Size Optimization Of Structures Research Articles

The lightweight design for the frame structure of FSEC

Vehicle light-weighting is aimed at reducing the curb weight of the vehicle to ensure its strength, safety, and performance, as well as to reduce fuel consumption and exhaust emissions. The use of modern simulation technology in structural optimization design is one of the most important methods to achieve structural lightweight. In this paper, we study the size optimization of the frame structure based on the rules and requirements specified in Formula Student Eclectic China (FSEC), following the race’s rules and requirements, while satisfying the vehicle’s dynamic and static performance requirements. First, a three-dimensional geometric model of the frame structure is developed, and the static and dynamic performance of the frame is simulated using the finite element method. Next, structural size optimization is carried out under the premise of ensuring structural performance. Finally, the feasibility of the optimized structure is evaluated by comparing its performance before and after optimization. The research results show that the final frame structure has been reduced by 7.6 kg and the weight reduction has reached 22.4%. All performance indices meet the requirements of the competition, and a good lightweight effect has been achieved.

Sizing and shape optimization of truss employing a hybrid constraint-handling technique and manta ray foraging optimization

This paper presents an efficient constraint-handling technique (CHT) for metaheuristic algorithms in the size and shape optimization of truss structures. During the search process, the proposed CHT utilizes an improved Deb rule to filter redundant structural analyses and maps the candidate designs onto the feasible boundary for structural optimization to improve its search ability and stability based on the mapping strategy. The performance of the newly developed Manta Ray Foraging Optimization (MRFO) algorithm using the proposed CHT in structural optimization was also examined. Five truss optimization problems are used to examine the efficiency of the hybrid CHT compared with the improved Deb rule, the EDP method, and the mapping strategy. Four widely used metaheuristic algorithms, including HS, PSO, TLBO, and CS, have also been used to evaluate the performance of the MRFO in structural optimization. Numerical results demonstrate that the hybrid CHT can markedly improve both the search capacity and computational efficiency of metaheuristic algorithms. The MRFO does not show obvious weakness compared with existing algorithms in structural optimization. A comparison analysis also shows that the performances of the hybrid CHT vary across optimization algorithms.

Optimal Design of Large-scale Dome Truss Structures with Multiple Frequency Constraints Using Success-history Based Adaptive Differential Evolution Algorithm

The success-history based adaptive differential evolution (SHADE) algorithm is an efficient modified version of the differential evolution (DE) algorithm, and it has been successfully applied to solve some real-world optimization problems. However, to the best of our knowledge, it has been rarely applied in the field of structural optimization. The optimal design of structures with frequency constraints is well known as a highly nonlinear and non-convex optimization problem with many local optima. In this paper, the SHADE algorithm is examined in the context of size optimization of large-scale truss structures with multiple frequency constraints. In SHADE, a historical memory of successful control parameter settings is used to guide the generation of new control parameters. In order to demonstrate the effectiveness and efficiency of SHADE, three truss optimization problems with multiple frequency constraints are presented. The three examples considered in this paper include a 600-bar single-layer dome-shaped truss, a 1180-bar single-layer dome-shaped truss, and a 1410-bar double-layer dome-shaped truss. The results obtained by the SHADE algorithm are presented and compared with the best-known results reported in the literature. Numerical results indicate the effectiveness and superior performance of SHADE over other algorithms in terms of solution accuracy and robustness. It is worth mentioning that in all the three cases considered, the optimal designs obtained by SHADE are the best ones reported in the literature so far. However, SHADE often requires fewer structural analyses than those required by the other algorithms.

MILP-based discrete sizing and topology optimization of truss structures: new formulation and benchmarking

Discrete sizing and topology optimization of truss structures subject to stress and displacement constraints has been formulated as a Mixed-Integer Linear Programming (MILP) problem. The computation time to solve a MILP problem to global optimality via a branch-and-cut solver highly depends on the problem size, the choice of design variables, and the quality of optimization constraint formulations. This paper presents a new formulation for discrete sizing and topology optimization of truss structures, which is benchmarked against two well-known existing formulations. Benchmarking is carried out through case studies to evaluate the influence of the number of structural members, candidate cross sections, load cases, and design constraints (e.g., stress and displacement limits) on computational performance. Results show that one of the existing formulations performs significantly worse than all other formulations. In most cases, the new formulation proposed in this work performs best to obtain near-optimal solutions and verify global optimality in the shortest computation time.

A firefly metaheuristic algorithm for structural size and shape optimization with dynamic constraint

A firefly metaheuristic algorithm for structural size and shape optimization with dynamic constraint

Cascade Structural Sizing Optimization with Large Numbers of Design Variables

In structural sizing optimization problems, the number of design variables typically used is relatively small. The aim of this work is to facilitate the use of large numbers of design variables in such problems, in order to enrich the set of available design options and offer the potential of achieving lower-cost optimal designs. For this purpose, the concept of cascading is employed, which allows an optimization problem to be tackled in a number of successive autonomous optimization stages. In this context, several design variable configurations are constructed, in order to utilize a different configuration at each cascade sizing optimization stage. Each new cascade stage is coupled with the previous one by initializing the new stage using the finally attained optimum design of the previous one. The first optimization stages of the cascade procedure make use of the coarsest configurations with small numbers of design variables and serve the purpose of basic design space exploration. The last stages exploit finer configurations with larger numbers of design variables and aim at fine-tuning the achieved optimal solution. The effectiveness of this sizing optimization approach is assessed using real-world aerospace and civil engineering design problems. Based on the numerical results reported herein, the proposed cascade optimization approach proves to be an effective tool for handling large numbers of design variables and the corresponding extensive design spaces in the framework of structural sizing optimization applications.

Isogeometric interval size optimization of beam structures

Based on beam theory in the framework of isogeometric analysis, an interval size optimization for beam structures is proposed, which not only realizes the lightweight of the beam structure, but also ensures the reliability of the structure. The exact geometry of the beam structure is expressed by non-uniform rational B-splines. According to Timoshenko beam theory, the isogeometric beam stiffness matrix is calculated, and static analysis is carried out. Using Taylor’s formulation and interval extension of the function, the manufacturing tolerance interval optimization model of the beam structure is transformed into a deterministic optimization model. The section size and tolerance of the beam structure are taken as design variables, the mass is taken as the objective function, and the torsional stiffness and bending stiffness are taken as constraint functions. The calculation formulation of second-order sensitivity is deduced, and the optimized results of the beam structure are obtained by using the method of moving asymptotes. The effectiveness of the optimization strategy of this method is proven by three numerical examples. This paper provides isogeometric analysis method to realize the section interval optimization of beam structures without meshing, which guides the lightweight design of beam structures.

Multidisciplinary Optimization for Weight Saving in a Variable Tapered Span-Morphing Wing Using Composite Materials—Application to the UAS-S4

This paper is a follow-up to earlier work on applying multidisciplinary numerical optimization to develop a morphing variable span of a tapered wing (MVSTW) to reduce its weight by using composite materials. This study creates a numerical environment of multidisciplinary optimization by integrating material selection, structural sizing, and topological optimization following aerodynamic optimization results with the aim to assess whether morphing wing optimization is feasible. This sophisticated technology is suggested for developing MVSTWs. As a first step, a problem-specific optimization approach is described for specifying the weight-saving structure of wing components using composite materials. The optimization was performed using several approaches; for example, aerodynamic optimization was performed with CFD and XFLR5 codes, the material selection was conducted using MATLAB code, and sizing and topology optimization was carried out using Altair’s OptiStruct and SolidThinking Inspire solvers. The goal of this research is to achieve the MVSTW’s structural rigidity standards by minimizing wing components’ weight while maximizing stiffness. According to the results of this optimization, the weight of the MVSTW was reduced significantly to 5.5 kg in comparison to the original UAS-S4 wing weight of 6.5kg. The optimization and Finite Element Method results also indicate that the developedmorphing variable span of a tapered wing can complete specified flight missions perfectly and without any mechanical breakdown.

A structural discrete size and topology optimization method with extended approximation concepts

This work focused on the discrete size and topology optimization problems for the structures that could be composed of bars, beams, plates, or a combination of them. A corresponding optimization method was put forward based on the approximate concepts that were extended from the one applied in the previous engineering method. In the proposed method, the primal problem was firstly transformed into a series of explicitly approximate problems involving both 0/1 topology and discrete size variables with the extended approximate concepts. 0/1 topology variables were determined with a genetic algorithm (GA), and the corresponding discrete size variables were optimized after determining 0/1 topology variables. In size optimization, the variables were firstly supposed as continuous and determined, as {overline{mathbf{X}}}^{{left( {mathbf{p}} right)}}, with a dual method through the second-level approximate problems. Then the available discrete size values adjacent to {overline{mathbf{X}}}^{{left( {mathbf{p}} right)}} were selected from the original discrete set, and the size variables could be further determined from these values with a GA. Structural analyses were only conducted before establishing the approximate problems in iteration cycles. Numerical examples were given to illustrate the performance of this method, and the results indicate that this method is quite efficient for the discrete size and topology optimization problem.

Structure design and optimization of ground moving and pole climbing inspection robot

PurposeThe purpose of this paper is to demonstrate a multipurpose inspection robot that can both walk on the ground and climb on poles. The structure design, size optimization, kinematics analysis, experiment and arithmetic of the robot are discussed in the paper.Design/methodology/approachThe robot consists of three adjustable modules and a two-degree-of-freedom parallel mechanism in tandem, and the wheel-finger mechanism of each module can realize wheel-finger opening and closing for fast movement and obstacle crossing. This paper uses geometric analysis and simulation analysis to derive size optimization, and vector coordinate method to derive kinematics. Finally, the experiment is carried out by simulating the working environment of the robot.FindingsThe robot can realize ground walking and ground turning through the robot entity prototype experiment on the built working environment and efficiently realize 0°–90° pole climbing by the assemble design, optimization and machining. In addition, the robot can also smoothly complete the state transition process from 0° ground to 90° pole climbing. Furthermore, the robot shows good environmental self-adaptation and can complete daily inspection work.Originality/valueThe robot can pitch and yaw at a large angle and has six-legged characteristics. It is a multipurpose inspection robot that can walk on the ground and climb on poles. And through structure design, size optimization, kinematics analysis and simulation, the existing robots’ common shortcomings such as poor barrier-crossing ability and poor environmental adaptability are solved.

Improved slime mould algorithm with elitist strategy and its application to structural optimization with natural frequency constraints

An improved slime mould algorithm (ISMA) is proposed and applied to the size optimization of truss structures with natural frequency constraints. The slime mould algorithm is a recently proposed metaheuristic inspired by the morphological changes of the acellular slime mould Physarum polycephalum while foraging. This algorithm has been successfully applied to some real-world optimization problems in science and industry. However, it is found that the classical SMA suffers from slow convergence and often converges prematurely to non-optimal solutions, especially for large-scale optimization problems. Compared to the classical SMA, two main improvements are introduced in the proposed ISMA: (1) In the replacement phase of the ISMA, an elitist strategy is adopted to replace the generational replacement strategy of the classical SMA. The elitist strategy aims to increase the convergence rate of the ISMA. (2) A slight modification is made to the exploration phase of the classical SMA to ensure a vast exploration of the search space. The suggested modification enables the ISMA to overcome the shortcoming of the premature convergence of the classical SMA. Finally, the efficiency and robustness of the ISMA are demonstrated through three large-scale benchmark dome trusses with natural frequency constraints. To our knowledge, this is the first time to apply SMA to structural optimization. It is shown that the proposed ISMA overcomes the problems of premature convergence and slow convergence rate of the classical SMA. Numerical results show that the ISMA outperforms the classical SMA and shows superior or comparable performance to other reported methods.

Isogeometric sizing and shape optimization of 3D beams and lattice structures at large deformations

A computational method for optimizing the shape of the centerline curve and the spatial variation of geometric and material sizing parameters of the cross-sections of elastic, 3-dimensional beams and beam structures subject to large deformations is presented in this work. The approach is based on the concept of isogeometric analysis, i.e., the representation of geometry and the discretization of the numerical solution using spline functions. Here, mixed isogeometric collocation methods are used to discretize the geometrically exact 3D beam model. These spline representations are extended to the parameterization of the design variables, which are the initial centerline curves of the beams, as well as cross-sectional sizing properties, which may be varying along the beam axis and can be functionally graded through the cross-sections. To tailor the mechanical deformation behavior of a beam or beam structure, a nonlinear optimization problem is formulated and solved using gradient-based methods. For this purpose, all required gradients and sensitivities are derived analytically. The potential of this holistic design optimization approach is demonstrated in application to tailoring of elastic metamaterials and beam lattice structures, as well as 4D printing of multi-material laminate beams.

Shape and size optimization of truss structures by Chaos game optimization considering frequency constraints

IntroductionAn engineering system consists of properly established activities and put together to achieve a predefined goal. These activities include analysis, design, construction, research, and development. Designing and constructing structural systems, including buildings, bridges, highways, and other complex systems, have been developed over the centuries. However, the evolution of these systems has been prolonged because the overall process is very costly and time-consuming, requiring primary human and material resources to be utilized. One of the options for overcoming these shortcomings is the utilization of metaheuristic algorithms as recently developed intelligent techniques. These algorithms can be utilized as upper-level search techniques for optimization procedures to achieve better results. ObjectivesShape and size optimization of truss structures are considered in this paper utilizing the Chaos Game Optimization (CGO) as one of the recently developed metaheuristic algorithms. The principles of chaos theory and fractal configuration are considered inspirational concepts. MethodsFor the numerical purpose, the 10-bar, 37-bar, 52-bar, 72-bar, and 120-bar truss structures as four of the benchmark problems in this field are considered as design examples in which the frequency constraints are considered as limits that have to be dealt with during the optimization procedure. Multiple optimization runs are also conducted for having a comprehensive statistical analysis, while a comparative investigation is also conducted with other algorithms in the literature. ResultsBased on the results of the CGO and other approaches from the literature, the CGO can provide better and competitive results in dealing with the considered truss design problems. ConclusionIn summary, the CGO can provide better solutions in dealing with the considered real-size structural design problems with higher levels of complexity.

Semi-analytical study on an integrated-system with separated heaving OWC and breakwater: Structure size optimization and gap resonance utilization

To complement the topic on the integration of Oscillating Water Column (OWC) device with breakwater structures, a novel integrated system composed of an offshore heaving OWC device and a floating stationary breakwater with a certain length of gap between each other is proposed. Under the framework of potential flow theory, corresponding theoretical model is established and solved by decomposing the boundary-value problems into one wave scattering component and two radiation components. Apart from the examinations concentrating on the influences from the geometrical configuration of the breakwater, the gap distance between the OWC device and the breakwater is changed in a broad range to identify its effects on the interested hydrodynamic performance. It is found that for a specific wave frequency, when the gap distance is well-tuned against the wave length to satisfy the condition of sloshing mode happening inside the gap, power extraction efficiency is much likely to achieve its maximum extent. In this way, the optimization in terms of gap distance is proved to be effective in enhancing wave power capturing within a wider range of wave conditions.

Size optimization of micro-frame structures for designing multiscale structures

Size optimization of micro-frame structures for designing multiscale structures

Optimal Design of Regenerative Cooling Structure Based on Backpropagation Neural Network

Aiming at the problems of relying on traditional experience and high cost of schemes selection in the current research on regenerative cooling design, this paper establishes an optimal design model based on the backpropagation (BP) neural network method. In this paper, the cooling structure is parameterized to realize the segmented description. A BP neural network is constructed through the chamber performance simulation data sets to get the mathematical description between structural size parameters and optimization objectives. Taking the specified thrust chamber lifetime, safety margin of chamber wall, and upper limit of maximum wall temperature and pressure loss as constraints, the Globalsearch algorithm is applied to obtain the optimal design results of the regenerative cooling structural size parameters. The results show that the trained BP neural network model is able to predict the regenerative cooling performance parameters with the calculation accuracy similar to numerical simulation. The study of the space shuttle main engine–main combustion chamber indicates that under the same thrust chamber operating parameters and coolant inlet parameters, the optimized regenerative cooling channel reduces both the maximum wall temperature and the coolant pressure loss, and improves the overall cooling performance.

Development of Knowledge-Based Engineering System for Structural Size Optimization of External Fixation Device

The development process of the knowledge-based engineering (KBE) system for the structural size optimization of external fixation device is presented in this paper. The system is based on algorithms for generative modeling, finite element model (FEM) analysis, and size optimization. All these algorithms are integrated into the CAD/CAM/CAE system CATIA. The initial CAD/FEM model of external fixation device is verified using experimental verification on the real design. Experimental testing is done for axial pressure. Axial stress and displacements are measured using tensometric analysis equipment. The proximal bone segment displacements were monitored by a displacement transducer, while the loading was controlled by a force transducer. Iterative hybrid optimization algorithm is developed by integration of global algorithm, based on the simulated annealing (SA) method and a local algorithm based on the conjugate gradient (CG) method. The cost function of size optimization is the minimization of the design volume. Constrains are given in a form of clinical interfragmentary displacement constrains, at the point of fracture and maximum allowed stresses for the material of the external fixation device. Optimization variables are chosen as design parameters of the external fixation device. The optimized model of external fixation device has smaller mass, better stress distribution, and smaller interfragmentary displacement, in correlation with the initial model.

Improved multi-objective Hybrid Genetic Algorithm for Shape and Size Optimization of Free-form latticed structures

Industrial and public buildings generally adopt spatial latticed structures as roofs, where the number of members is too large for the traditional genetic algorithm (GA) to conduct size optimization. In this paper, an improved multi-objective hybrid genetic algorithm incorporating the fully stressed design (FSD), called NSGA-II-FSD, is proposed for the shape and size optimization of large-scale free-form spatial latticed structures. The proposed method uses the B-spline theory, which makes it easier to generate free-form surfaces that meet the aesthetic requirements. The total mass and strain energy of the structure are selected as the objective functions, and the strength, as well as the stability of the member, are taken as the constraints. By incorporating the FSD, one can also set the stress ratio limit and get an optimal set of cross-sections of the members under the desired margin of safety. Besides, a significant mutation strategy is proposed in order to expand the searching boundary, which can avoid premature convergence. Through numerical examples of a cylindrical latticed shell and a free-form space truss , it is proved that the proposed method is effective, and engineers can choose the solution according to their preferences in practical design. • Method for shape and size optimization of latticed structures is proposed. • Proposed method can handle multi-objective optimization problems. • A significant mutation strategy is proposed to expand the searching boundary. • The improved FSD is effective to solve the problems with multiple load cases. • All individuals in Pareto front can be directly adopted by designers.

Stiffness modelling of flexible support module for Large-aperture laser transmission unit

Large-aperture laser transmission unit (LLTU) is a device that focuses the laser beam to the center of the target, which are often designed as compliant mechanisms to achieve micro displacement adjustment. In the traditional mechanisms, they are designed as integrated micromanipulation systems, and driven by piezoelectric ceramics. However, most of these researches only focuses on motion accuracy, due to the lack of consideration of large load problems, the application is greatly limited. To this end, a flexible support module (FSM), as well as its stiffness model, was presented in this paper. Combined with finite element method (FEM) of FSM, structure size optimization was also completed, successfully solved the problems of stress concentration and load of FSM in engineering application. Moreover, a dual vision-based measurement method was introduced, to verify the stiffness model and analyze the repetitive error of FSM. From this result, the prototype enabled 5 mm and 0.007 rad of working area with average error of 0.3192 mm and -0.0036 rad. The repeatable error is within 7%, and will decreased to 4% with internal stress released in 5~15min.

Structure-Size Optimization and Fabrication of 3.7 GHz Film Bulk Acoustic Resonator Based on AlN Thin Film

Traditional radio frequency filters cannot meet the demands of miniaturization, high frequency operation, integration, and broadband capacity in new-generation communication system owing to their larger volumes. A thin film bulk acoustic resonator (FBAR) is therefore suggested as an optimum solution because of its small volume and a good performance. In this study, the COMSOL multiphysics software was used to build 2 D and 3 D finite element models to analyze the harmonic characteristics of the FBAR. Based on the optimized structural parameters, the FBAR was fabricated with series resonant frequency, parallel resonant frequency, and effective coupling coefficient values of 3.705, and 3.82 GHz, and 7.4%, respectively. Compared with the simulated FBAR results, the effective coupling coefficient of the fabricated FBAR declined by only 0.1%, almost achieving the desired performance.