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.

Structural Optimization of Hatch Cover Based on Bi-directional Evolutionary Structure Optimization and Surrogate Model Method

Weight reduction has attracted much attention among ship designers and ship owners.In the present work,based on an improved bi-directional evolutionary structural optimization(BESO) method and surrogate model method,we propose a hybrid optimization method for the structural design optimization of beam-plate structures,which covers three optimization levels:dimension optimization,topology optimization and section optimization.The objective of the proposed optimization method is to minimize the weight of design object under a group of constraints.The kernel optimization procedure(KOP) uses BESO to obtain the optimal topology from a ground structure.To deal with beam-plate structures,the traditional BESO method is improved by using cubic box as the unit cell instead of solid unit to construct periodic lattice structure.In the first optimization level,a series of ground structures are generated based on different dimensional parameter combinations,the KOP is performed to all the ground structures,the response surface model of optimal objective values and dimension parameters is created,and then the optimal dimension parameters can be obtained.In the second optimization level,the optimal topology is obtained by using the KOP according to the optimal dimension parameters.In the third optimization level,response surface method(RSM) is used to determine the section parameters.The proposed method is applied to a hatch cover structure design.The locations and shapes of all the structural members are determined from an oversized ground structure.The results show that the proposed method leads to a greater weight saving,compared with the original design and genetic algorithm(GA) based optimization results.

A Modified Bi-Directional Evolutionary Structural Optimization Procedure with Variable Evolutionary Volume Ratio Applied to Multi-Objective Topology Optimization Problem

Natural frequency and dynamic stiffness under transient loading are two key performances for structural design related to automotive,aviation and construction industries.This article aims to tackle the multi-objective topological optimization problem considering dynamic stiffness and natural frequency using modified version of bi-directional evolutionary structural optimization(BESO).The conventional BESO is provided with constant evolutionary volume ratio(EVR),whereas low EVR greatly retards the optimization process and high EVR improperly removes the efficient elements.To address the issue,the modified BESO with variable EVR is introduced.To compromise the natural frequency and the dynamic stiffness,a weighting scheme of sensitivity numbers is employed to form the Pareto solution space.Several numerical examples demonstrate that the optimal solutions obtained from the modified BESO method have good agreement with those from the classic BESO method.Most importantly,the dynamic removal strategy with the variable EVR sharply springs up the optimization process.Therefore,it is concluded that the modified BESO method with variable EVR can solve structural design problems using multi-objective optimization.

Evolutionary Pattern and Effect of Administrative Division Adjustment During Urbanization of China:Empirical Analysis on Multiple Scales

The adjustment of administrative divisions is one of the important factors guiding China's urbanization, which has profound economic and social effects for regional development. In this paper, we comprehensively describe the process of the adjustment of administrative divisions at provincial and municipal levels in China and summarize the effects on the basic structure and patterns of the spatial development. We quantitatively assess the effects on fields such as urbanization and social economy through the use of multidimensional scaling. The results show that: 1) Upgrading county to municipality(or city-governed district) is the main way of adjusting the administrative divisions. It is also an important factor in the spatial differentiation of interprovincial urbanization. China's population urbanization can be divided into four patterns including interprovincial migration, provincial migration, natural growth, and growth caused by the adjustment of administrative divisions, which is also the main reason for the increased Chinese urbanization rate at the provincial level. 2) Taking the city of Beijing as an example, we generalize five adjustment patterns made to administrative divisions: the set-up of sub-districts, the set-up of regional offices, the upgrading of townships to sub-districts, the upgrading of townships to towns, and the set-up of towns and the addition of new regional offices. We summarize the municipal urban spatial structure, including the sub-district office area in the central urban area, the regional office area in the new urban area, the mixed area of villages, towns, and sub-district offices in the suburb area, and the township area in the outer suburb area. 3) The adjustment of administrative divisions triggers a significant circulative accumulation effect, resulting in the spatial locking of population and industrial agglomeration. It affects the evolution of the urban spatial form and plays an important role in shaping the urban spatial structure to move to the characteristic of multicenter. In general, the adjustment of administrative divisions was an important factor affecting the inflated statistical level of urbanization and also an important driving force for the evolution of Chinese urban spatial organization structure.

EVOLUTIONARY MODEL OF FREE ECONOMIC ZONES——Different Generations and Structural Features

Free economic zone (FEZ) has a long history and plays a more and more important role in the world economy. Most studies, however, focused on the theoretical analysis of benefit and cost as well as the economic role of FEZ in the less developed countries and little attention has been paid to the evolution of FEZ. This paper will improve the above-mentioned studies and put forward the structural and spatial evolutionary model of FEZ by analyzing the development of objectives, preferential policy, governance structure, industrial sectors and location of FEZs based on the international economic and political development. FEZs develop towards: 1) more comprehensive and macro objectives, 2) more industry-oriented and multi-preferential policies, 3) more cross-national and combination zones with administrative areas, 4) more technology-intensive and multi-industries, 5) more flexible location and larger spatial dimensions, 6) more rapid evolution and typologies, and 7) more economic integration to the host economy.

Topology Optimization with Aperiodic Load Fatigue Constraints Based on Bidirectional Evolutionary Structural Optimization

Because of descriptive nonlinearity and computational inefficiency,topology optimization with fatigue life under aperiodic loads has developed slowly.A fatigue constraint topology optimization method based on bidirectional evolutionary structural optimization(BESO)under an aperiodic load is proposed in this paper.In viewof the severe nonlinearity of fatigue damagewith respect to design variables,effective stress cycles are extracted through transient dynamic analysis.Based on the Miner cumulative damage theory and life requirements,a fatigue constraint is first quantified and then transformed into a stress problem.Then,a normalized termination criterion is proposed by approximatemaximum stress measured by global stress using a P-normaggregation function.Finally,optimization examples show that the proposed algorithm can not only meet the requirements of fatigue life but also obtain a reasonable configuration.

Stress Relaxation and Sensitivity Weight for Bi-Directional Evolutionary Structural Optimization to Improve the Computational Efficiency and Stabilization on Stress-Based Topology Optimization

Stress-based topology optimization is one of the most concerns of structural optimization and receives much attention in a wide range of engineering designs.To solve the inherent issues of stress-based topology optimization,many schemes are added to the conventional bi-directional evolutionary structural optimization(BESO)method in the previous studies.However,these schemes degrade the generality of BESO and increase the computational cost.This study proposes an improved topology optimization method for the continuum structures considering stress minimization in the framework of the conventional BESO method.A global stress measure constructed by p-norm function is treated as the objective function.To stabilize the optimization process,both qp-relaxation and sensitivity weight scheme are introduced.Design variables are updated by the conventional BESO method.Several 2D and 3D examples are used to demonstrate the validity of the proposed method.The results show that the optimization process can be stabilized by qp-relaxation.The value of q and p are crucial to reasonable solutions.The proposed sensitivity weight scheme further stabilizes the optimization process and evenly distributes the stress field.The computational efficiency of the proposed method is higher than the previous methods because it keeps the generality of BESO and does not need additional schemes.

Comparison on construction of strut-and-tie models for reinforced concrete deep beams

With consideration of the differences between concrete and steel,three solutions using genetic evolutionary structural optimization algorithm were presented to automatically develop optimal strut-and-tie model for deep beams.In the finite element analysis of the first method,the concrete and steel rebar are modeled by a plane element and a bar element,respectively.In the second method,the concrete and steel are assigned to two different plane elements,whereas in the third method only one kind of plane element is used with no consideration of the differences of the two materials.A simply supported beam under two point loads was presented as an example to verify the validity of the three proposed methods.The results indicates that all the three methods can generate optimal strut-and-tie models and the third algorithm has powerful capability in searching more optimal results with less computational effort.The effectiveness of the proposed algorithm III has also been demonstrated by other two examples.

Structural Topology Optimization by Combining BESO with Reinforcement Learning

In this paper,a new algorithm combining the features of bi-direction evolutionary structural optimization(BESO)and reinforcement learning(RL)is proposed for continuum structural topology optimization(STO).In contrast to conventional approaches which only generate a certain quasi-optimal solution,the goal of the combined method is to provide more quasi-optimal solutions for designers such as the idea of generative design.Two key components were adopted.First,besides sensitivity,value function updated by Monte-Carlo reinforcement learning was utilized to measure the importance of each element,which made the solving process convergent and closer to the optimum.Second,ε-greedy policy added a random perturbation to the main search direction so as to extend the search ability.Finally,the quality and diversity of solutions could be guaranteed by controlling the value of compliance as well as Intersection-over-Union(IoU).Results of several 2D and 3D compliance minimization problems,including a geometrically nonlinear case,show that the combined method is capable of generating a group of good and different solutions that satisfy various possible requirements in engineering design within acceptable computation cost.

Biologically Inspired Girder Structure for the Synchrotron Radiation Facility PETRA IV

Lightweight structures are widely used across different industry sectors.However,they get easily excited by external influences,such as vibrations.Undesired high vibration amplitudes can be avoided by shifting the structural eigenfrequencies,which can be achieved adapting the structural design considering optimisation procedures and structures primarily inspired by diatoms.This procedures has been applied to the development process of a girder structure installed in a synchrotron radiation facility to support heavy magnets and other components.The objective was to design a 2.9 m long girder structure with high eigenfrequencies,a high stiffness and a low mass.Based on a topology optimisation result,a parametric beam–shell model including biologically inspired structures(e.g.,Voronoi combs,ribs,and soft and organic-looking transitions)was built up.The subsequent cross-sectional optimisation using evolutionary strategic optimisation revealed an optimum girder structure,which was successfully manufactured using the casting technology.Eigenfrequency measurements validated the numerical models.Future changes in the specifications can be implemented in the bio-inspired development process to obtain adapted girder structures.

Layout optimization of steel reinforcement in concrete structure using a truss-continuum model

Owing to advancement in advanced manufacturing technology,the reinforcement design of concrete structures has become an important topic in structural engineering.Based on bi-directional evolutionary structural optimization(BESO),a new approach is developed in this study to optimize the reinforcement layout in steel-reinforced concrete(SRC)structures.This approach combines a minimum compliance objective function with a hybrid trusscontinuum model.Furthermore,a modified bi-directional evolutionary structural optimization(M-BESO)method is proposed to control the level of tensile stress in concrete.To fully utilize the tensile strength of steel and the compressive strength of concrete,the optimization sensitivity of steel in a concrete–steel composite is integrated with the average normal stress of a neighboring concrete.To demonstrate the effectiveness of the proposed procedures,reinforcement layout optimizations of a simply supported beam,a corbel,and a wall with a window are conducted.Clear steel trajectories of SRC structures can be obtained using both methods.The area of critical tensile stress in concrete yielded by the M-BESO is more than 40%lower than that yielded by the uniform design and BESO.Hence,the M-BESO facilitates a fully digital workflow that can be extremely effective for improving the design of steel reinforcements in concrete structures.

COMPUTER PROGRAM FOR DIRECTED STRUCTURE TOPOLOGY OPTIMIZATION

To compensate for the imperfection of traditional bi-directional evolutionary structural optimization, material interpolation scheme and sensitivity filter functions are introduced. A suitable filter can overcome the checkerboard and mesh-dependency. And the historical information on accurate elemental sensitivity numbers are used to keep the objective function converging steadily. Apart from rational intervals of the relevant important parameters, the concept of distinguishing between active and non-active elements design is proposed, which can be widely used for improving the function and artistry of structures directly, especially for a one whose accurate size is not given. Furthermore, user-friendly software packages are developed to enhance its accessibility for practicing engineers and architects. And to reduce the time cost for large timeconsuming complex structure optimization, parallel computing is built-in in the MATLAB codes. The program is easy to use for engineers who may not be familiar with either FEA or structure optimization. And developers can make a deep research on the algorithm by changing the MATLAB codes. Several classical examples are given to show that the improved BESO method is superior for its handy and utility computer program software.

Structural-acoustic topology optimization analysis based on evolutionary structural optimization approach

The continuum structural-acoustic topology optimization with external loading is investigated herein. Finite element method （FEM） is used to obtain the structural frequency response and boundary element method （BEM） is adopted to perform exterior acoustic radiation analysis. The evolutionary structural optimization （ESO） is served as an optimization method in structural-acoustic radiation topology analysis. The acoustic radiation optimization of a plate under harmonic excitation is given for example. The numerical results show that using ESO solution to analyze structural-acoustic topology optimization is feasible and effective.

Detail control strategies for topology optimization in architectural design and development

With the ability to generate forms with high efficiency and elegant geometry,topology optimization has been increasingly used in architectural and structural designs.However,the conventional topology optimization techniques aim at achieving the structurally most efficient solution without any potential for architects or designers to control the design details.This paper introduces three strategies based on Bi-directional Evolutionary Structural Optimization(BESO)method to artificially pre-design the topological optimized structures.These strategies have been successfully applied in the computational morphogenesis of various structures for solving practical design problems.The results demonstrate that the developed methodology can provide the designer with structurally efficient and topologically different solutions according to their proposed designs with multi-filter radii,multi-volume fractions,and multi-weighting coefficients.This work establishes a general approach to integrating objective topology optimization methods with subjective human design preferences,which has great potential for practical applications in architecture and engineering industry.

Advances in Low-Level Jet Research and Future Prospects

The low-level jet （LLJ） is closely related to severe rainfall events, air pollution, wind energy utilization, aviation safety, sandstorms, forest fire, and other weather and climate phenomena. Therefore, it has attracted considerable attention since its discovery. Scientists have carried out many studies on LLJs and made significant achievements during the past five or six decades. This article summarizes and assesses the current knowledge on this subject, and focuses in particular on three aspects： 1） LLJ classification, definition, distribution, and structure; 2） LLJ formation and evolutionary mechanisms; and 3） relationships between LLJ and rainfall, as well as other interdisciplinary fields. After comparing the status of LLJ research at home （China） and abroad, we then discuss the shortcomings of LLJ research in China. We suggest that this includes： coarse definitions of the LLJ, lack of observations and inadequate quality control, few thorough explorations of LLJ characteristics and formation mechanisms, and limited studies in interdisciplinary fields. The future prospects for several LLJ research avenues are also speculated.