thermal deformation and the electromagnetic (EM) loads caused by 1.5 MA plasma disruption in 3.5 T magnetic field have to be taken into account in the design of the HT-7U vacuum vessel Finite element method was employed for structure analysis of the vacuum vessel.

Optimized geometry and electronic structure of graphyne-like silicyne nanoribbons

Silicyne, a silicon allotrope, which is closely related to silicene and has graphyne-like structure, is theoretically in- vestigated in this work. Its optimized geometry and electronic band structure are calculated by means of the first-principles frozen-core projector-augmented wave method implemented in the Vienna ab initio simulation package （VASP）. We find that the lattice parameter is 9.5A, the silicon chain between hexagons is composed of disilynic linkages （-Si≡Si-） rather than cumulative linkages （=Si=Si=）, and the binding energy is -3.41 eV per atom. The band structure is calculated by adopting the generalized gradient approximation and hybrid functionals. The band gap produced by the HSE06 functional is 0.73 eV, which is nearly triple that by the generalized gradient approximation of Perdew-Burke-Emzerhof functional.

How to Optimize the Structure of Agricultural Products in the Context of Reform of the Supply Front?

Based on reform of the supply front,this paper analyzes the main constraints on China's current structure of agricultural products,including irrational allocation of resources between agricultural products,prominent problems concerning agricultural product quality and safety,disconnection between market demand and agricultural product R&D,and low processing capacity of agricultural products. Based on summing up the experience of the countries with developed agriculture,this paper proposes the path and mechanism for the optimization of structure of agricultural products in China: optimizing resource allocation of agricultural products; improving the quality of agricultural products; enhancing the R&D capacity of agricultural enterprises; promoting the processing and conversion capacity of agricultural products; perfecting the policy support and subsidy mode.

Optimization models of stand structure and selective cutting cycle for large diameter trees of broadleaved forest in Changbai Mountain

The optimum models of harvesting yield and net profits of large diameter trees for broadleaved forest were developed, of which include matrix growth sub-model, harvesting cost and wood price sub-models, based on the data from Hongshi Forestry Bureau, in Changbai Mountain region, Jilin Province, China. The data were measured in 232 permanent sample plots. With the data of permanent sample plots, the parameters of transition probability and ingrowth models were estimated, and some models were compared and partly modified. During the simulation of stand structure, four factors such as largest diameter residual tree （LDT）, the ratio of the number of trees in a given diameter class to those in the next larger diameter class （q）, residual basal area （RBA） and selective cutting cycle （C） were considered. The simulation results showed that the optimum stand structure parameters for large diameter trees are as follows： q is 1.2, LDT is 46cm, RBA is larger than 26 m^2 and selective cutting cycle time （C） is between 10 and 20 years.