Optimization Of Frame Structures Research Articles

GPU-based parallel programming for FEM analysis in the optimization of steel frames

ABSTRACT Optimization of large-scale frame structures consumes a vast amount of time since the analysis of such complex systems contains several iterative processes. Mitigating computational burden and reducing this time to a reasonable level is possible by running GPU (Graphical Processing Unit) processors, which can be found on standard computers. This study presents an algorithm for the acceleration of size optimization of steel frames by using the BBO (Biogeography-Based Optimization) method that is suitable for GPU architecture. The GPU-based parallel algorithm, designed for FEM (Finite Element Method) analysis, is applied to three hypothetical steel-frame case structures with different numbers of members and nodes; and processed on four different computers which are available on the market. The presented case studies revealed that the proposed solution’s efficiency increases as the number of members increases and confirmed the ability of the acceleration algorithm for optimization of large-scale frame structures and provided time efficiency.

On optimization of lightweight planar frame structures: an evolving ground structure approach

On optimization of lightweight planar frame structures: an evolving ground structure approach

An intelligent body frame structure modeling and optimization system based on conceptual design

The conceptual design stage is an indispensable and important stage in the development of the modern body. However, due to the lack of sufficient body structure parameter support, the design defects generated at this time are difficult to make up for in the subsequent design stage. Therefore, it is of great significance to develop a conceptual design software for body structure that integrates design, analysis, and optimization. This paper proposes an intelligent body frame structure modeling and optimization system based on conceptual design, S-iVCD (Intelligent System for Conceptual Design of Vehicle Body Structure). Based on deep learning methods and body design sketches, a conceptual model of body structure is quickly established. Based on the data parameters stored in the Excel table, the system is seamlessly connected to the domestic independent finite element software SIPESC to calculate the simulated working conditions. The body structure optimization module is driven by the MMA (method of moving asymptotes), and takes the body structure performance and total mass as the optimization goals or constraints of the mathematical model to achieve body structure performance improvement and lightweight design.

Modified genetic algorithm for optimal design of truss structures

In this paper, topology and shape optimization of truss or frame structures is discussed. The optimization starts from a structure, into which a finite number of nodesare set; all the nodes are connected together by trusses in all possible variants. Unfit variants of the truss system are rejected. Two alternative ways of the optimization are compared: topology optimization starting from initial structure with a larger number of nodes, and topology optimization starting from initial structure with smaller number of nodes but with additional shape optimization of the obtained topology. The topology optimization is solved with original modified genetic algorithm, giving better results in comparison with classical genetic algorithm. Instead of further development of constraint system, the additional step is introduced into algorithm – purification of genotype, which allows complementary improvement of particular population individuals, and together for the optimization process retains more possibilities than stiffening of constraints. The shape optimization is solved by classical genetic algorithm. Both strategies effectively improve the solution, however the common topology/shape optimization requires less computer resources. All numerical examples are obtained with original software developed by the authors.

A novel multi-hybrid differential evolution algorithm for optimization of frame structures

Differential evolution (DE) is a robust optimizer designed for solving complex domain research problems in the computational intelligence community. In the present work, a multi-hybrid DE (MHDE) is proposed for improving the overall working capability of the algorithm without compromising the solution quality. Adaptive parameters, enhanced mutation, enhanced crossover, reducing population, iterative division and Gaussian random sampling are some of the major characteristics of the proposed MHDE algorithm. Firstly, an iterative division for improved exploration and exploitation is used, then an adaptive proportional population size reduction mechanism is followed for reducing the computational complexity. It also incorporated Weibull distribution and Gaussian random sampling to mitigate premature convergence. The proposed framework is validated by using IEEE CEC benchmark suites (CEC 2005, CEC 2014 and CEC 2017). The algorithm is applied to four engineering design problems and for the weight minimization of three frame design problems. Experimental results are analysed and compared with recent hybrid algorithms such as laplacian biogeography based optimization, adaptive differential evolution with archive (JADE), success history based DE, self adaptive DE, LSHADE, MVMO, fractional-order calculus-based flower pollination algorithm, sine cosine crow search algorithm and others. Statistically, the Friedman and Wilcoxon rank sum tests prove that the proposed algorithm fares better than others.

Joint Optimization of Frame Structure and Power Allocation for URLLC in Short Blocklength Regime

Joint Optimization of Frame Structure and Power Allocation for URLLC in Short Blocklength Regime

Numerical design optimization of real size complex steel space frame structures using a novel adaptive cuckoo search method

AbstractIn this study, real size complex steel space frame structures are numerically designed to achieve optimal design weight. For this aim, standard cuckoo search algorithm is rectified through a newly proposed adaptive method over two fundamental algorithmic parameters of alien egg probability detection (Pa) and step size control (α) to overcome incompetency of trapping into local optima. Besides, to strengthen exploitation phase of newly proposed algorithm, it is boosted with greedy selection (GS). So, novel algorithm has more promising exploration and exploitation capabilities. An 8‐story, 1024‐member and a 20‐story, 1860‐member real size complex steel space frame structures are selected as design examples. Also, initially to verify the supremacy of novel algorithm, a well‐known welded beam is optimized as a benchmark structural design problem. Afterwards, the steel space frame structures are optimally designed via novel algorithm. Since ready steel section lists are utilized as selection pool for design variables, discrete programming problem is come into existence. The dead, live, snow, and wind design loads acting on frame structures are calculated in direction of ASCE 7‐05 provisions. Furthermore, the structural design constraints are determined from LRFD‐AISC specifications. Eventually, the newly proposed adaptive cuckoo search algorithm boosted with GS presents outstanding algorithmic performance.

Low-carbon design optimization of reinforced concrete building structures using genetic algorithm

ABSTRACT Embodied carbon emissions are getting increased attention to realize low-carbon buildings. Low-carbon designs have been explored by conducting both member-level and structure-level analyses for concrete structures. However, methods for combining two-tiered research need to be further developed to reduce the cost of design optimization. This study aims to propose a hybrid iterative approach for the low-carbon optimization of concrete framed structures. Accordingly, the integrated structural analysis was applied to design the initial scheme, subproject-based emission assessment was applied to identify the carbon-intensive structural components, and a genetic algorithm was applied to optimize the desired components subjected to relevant design constraints. A case study was made on a residential building to verify the feasibility of the proposed approach. The optimization results indicated that a potential 18.3% and 4.2% reduction in the embodied emissions from the beams and the building main body were achieved, respectively. A further discussion also proposed that an optimized scheme for interior walls using lightweight panels resulted in a 12% reduction in carbon emissions compared to the initial scheme using masonry walls. The proposed method and results can facilitate understanding the low-carbon design optimization of reinforced concrete structures and, therefore, contribute to carbon reduction of the construction industry.

Finite Element Analysis and Optimization of Hydrogen Fuel Cell City Bus Body Frame Structure

Hydrogen fuel cell city bus is a type of new energy public transportation. In this paper, in order to evaluate the safety performance of a newly developed hydrogen fuel cell city bus body frame designed by the collaborating enterprise, finite element analysis is conducted to investigate its structural mechanics and dynamic characteristics under four typical operating conditions, including horizontal bending, ultimate torsion, emergency cornering, and emergency braking. Based on the simulation results, although the body frame of the bus meets the stiffness design requirements and avoids body resonance, it exhibits maximum stresses of 328.9 MPa and 348.6 MPa under emergency cornering and ultimate torsion conditions, respectively, exceeding the material yield strength and failing to satisfy the strength design requirements. Therefore, the size optimization method is employed to optimize the thickness of the body frame components. After optimization, the maximum stresses are reduced to 262.7 MPa and 300.6 MPa, respectively, representing a reduction of up to 20.13%. The optimization significantly improves performance and meets the strength design requirements. Furthermore, the body frame is lightened by 106 kg, achieving the goal of weight reduction.

Optimization of frame structure coach 29/34 seats in static durability state

The stress and deformation of the body frame and chassis frame of a coach subjected to bending, torsion, emergency braking and returning must be considered during the design and manufacture of passenger vehicles. The model of 29/34-seat coach in this investigation is a newly designed vehicle based on the old 29/34-seat coach; the most significant change has been to the chassis. It is vital to ensure it remains safe and durable when the vehicle operates on the road in the 4 cases mentioned above. Therefore, the purpose of this study is to optimise and maintain in a stable state the chassis structure of the 29/34-seat coach by using the Taguchi method based on grey relational analysis. This study has as design variables changes to the number of crossbars on the roof and the thickness of those bars, as the goal is to reduce vehicle weight while ensuring chassis durability. The finite element analysis applied the OptiStruct module of HyperMesh to analyse deformation and stress of the coach chassis. The optimal outcomes indicated that the error between predictive value and the optimal value of the grey relational grade of the proposed optimisation method and the regression analysis are 6% and 1.05%, respectively. The finite element analysis results indicated that when the design variables changed, the deformation and stress of the chassis changed significantly. The proposed optimisation method greatly reduced the deformation and stress of the vehicle. The optimal values of deformation and stress are also recorded in 4 cases: for the bending process 9.675 mm and 153.61 MPa were recorded; for the torsion process, 11.849 mm and 168.61 MPa; for the braking process, 10.569 mm and 161.66 MPa; for the rotation process, 16.162 mm and 200.5 MPa. The Taguchi method based on grey relational analysis helped to reduce vehicle weight by 11.5%. These results are comparable to previous publications.

Reliability-based design optimization of post-tensioned self-centering rocking steel frame structures

This paper reports the Reliability-Based Design Optimization (RBDO) of post-tensioned self-centering rocking steel frame structures with buckling-restrained bracing systems. The objective was to investigate the reliability index, optimization of self-centering structures to reach minimum weight using metaheuristic algorithms, and their application in linear and nonlinear reliability problems. For this purpose, three steel structures (10-, 15-, and 20-storey structures) were each evaluated with three steel framing systems (buckling-restrained bracing, post-tensioned self-centering multiple rocking steel frame with buckling-restrained bracing, and post-tensioned self-centering single rocking steel frame with buckling-restrained bracing), making a total of nine models. Subsequently, specific 2D frames of the structural models were numerically simulated using nonlinear dynamic analysis (NDA) in OpenSees software. Optimization was carried out in two stages: with and without considering the uncertainties. Finally, for calculating the failure probability and structural reliability index, Monte-Carlo Simulation (MCS) was employed. Results indicate that, although considering the reliability index leads to heavier structures, structural safety was increased and failure probability was reduced to even lower specified levels. Furthermore, among the incorporated algorithms, the Colliding Bodies Optimization (CBO) and Charged System Search (CSS) algorithms proved to have superior performances in terms of accuracy and converging time. On average, using these two algorithms for cases without uncertainty resulted in maximum weight reductions of 36%, 30%, and 32% for 10-, 15-, and 20-storey structures. In addition, for cases with uncertainty, these two algorithms with reliability index (β) of 2 respectively reduced the weight of 10-, 15-, and 20-storey structures by 21%. Also, it was shown that not considering the uncertainties can increase the failure probability by up to 23%.

Billion-design-variable-scale topology optimization of vehicle frame structure in multiple-load case

In topology optimization, sufficient resolution and a constraint volume of less than 1% are required to obtain a practical vehicle body structure without solid circular-section frames. To meet the requirement for sufficient resolution, the authors are developing voxel topology optimization software, including a finite element solver that utilizes the building cube method framework available in massively parallel environments. The authors have performed a topology optimization of billions of elements intended for a vehicle frame using 35,000–66,000 processors and measured its parallel performance. In addition, four different methods to treat multiple-load cases required for vehicle performance into single objective functions are examined. As a result, normalizing compliance with the appropriate target energy obtained by the original body-in-white frame balances the optimization performance across cases. In the single-load case, thick solid beams are generated through optimization. In contrast, such solid frames are suppressed in multiple-load cases, resulting in a structure similar to a practical body-in-white frame.

Optimization of framed structures subjected to blast loading using equivalent static loads method

In this study, the optimum design of a three-dimensional framed steel structure subjected to blast loading is considered. The main idea of this research is to develop a practical formulation for the design optimization problem and to study the effect of including blast loads in the design process. The optimization problem is formulated to minimize the total weight of the structure subjected to American Institution of Steel Construction (AISC) strength requirements and blast design displacement constraints. The design variables for beams and columns are the discrete values of the W-shapes selected from the AISC tables. A car carrying 250 lbs of trinitrotoluene with a 50 ft standoff distance from the front face is modeled as the source of the blast loading. Pressure–time histories are calculated on the front, sides, roof, and rear faces of the structure. Since the problem functions are not differentiable with respect to the design variables, the gradient-based optimization algorithms cannot be used to solve the problem. Therefore, metaheuristic algorithms are used to solve the optimization problem. Linear and nonlinear dynamic analyses are carried out in the optimization process. The problems are solved using metaheuristic optimization with the equivalent static loads method (MOESL). In MOESL, the dynamic load is transformed into equivalent static loads (ESLs) then the linear static analysis is carried out in the optimization process. The problems are 4-bay × 4-bay × 3-story frames under serviceability and blast loading. It is shown that a penalty on the optimum structural weight is substantial for designing structures to withstand blast loads.

Τopology Optimization under a Single Displacement Constraint Using a Strain Energy Criterion

Based on a previous concept that has been successfully applied to the sizing optimization of truss and frame structures, this work extends and improves the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. To make the proposed methodology transparent to other researchers and at the same time meaningful, the numerical value of the displacement constraint was taken to be equal to that obtained through the well-known Solid Isotropic Material with Penalization (SIMP) method under the same boundary conditions and the same external forces. The proposed method is more efficient than the SIMP method while leading to topologies very close to those obtained by the latter.

Optimum design of steel frames with sizing and orientation design variables using a reformulated evolution strategy

Sizing optimization of steel frame structures has been traditionally conducted based on fixed orientations of structural members. However, it seems more expedient to search for an optimum design where orientations of column members are considered as design variables together with sizing of all members for the minimum weight design of a steel frame. In order to solve the resulting optimization problem effectively, a reformulated evolution strategy (ES) algorithm is proposed and employed in the present study. The numerical investigations are carried out using three test problems regarding the optimum design of steel space frames. In each test problem, a frame is first designed for the minimum weight considering sizing design variables only, where initial orientations of the column members are kept unchanged. Next, sizing and orientation design variables are considered simultaneously for minimizing the weight of the same frame. The results obtained in the foregoing two cases are compared and the associated optimal layouts for the column orientations are depicted. The study reveals that the optimal selection of column orientations has a significant influence on the minimum weight design of steel frames.

An efficient differential evolution-based method for optimization of steel frame structures using direct analysis

Sizing optimization of steel frames using direct analysis is a highly complex optimization problem with discrete design variables and highly nonlinear constraints of structural safety and serviceability conditions. To tackle this problem, this study develops an improved differential evolution (DE), namely 2EpDE, with a new mutation technique using two p-best individuals. The results of twenty benchmark functions and four real-world constrained optimization problems prove that 2EpDE effectively saves computational efforts and searches for better global optimal solutions. A framework for the optimization of steel frames is then proposed using a combination of 2EpDE, Multi-Comparison Technique (MCT), and Promising Individual Method (PIM). The strength and serviceability constraints of the optimization are evaluated by direct analysis that can accurately perform the nonlinear inelastic behaviors of the structure. Two examples including two-story and six-story space frames are optimized to evaluate the efficiency of the proposed method. Compared to Jaya and Particle Swarm Optimization (PSO), the proposed method can save more than 35% of computational efforts and yields better optimum results.

Progressive collapse design optimization of RC frame structures using high-performance computing

Structural progressive collapse design is essential for improving the robustness of structures against accidental local loads. In this study, a design framework was developed for optimizing the nonlinear dynamic progressive collapse design of reinforced concrete (RC) frame structures. An objective function featuring both structural response and material consumption was combined with a cluster computing technology and the global optimization algorithm to optimize a structure for resisting progressive collapse. A four-story RC frame was taken as an example. The design framework was adopted to achieve precise control of its structural progressive collapse response with optimization of the material consumption to the maximum extent. The design outcomes of global and sequential design schemes, including structural resistance and material consumption, were compared to devise the best optimized progressive collapse design strategy. This research can serve as a reference for the development of efficient and accurate structural progressive collapse design methods.

Modified adolescent identity search algorithm for optimization of steel skeletal frame structures

Modified adolescent identity search algorithm for optimization of steel skeletal frame structures

Subdomain hybrid cellular automata method for material optimization of thin-walled frame structure under transverse impact

In this paper, a subdomain hybrid cellular automata method is proposed to carry out the material optimization of thin-walled frame structure under transverse impact with minimum material cost, which is a typical optimal solution searching problem including many discrete variables. A nominal flow stress is introduced to convert the discrete design variables (cell materials) to be continuous for the update of cell materials. The global optimal searching ability of the proposed method is improved by the material update rule based on the step internal energy density target, which is adaptively defined during the material optimization to avoid the optimal solution jumping into a local one. PID control is employed to improve the robustness of the proposed method. The subdomain cellular automata model of a car body frame under transverse impact is constructed to separately perform the material and cost optimization by the proposed method and a parallel efficient global optimization method. The total material cost converges to CNY 1051 within 271 iterations using 32 CPUs by the parallel method and CNY 1101 within 8 iterations using 8 CPUs by the proposed method. The material optimization efficiency is significantly improved by the proposed method with good global searching ability.

Independent Encoding vs. Joint Encoding: Short Frame Structure Optimization for Heterogeneous URLLC Systems

Independent Encoding vs. Joint Encoding: Short Frame Structure Optimization for Heterogeneous URLLC Systems