Size Optimization Of Structures Research Articles

Improved black hole and multiverse algorithms for discrete sizing optimization of planar structures

ABSTRACTThis study compares two novel nature-inspired algorithms developed based on cosmology for discrete sizing optimization of structures. The first metaheuristic is the black hole, which is inspired by the black hole phenomenon. The second one is the multiverse, and the main inspiration for this algorithm is based on three concepts in cosmology: white holes, black holes and wormholes. Moreover, an improved version of each algorithm, termed improved black hole (IBH) and improved multiverse (IMV), is proposed to overcome the defects of their original versions in tackling the discrete sizing structural optimization problems. Three types of structure, i.e. steel trusses, steel frames and reinforced concrete frames, are presented to illustrate the efficiency of the proposed IBH and IMV algorithms. The numerical results demonstrate the excellence of the proposed improved algorithms compared with other state-of-the-art metaheuristics in the literature, in terms of their optimum solutions and reliability.

Isogeometric sizing and shape optimization of thin structures with a solid-shell approach

This work explores the use of solid-shell elements in the the framework of isogeometric shape optimization of shells. The main difference of these elements with respect to pure shell ones is their volumetric nature which can provide recognized benefits to analyze, for example, structures with non-linear behaviors. From the design point of view, we show that this geometric representation of the thickness is also of great interest since it offers new possibilities: continuous sizing variations can be imposed by modifying the distance between the control points of the outer surfaces. In other words, shape and sizing optimization can be performed in an identical manner. Firstly, we carry out a range of numerical experiments in order to carefully compare the results with the commonly adopted technique based on the Kirchhoff-Love formulation. These studies reveal that both solid-shell and Kirchhoff-Love strategies lead to very similar optimal shapes. Then, we apply a bi-step strategy to integrate shape and sizing optimization. We highlight the potential of the proposed approach on a stiffened cylinder where the cross section along the stiffener is optimized leading to a final design with smooth thickness variations. Finally, we combine the benefits of both Kirchhoff-Love and solid-shell formulations by setting up a multi-model optimization process to efficiently design a roof.

Finite-Element-Mesh Based Method for Modeling and Optimization of Lattice Structures for Additive Manufacturing.

A parameterization modeling method based on finite element mesh to create complex large-scale lattice structures for AM is presented, and a corresponding approach for size optimization of lattice structures is also developed. In the modeling method, meshing technique is employed to obtain the meshes and nodes of lattice structures for a given geometry. Then, a parametric description of lattice unit cells based on the element type, element nodes and their connecting relationships is developed. Once the unit cell design is selected, the initial lattice structure can be assembled by the unit cells in each finite element. Furthermore, modification of lattice structures can be operated by moving mesh nodes and changing cross-sectional areas of bars. The graded and non-uniform lattice structures can be constructed easily based on the proposed modeling method. Moreover, a size optimization algorithm based on moving iso-surface threshold (MIST) method is proposed to optimize lattice structures for enhancing the mechanical performance. To demonstrate the effectiveness of the proposed method, numerical examples and experimental testing are presented, and experimental testing shows 11% improved stiffness of the optimized non-uniform lattice structure than uniform one.

Border-search and jump reduction method for size optimization of spatial truss structures

This paper proposes a sensitivity-based border-search and jump reduction method for optimum design of spatial trusses. It is considered as a two-phase optimization approach, where at the first phase, the first local optimum is found by few analyses, after the whole searching space is limited employing an efficient random strategy, and the second phase involves finding a sequence of local optimum points using the variables sensitivity with respect to corresponding values of constraints violation. To reach the global solution at phase two, a sequence of two sensitivity-based operators of border-search operator and jump operator are introduced until convergence is occurred. Sensitivity analysis is performed using numerical finite difference method. To do structural analysis, a link between open source software of OpenSees and MATLAB was developed. Spatial truss problems were attempted for optimization in order to show the fastness and efficiency of proposed technique. Results were compared with those reported in the literature. It shows that the proposed method is competitive with the other optimization methods with a significant reduction in number of analyses carried.

Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimizat...

Combined size and shape optimization of truss structures using subset simulation optimization

This paper presents an approach to solve the combined size and shape design optimization problems using recently developed subset simulation optimization for both continuous and discrete design variables. Except for the componentwise Metropolis–Hasting algorithm, a recently developed adaptive conditional sampling algorithm is also employed as an alternative approach for generating new conditional samples (candidate designs) for each simulation level, which enhances the accuracy and stability of the optimization process. Besides, a double-criterion sorting algorithm is used to handle the design constraints and integrate them in the generation of conditional samples during the Markov Chain Monte Carlo simulation, and the inverse transform method is employed to deal with the discrete design variables. Totally, four numerical examples are considered, including a 15-bar 2D truss, an 18-bar 2D truss, a 39-bar 3D truss and a truss-type landing gear of an unmanned aerial vehicle. The optimal designs obtained from subset simulation optimization using either the componentwise Metropolis–Hasting algorithm or the adaptive conditional sampling algorithm succeed in substantially reducing the weights of the truss-type structures under design constraints in terms of the member stress, the Euler buckling and the nodal displacement. The computational results indicate the proposed method can be taken as an alternative tool for structural optimization design on truss structures when involving the combined size and shape design.

Light-Weight Design Method for Force-Performance-Structure of Complex Structural Part Based Co-operative Optimization

A light-weight design method of integrated structural topology and size co-optimization for the force-performance-structure of complex structural parts is presented in this paper. Firstly, the supporting function of a complex structural part is built to map the force transmission, where the force exerted areas and constraints are considered as connecting structure and the structural configuration, to determine the part performance as well as the force routines. Then the connecting structure design model, aiming to optimize the static and dynamic performances on connection configuration, is developed, and the optimum design of the characteristic parameters is carried out by means of the collaborative optimization method, namely, the integrated structural topology optimization and size optimization. In this design model, the objective is to maximize the connecting stiffness. Based on the relationship between the force and the structural configuration of a part, the optimal force transmission routine that can meet the performance requirements is obtained using the structural topology optimization technology. Accordingly, the light-weight design of conceptual configuration for complex parts under multi-objective and multi-condition can be realized. Finally, based on the proposed collaborative optimization design method, the optimal performance and optimal structure of the complex parts with light weight are realized, and the reasonable structural unit configuration and size characteristic parameters are obtained. A bed structure of gantry-type machining center is designed by using the proposed light-weight structure design method in this paper, as an illustrative example. The bed after the design optimization is lighter 8% than original one, and the rail deformation is reduced by 5%. Moreover, the lightweight design of the bed is achieved with enhanced performance to show the effectiveness of the proposed method.

Design and Development of a Guide Bracket for Horizontal band Sawing Machine by Geometrical Optimization

All modern manufacturing units are striving to develop a cost effective product with optimized reduced weight by using CAE driven design process. In this scenario the product design is stimulated by structural optimization tools like geometrical (topology) optimization, shape optimization or size optimization. For conservation of natural resources and optimum energy utilization, weight reduction has been the main focus of machine tool manufacturers in the present scenario. Weight reduction can be achieved by the introduction of better material, better manufacturing processes and design optimization. In automobile and aircraft sector, geometrical optimization has become an integral tool of product design and development. Geometry (topology) assisted design model gives optimized results which are better and innovative in terms of product design with enhanced structural performance and stability. In other words, simulation saves time, reduces costs, and strengthens the competitiveness of companies, thus strengthened market position.

Chaotic enhanced colliding bodies algorithms for size optimization of truss structures

Colliding bodies optimization (CBO) is a recently developed population-based metaheuristic algorithm that mimics the collision between two bodies, where the momentum conservation law is utilized to determine the new positions of the agents in the search space. To overcome some deficiencies in the CBO like slow convergence and getting trapped in local minima, an enhanced version of the algorithm, ECBO, is proposed. One of the efficient techniques to improve the performances of the metaheuristic algorithms is adding chaos to their structure. In this paper, chaos is incorporated into the ECBO through three types of embeddings and ten chaotic maps. Proposing different chaotic versions, finding the best version among chaotic versions and improving the efficiency of the standard CBO and ECBO are the main achievements of this study. The results of examining some mathematical and engineering problems show how some chaotic ECBO variants can enhance the performance of the standard ECBO.

Multi-objective sizing and topology optimization of truss structures using genetic programming based on a new adaptive mutant operator

Most real-world engineering problems deal with multiple conflicting objectives simultaneously. In order to address this issue in truss optimization, this paper presents a multi-objective genetic programming approach for sizing and topology optimization of trusses. It aims to find the optimal cross-sectional areas and connectivities between the nodes to achieve a set of trade-off solutions to satisfy all the optimization objective functions subjected to some constraints such as kinematic stability, maximum allowable stress in members and nodal deflections. It also uses the variable-length representation of potential solutions in the shape of computer programs and evolves to the potential final set of solutions. This approach also employs an adaptive mutant factor besides the classical genetic operators to improve the exploring capabilities of Genetic Programming in structural optimization. The intrinsic features of genetic programming help to identify redundant truss members and nodes in the design space, while no violation of constraints occurs. Our approach applied to some numerical examples and found a better non-dominated solution set in the most cases in comparison with the competent methods available in the literature.

Improved thermal exchange optimization algorithm for optimal design of skeletal structures

Thermal Exchange Optimization (TEO) is a newly developed algorithm which mimics the thermal exchange between a solid object and its surrounding fluid. In this paper, an improved version of the TEO is developed to fix the shortcomings of the standard version. To demonstrate the viability of the new algorithm, the CEC 2016\'s single objective problems are considered along with the discrete size optimization of benchmark skeletal structures. Problem specific constraints are handled using a fly-back mechanism. The results show the validity of the improved TEO method compared to its standard version and a number of well-known algorithms.

Multi-objective Optimized Noise Reduction Design of Complicated Structure-Borne Acoustic Radiation Under Multiple Constrains

Problems with regard to the optimized design of structure-borne acoustic radiation in the intermediate-frequency region were first studied in this paper. The multi-objective optimization model was established based on structural dynamic response equation and acoustic radiation equation. Acoustic vibration analysis of cavity structural model was conducted to determine intra-cavity noise sources under different random excitation conditions, and then appropriate design variables were selected. Results indicated that after structural size optimization under different excitation conditions, the intra-cavity sound pressure levels lowered to a certain degree. Particularly in the low-frequency region, the maximum decreasing amplitude of sound pressure level could reach 5???7 dB, and the acoustic performance of cavity structure improved favourably.

Efficient size and shape optimization of truss structures subject to stress and local buckling constraints using sequential linear programming

The advance in digital fabrication technologies and additive manufacturing allows for the fabrication of complex truss structure designs but at the same time posing challenging structural optimization problems to capitalize on this new design freedom. In response to this, an iterative approach in which Sequential Linear Programming (SLP) is used to simultaneously solve a size and shape optimization sub-problem subject to local stress and Euler buckling constraints is proposed in this work. To accomplish this, a first order Taylor expansion for the nodal movement and the buckling constraint is derived to conform to the SLP problem formulation. At each iteration a post-processing step is initiated to map a design vector to the exact buckling constraint boundary in order to facilitate the overall efficiency. The method is verified against an exact non-linear optimization problem formulation on a range of benchmark examples obtained from the literature. The results show that the proposed method produces optimized designs that are either close or identical to the solutions obtained by the non-linear problem formulation while significantly decreasing the computational time. This enables more efficient size and shape optimization of truss structures considering practical engineering constraints.

An Optimization Method for Design of Acoustic Metamaterial Structure

Pentamode (PM) metamaterial is a kind of acoustic metamaterial generally designed from a general material and made by a periodic array of micro-truss structures. The paper presents an optimization method for the design of PM metamaterial structure, and this kind of structure has usually special physical properties to guide the acoustic wave to propagate according to the design path. In order to construct the optimization model, the micro-truss unit cell is firstly investigated deeply, and the relationship between the effective elastic modulus of PM materials and the structural parameters of micro-truss unit cells is established. With incorporating the transformation acoustics algorithm into the optimization process to predict the theoretic material parameters of the current design structure, the constraint of the material property in the design structure is converted into the rod size constraint of micro-truss. As a result, the design of PM material structures can be realized as a problem of structure size optimization, and the optimized result can meet the requirement of PM metamaterial property and the theory of transformation acoustics. And also, the total stability of the PM material structure is also ensured by the balance rod forces constraints in the optimization process. Finally, a numerical example of PM material structure is presented.

An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints

This paper presents a novel adaptive hybrid evolutionary firefly algorithm (AHEFA) for shape and size optimization of truss structures under multiple frequency constraints. This algorithm is a hybridization of the differential evolution (DE) algorithm and the firefly algorithm (FA). An automatically adapted parameter is utilized to select an appropriate mutation scheme for an effective trade-off between the global and local search abilities. An elitist technique is applied to the selection phase to choose the best individuals. Accordingly, the convergence rate is significantly improved with the high solution accuracy. Six numerical examples are examined for the validity of the present algorithm.

Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics

Abstract In this study, simultaneous size, shape, and topology optimization of planar and space trusses are investigated. Moreover, the trusses are subjected to constraints for element stresses, nodal displacements, and kinematic stability conditions. Truss Topology Optimization (TTO) removes the superfluous elements and nodes from the ground structure. In this method, the difficulties arise due to unacceptable and singular topologies; therefore, the Grubler's criterion and the positive definiteness are used to handle such issue. Moreover, the TTO is challenging due to its search space, which is implicit, non-convex, non-linear, and often leading to divergence. Therefore, mutation-based metaheuristics are proposed to investigate them. This study compares the performance of four improved metaheuristics (viz. Improved Teaching–Learning-Based Optimization (ITLBO), Improved Heat Transfer Search (IHTS), Improved Water Wave Optimization (IWWO), and Improved Passing Vehicle Search (IPVS)) and four basic metaheuristics (viz. TLBO, HTS, WWO, and PVS) in order to solve structural optimization problems. Highlights Improvements in four recently designed metaheuristics. Use of random mutation-based search technique. Applications on challenging/benchmark problems of simultaneous size, shape, and topology optimization of truss structures. Improvements effective over basic metaheuristics.

Sizing, layout and topology design optimization of truss structures using the Jaya algorithm

A very recently developed metaheuristic method called Jaya algorithm (JA) is implemented in this study for sizing and layout optimization of truss structures. The main feature of JA is that it does not require setting algorithm-specific parameters. The algorithm has a very simple formulation where the basic idea is to approach the best solution and escape from the worst solution. The original JA formulation is modified in this research in order to improve convergence speed and reduce the number of structural analyses required in the optimization process. The suitability of JA for truss optimization is investigated by solving six classical weight minimization problems of truss structures including sizing, layout and large-scale optimization problems with up to 204 design variables. Discrete sizing/layout variables and simplified topology optimization also are considered. The test problems solved in this study are very common benchmarks in structural optimization and practically describe all scenarios that may be faced by designers. The results demonstrate that JA can obtain better designs than those of the other state-of-the-art metaheuristic and gradient-based optimization methods in terms of optimized weight, standard deviation and number of structural analyses.

New biomimetic approach to the aircraft wing structural design based on aeroelastic analysis

Abstract This paper presents a new biomimetic approach to the structural design. For the purpose of aircraft wing design the numerical environment combining simultaneous structural size, shape, and topology optimization based on aeroelastic analysis was developed. For the design of aircraft elements the optimization process must be treated as a multi-load case task, because during the fluid structure interaction analysis each step represents a different structural load case. Also, considering different angles of attack, during the CFD computation each result is considered. The method-specific features (such as domain independence, functional configurations during the process of optimization, and multiple load case solution implemented in the optimization scenario) enable the optimal structural form. To illustrate the algorithm functionality, the problem of determining the optimal internal wing structure was presented. The optimal internal wing structure resulting from aeroelastic computation with different angles of attack has been presented.

Accelerated multi-gravitational search algorithm for size optimization of truss structures

Abstract Weak local exploitation capability of the gravitational search algorithm (GSA) and its slow convergence rate in final iterations have been demonstrated in the literature. This paper presents a modified GSA denoted here as the accelerated multi-gravitational search algorithm (AMGSA) that exhibits an improved convergence rate. In AMGSA, the simplex crossover (SPX) and the operator mutation of the breeder genetic algorithm (BGA) are incorporated with the multi-gravitational search algorithm (MGSA) to achieve an algorithm with a good exploration-exploitation balance. MGSA is adopted to prevent stagnation of the search into a local optimum (i.e. to improve the exploration capability), while the SPX and the BGA mutation operator are used to bias the search toward promising areas of the search space (i.e. to promote local exploitation). The performance of AMGSA is evaluated using several benchmark truss optimization examples. Results indicate that AMGSA not only exhibits an improved balance between the exploration and exploitation schemes but also shows competitive promise in effectively and efficiently solving large-scale optimization problems as it requires a significantly lower number of structural analyses compared to other algorithms that it is checked against.

The d-arched piezoelectric-triboelectric hybrid nanogenerator as a self-powered vibration sensor

With the rapid development of traditional sensors, the long-time reliable power supply has been one of the severe problems to restrict the sensors’ wide applications in daily life. Here, this paper presents a d-arched sensor consisting of piezoelectric-triboelectric energy harvesting unit, which can be treated as a real-time self-powered vibration sensor which can simultaneously convert mechanical energy into electrical energy. The d-arched sensor with middle shared electrode based on piezoelectric-triboelectric hybrid mechanisms can increase sensitivity and measuring range through improving the corresponding output voltage and current performance. After surface micro-nano structural design and size optimization, the E-piezoelectric output voltage and current increase by 25% and 42.6% at a frequency of 10Hz and mechanical force of 5N, correspondingly, the E-triboelectric output voltage and current increase by 21.9% and 69.3%, respectively. Moreover, the d-arched hybrid nanogenerator (NG) as a sensor presents that the sensitivities of the sensor are 3.65μW/g and 6.14μW/g under the vibration amplitude of 3mm and 6mm, accordingly the linearity errors of the sensor are 4.23% and 5.12% under the vibration amplitude of 3mm and 6mm, respectively. The measurement demonstrates that a good linearity between the E-piezoelectric output power and the acceleration of vibration. Therefore, it is evident that the d-arched hybrid NG can be used as a vibration sensor.