Concurrent multi-scale design optimization of composite frame structures using the Heaviside penalization of discrete material model

This paper deals with the concurrent multi-scale optimization design of frame structure composed of glass or carbon fiber reinforced polymer laminates. In the composite frame structure, the fiber winding angle at the micro-material scale and the geometrical parameter of components of the frame in the macro-structural scale are introduced as the independent variables on the two geometrical scales. Considering manufacturing requirements, discrete fiber winding angles are specified for the micro design variable. The improved Heaviside penalization discrete material optimization interpolation scheme has been applied to achieve the discrete optimization design of the fiber winding angle. An optimization model based on the minimum structural compliance and the specified fiber material volume constraint has been established. The sensitivity information about the two geometrical scales design variables are also deduced considering the characteristics of discrete fiber winding angles. The optimization results of the fiber winding angle or the macro structural topology on the two single geometrical scales, together with the concurrent two-scale optimization, is separately studied and compared in the paper. Numerical examples in the paper show that the concurrent multi-scale optimization can further explore the coupling effect between the macro-structure and micro-material of the composite to achieve an ultralight design of the composite frame structure. The novel two geometrical scales optimization model provides a new opportunity for the design of composite structure in aerospace and other industries.

APPROACH FOR LAYOUT OPTIMIZATION OF TRUSS STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS, DISPLACEMENT AND STABILITY CONSTRAINTS

A mathematical model was developed for layout optimization of truss structures with discrete variables subjected to dynamic stress, dynamic displacement and dynamic stability constraints. By using the quasi-static method, the mathematical model of structure optimization under dynamic stress, dynamic displacement and dynamic stability constraints were transformed into one subjected to static stress, displacement and stability constraints. The optimization procedures include two levels, i.e., the topology optimization and the shape optimization. In each level, the comprehensive algorithm was used and the relative difference quotients of two kinds of variables were used to search the optimum solution. A comparison between the optimum results of model with stability constraints and the optimum results of model without stability constraint was given. And that shows the stability constraints have a great effect on the optimum solutions.

An extended stress-based method for orientation angle optimization of laminated composite structures

Orientation optimization plays an important role in the lay-up design of composite structures.Earlier orientation optimization methods face the main problem of huge number of design variables.Recently,a patch concept is proposed to reduce the number of design variables.However,the traditional stress-based method can not deal with patch orientation optimization of composite structures.In this paper,we propose an extended stress-based method to deal with such problems.The considered problems are to minimize the mean compliance under multiple load cases or to maximize the eigenvalues of a composite structure.Four numerical examples are solved to demonstrate the efficiency of the new method.It is shown that the new method has the ability to deal with constraints on orientation angle,such as symmetric,antisymmetric and discrete orientation angle constraints.The iteration is less time-consuming because no sensitivity analysis is needed and a quick convergence rate can be achieved.

Reliability based multiobjective optimization for design of structures subject to random vibrations

Based on a multiobjective approach whose objective function (OF) vector collects stochastic reliability performance and structural cost indices, a structural optimization criterion for mechanical systems subject to random vibrations is presented for supporting engineer’s design. This criterion differs from the most commonly used conventional optimum design criterion for random vibrating structure, which is based on minimizing displacement or acceleration variance of main structure responses, without considering explicitly required performances against failure. The proposed criterion can properly take into account the design-reliability required performances, and it becomes a more efficient support for structural engineering decision making. The multiobjective optimum (MOO) design of a tuned mass damper (TMD) has been developed in a typical seismic design problem, to control structural vibration induced on a multi-storey building structure excited by nonstationary base acceleration random process. A numerical example for a three-storey building is developed and a sensitivity analysis is carried out. The results are shown in a useful manner for TMD design decision support.

Contrastive analysis and crashworthiness optimization of two composite thin-walled structures

For the safety protection of passengers when train crashes occur, special structures are crucially needed as a kind of indispensable energy absorbing device. With the help of the structures, crash kinetic-energy can be completely absorbed or dissipated for the aim of safety. Two composite structures(circumscribed circle structure and inscribed circle structure) were constructed. In addition, comparison and optimization of the crashworthy characteristic of the two structures were carried out based on the method of explicit finite element analysis(FEA) and Kriging surrogate model. According to the result of Kriging surrogate model, conclusions can be safely drawn that the specific energy absorption(SEA) and ratio of specific energy absorption to initial peak force(REAF) of circumscribed circle structure are lager than those of inscribed circle structure under the same design parameters. In other words, circumscribed circle structure has better performances with higher energy-absorbing ability and lower initial peak force. Besides, error analysis was adopted and the result of which indicates that the Kriging surrogate model has high nonlinear fitting precision. What is more, the SEA and REAF optimum values of the two structures have been obtained through analysis, and the crushing results have been illustrated when the two structures reach optimum SEA and REAF.

A METHOD FOR TOPOLOGICAL OPTIMIZATION OF STRUCTURES WITH DISCRETE VARIABLES UNDER DYNAMIC STRESS AND DISPLACEMENT CONSTRAINTS

A method for topological optimization of structures with discrete variables subjected to dynamic stress and displacement constraints is presented. By using the quasistatic method, the structure optimization problem under dynamic stress and displacement constraints is converted into one subjected to static stress and displacement constraints. The comprehensive algorithm for topological optimization of structures with discrete variables is used to find the optimum solution.

A COMBINAT0RIAL ALGORITHM FOR THE DISCRETE OPTIMIZATION OF STRUCTURES

The definition of local optimum solution of the discrete optimization is first given.and then a comprehensive combinatorial algorithm is proposed in this paper. Two-leveloptimum method is used in the algorithm. In the first level optimization, anapproximate local optimum solution X is found by using the heuristic algorithm,relative difference quotient algorithm. with high computational efficiency and highperformance demonstrated by the performance test of random samples. In the secondlevel, a mathematical model of (- 1, 0, 1) programming is established first, and then itis changed into (0, 1) programming model. The local optimum solution X will befrom the (0. 1) programming by using the delimitative and combinatorial algorithm orthe relative difference quotient algorithm. By this algorithm, the local optimumsolution can be obtained certainly, and a method is provnded to judge whether or notthe approximate optimum solution obtained by heuristic algorithm is an optimumsolution. The above comprehensive combinatorial algorithm has higher computationalefficiency.

Shape and Size Optimization of Truss Structures under Frequency Constraints Based on Hybrid Sine Cosine Firefly Algorithm

Shape and size optimization with frequency constraints is a highly nonlinear problem withmixed design variables,non-convex search space,and multiple local optima.Therefore,a hybrid sine cosine firefly algorithm(HSCFA)is proposed to acquire more accurate solutions with less finite element analysis.The full attraction model of firefly algorithm(FA)is analyzed,and the factors that affect its computational efficiency and accuracy are revealed.A modified FA with simplified attraction model and adaptive parameter of sine cosine algorithm(SCA)is proposed to reduce the computational complexity and enhance the convergence rate.Then,the population is classified,and different populations are updated by modified FA and SCA respectively.Besides,the random search strategy based on Lévy flight is adopted to update the stagnant or infeasible solutions to enhance the population diversity.Elitist selection technique is applied to save the promising solutions and further improve the convergence rate.Moreover,the adaptive penalty function is employed to deal with the constraints.Finally,the performance of HSCFA is demonstrated through the numerical examples with nonstructural masses and frequency constraints.The results show that HSCFA is an efficient and competitive tool for shape and size optimization problems with frequency constraints.

A Smooth Bidirectional Evolutionary Structural Optimization of Vibrational Structures for Natural Frequency and Dynamic Compliance

A smooth bidirectional evolutionary structural optimization(SBESO),as a bidirectional version of SESO is proposed to solve the topological optimization of vibrating continuum structures for natural frequencies and dynamic compliance under the transient load.A weighted function is introduced to regulate the mass and stiffness matrix of an element,which has the inefficient element gradually removed from the design domain as if it were undergoing damage.Aiming at maximizing the natural frequency of a structure,the frequency optimization formulation is proposed using the SBESO technique.The effects of various weight functions including constant,linear and sine functions on structural optimization are compared.With the equivalent static load(ESL)method,the dynamic stiffness optimization of a structure is formulated by the SBESO technique.Numerical examples show that compared with the classic BESO method,the SBESO method can efficiently suppress the excessive element deletion by adjusting the element deletion rate and weight function.It is also found that the proposed SBESO technique can obtain an efficient configuration and smooth boundary and demonstrate the advantages over the classic BESO technique.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

Vibration Control of the Rail Grinding Vehicle with Abrasive Belt Based on Structural Optimization and Lightweight Design

As a new grinding and maintenance technology,rail belt grinding shows significant advantages in many applications The dynamic characteristics of the rail belt grinding vehicle largely determines its grinding performance and service life.In order to explore the vibration control method of the rail grinding vehicle with abrasive belt,the vibration response changes in structural optimization and lightweight design are respectively analyzed through transient response and random vibration simulations in this paper.Firstly,the transient response simulation analysis of the rail grinding vehicle with abrasive belt is carried out under operating conditions and non-operating conditions.Secondly,the vibration control of the grinding vehicle is implemented by setting vibration isolation elements,optimizing the structure,and increasing damping.Thirdly,in order to further explore the dynamic characteristics of the rail grinding vehicle,the random vibration simulation analysis of the grinding vehicle is carried out under the condition of the horizontal irregularity of the American AAR6 track.Finally,by replacing the Q235 steel frame material with 7075 aluminum alloy and LA43M magnesium alloy,both vibration control and lightweight design can be achieved simultaneously.The results of transient dynamic response analysis show that the acceleration of most positions in the two working conditions exceeds the standard value in GB/T 17426-1998 standard.By optimizing the structure of the grinding vehicle in three ways,the average vibration acceleration of the whole car is reduced by about 55.1%from 15.6 m/s^(2) to 7.0 m/s^(2).The results of random vibration analysis show that the grinding vehicle with Q235 steel frame does not meet the safety conditions of 3σ.By changing frame material,the maximum vibration stress of the vehicle can be reduced from 240.7 MPa to 160.0 MPa and the weight of the grinding vehicle is reduced by about 21.7%from 1500 kg to 1175 kg.The modal analysis results indicate that the vibration control of the grinding vehicle can be realized by optimizing the structure and replacing the materials with lower stiffness under the premise of ensuring the overall strength.The study provides the basis for the development of lightweight,diversified and efficient rail grinding equipment.

A novel triple periodic minimal surface-like plate lattice and its data-driven optimization method for superior mechanical properties

Lattice structures can be designed to achieve unique mechanical properties and have attracted increasing attention for applications in high-end industrial equipment,along with the advances in additive manufacturing(AM)technologies.In this work,a novel design of plate lattice structures described by a parametric model is proposed to enrich the design space of plate lattice structures with high connectivity suitable for AM processes.The parametric model takes the basic unit of the triple periodic minimal surface(TPMS)lattice as a skeleton and adopts a set of generation parameters to determine the plate lattice structure with different topologies,which takes the advantages of both plate lattices for superior specific mechanical properties and TPMS lattices for high connectivity,and therefore is referred to as a TPMS-like plate lattice(TLPL).Furthermore,a data-driven shape optimization method is proposed to optimize the TLPL structure for maximum mechanical properties with or without the isotropic constraints.In this method,the genetic algorithm for the optimization is utilized for global search capability,and an artificial neural network(ANN)model for individual fitness estimation is integrated for high efficiency.A set of optimized TLPLs at different relative densities are experimentally validated by the selective laser melting(SLM)fabricated samples.It is confirmed that the optimized TLPLs could achieve elastic isotropy and have superior stiffness over other isotropic lattice structures.

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.

Structural optimization of a reusable seismic frame active link

Circular design encompasses the use of inventive construction methodologies that possess the capability to be readily dismantled,repurposed,or recycled upon reaching the conclusion of their functional lifespan.This work specifically examines the creation of a reusable design case-study idea for seismic frame design,which is commonly employed in steel-frame constructions in New Zealand.A reusable optimized design for the full seismic frame was proposed in the research.Optimizing the dimensions of welded structures,whether in terms of weight or cost,leads to a decrease in the weight of the steel utilized.The decrease in weight is directly associated with a decrease in environ-mental impact,as the environmental impact is directly proportional to the mass of the construction.The environmental consequences associated with welding technique are contingent upon the dimensions of the weld,hence exerting an indirect influence on the overall mass of the structure.Given the presence of mass dependence in all three areas,albeit in distinct manners,this work employed a multi-objective function optimization strategy to simultaneously address these areas while also partially evaluating them separately.On this way substantial reductions can be achieved both at structural mass and environmental effects.

Genetic Optimization via Diverse Crossover Intelligence

An intelligent crossover methodology within the genetic algorithm (GA) is explored within both mathematical and finite element arenas improving both design and solution convergence time. This improved intelligent crossover outperforms the traditional genetic algorithm combined with a rule-based approach utilizing domain specific knowledge developed by Webb, et al. [1]. The encoding of the improved crossover consists of two chromosome strings within the genetic algorithm where the first string represents the design or solution string, and the second string represents chromosome crossover string intelligence. This improved crossover methodology saves the best population members or designs evaluated from each generation and applies crossover chromosome intelligence to the best saved population members paired with globally selected parents. Enhanced features of this crossover methodology employ the random selection of the best designs from the prior generation as a potential parent coupled with alternating intelligence pairing methods. In addition to this approach, two globally selected parents possess the ability to mate utilizing crossover chromosome string intelligence maintaining the integrity of a global GA search. Overall, the final population following crossover employs both global and best generation design chromosome strings to maximize creativity while enhancing the solution search. This is a modification to a conventional GA that can be translated into GA encoding. This technique is explored initially through a Base 10 mathematical application followed by the examination of plate structural optimization considering stress and displacement constraints. Results from crossover intelligence are compared with the conventional genetic algorithm and from Webb, et al. [1] which illustrates the outcome of a two phase genetic optimization algorithm.

POST-BUCKLING ANALYSIS AND STRUCTURE OPTIMIZATION OF INTEGRAL FUSELAGE PANEL SUBJECTED TO AXIAL COMPRESSION LOAD

Build-up panels for the commercial aircraft fuselage subjected to the axial compression load are studied by both experimental and theoretical methods.An integral panel is designed with the same overall size and weight as the build-up structure,and finite element models（FEMs）of these two panels are established.Experimental results of build-up panels agree well with the FEM results with the nonliearity and the large deformation,so FEMs are validated.FEM calculation results of these two panels indicate that the failure mode of the integral panel is different from that of the build-up panel,and the failure load increases by 18.4% up to post-buckling.Furthermore,the integral structure is optimized by using the multi-island genetic algorithm and the sequential quadratic programming.Compared with the initial design,the optimal mass is reduced by 8.7% and the strength is unchanged.

Shape Optimization With Sensitivity Analysis in Local Domain

For complicated geometries, it is ineflicient to integrate over the entire domain. A new approach for optimization is presented here, based on sensitivity analysis of local do- main and deformation of full domain. Accurate results of design sensitivity analysis are ob- tained with this approach in shape optimization. This method is shown to be efficient when used in optimization programs and results in less distortion of the mesh.

APPROXIMATION TECHNIQUES FOR APPLICATION OF GENETIC ALGORITHMS TO STRUCTURAL OPTIMIZATION

Although the genetic algorithm (GA) has very powerful robustness and fitness, it needs a large size of population and a large number of iterations to reach the optimum result. Especially when GA is used in complex structural optimization problems, if the structural reanalysis technique is not adopted, the more the number of finite element analysis (FEA) is, the more the consuming time is. In the conventional structural optimization the number of FEA can be reduced by the structural reanalysis technique based on the approximation techniques and sensitivity analysis. With these techniques, this paper provides a new approximation model-segment approximation model, adopted for the GA application. This segment approximation model can decrease the number of FEA and increase the convergence rate of GA. So it can apparently decrease the computation time of GA. Two examples demonstrate the availability of the new segment approximation model.

Recent development in structural design and optimization

With the fast development of computational mechanics and the capacity as well as the speed of modern computers,simulation-based structural optimization has become an indispensable tool in the design process of competitive products.This paper presents a brief description of the current status of structural optimization by reviewing some significant progress made in the last decades.Potential research topics are also discussed.The entire literatures of the field are not covered due to the limitation of the length of paper.The scope of this review is limited and closely related to the authors＇ own research interests.

Composite Structural Optimization by Genetic Algorithm and Neural Network Response Surface Modeling

Neural-Network Response Surfaces （NNRS） is applied to replace the actual expensive finite element analysis during the composite structural optimization process. The Orthotropic Experiment Method （OEM） is used to select the most appropriate design samples for network training. The trained response surfaces can either be objective function or constraint conditions. Together with other conven- tional constraints, an optimization model is then set up and can be solved by Genetic Algorithm （GA）. This allows the separation between design analysis modeling and optimization searching. Through an example of a hat-stiffened composite plate design, the weight response surface is constructed to be objective function, and strength and buckling response surfaces as constraints; and all of them are trained through NASTRAN finite element analysis. The results of optimization study illustrate that the cycles of structural analysis ean be remarkably reduced or even eliminated during the optimization, thus greatly raising the efficiency of optimization process. It also observed that NNRS approximation can achieve equal or even better accuracy than conventional functional response surfaces.