A.A. Polynkine, F. Van Keulen and V.V. Toropov
Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the…
Abstract
Presents an approach for optimal design of geometrically non‐linear structures, using adaptive mesh refinement (AMR). The optimization technique adopted is based on the multi‐point approximation method. The finite element method is used for the structural analysis. Reformulation of the optimal design problem is applied to circumvent complications caused by the non‐linear behaviour of the structure. The latter may lead to bifurcations, limit points and/or significant reduction of the structural stiffness for individual intermediate designs generated by an optimization algorithm. Discretization errors are controlled using AMR. To reduce computational costs, the requested global and local discretization errors are not taken as fixed values but are specified on the basis of the current status of the optimization process. In the beginning relatively large errors are accepted, while as the process progresses discretization errors are reduced. The method is applied to thin‐walled structures with geometrically non‐linear behaviour.
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In this paper a structural optimization technique based on a modified genetic algorithm (GA) is presented. The technique is developed to deal with discrete design optimization of…
Abstract
In this paper a structural optimization technique based on a modified genetic algorithm (GA) is presented. The technique is developed to deal with discrete design optimization of structural steelwork. Also, the paper discusses the effect of different approaches, employed for the determination of the effective buckling length of a column, on the optimum design. In order to consider realistic steelwork design problems, a modified GA has been linked to a system of structural design rules (British Standards BS 5950 and BS 6399), interacting with a finite element package. In the formulation of the optimization problem, the objective function is the total weight of the structural members, as it gives a reasonably accurate estimation of the cost. The cross‐sectional properties of the structural members, which form the set of design variables, are chosen from two separate catalogues (universal beams and columns) covered by the British Standard BS 4. The minimum weight designs of two plane steel frame structures subjected to realistic multiple loading cases are obtained. These examples show that the modified GA in combination with structural design rules and more accurate analysis provides an efficient tool for practicing designers of steel frame structures. Finally, it is shown that the resulting design optimization is considerably influenced by a specific choice of a technique employed for the evaluation of the effective buckling length of structural members.
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This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design…
Abstract
Purpose
This paper aims to present a new method, named as augmented polynomial dimensional decomposition (PDD) method, for robust design optimization (RDO) and reliability-based design optimization (RBDO) subject to mixed design variables comprising both distributional and structural design variables.
Design/methodology/approach
The method involves a new augmented PDD of a high-dimensional stochastic response for statistical moments and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms.
Findings
New closed-form formulae are presented for the design sensitivities of moments that are simultaneously determined along with the moments. A finite-difference approximation integrated with the embedded Monte Carlo simulation of the augmented PDD is put forward for design sensitivities of the failure probability.
Originality/value
In conjunction with the multi-point, single-step design process, the new method provides an efficient means to solve a general stochastic design problem entailing mixed design variables with a large design space. Numerical results, including a three-hole bracket design, indicate that the proposed methods provide accurate and computationally efficient sensitivity estimates and optimal solutions for RDO and RBDO problems.
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This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics…
Abstract
This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.
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Dianzi Liu, Chengyang Liu, Chuanwei Zhang, Chao Xu, Ziliang Du and Zhiqiang Wan
In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear…
Abstract
Purpose
In real-world cases, it is common to encounter mixed discrete-continuous problems where some or all of the variables may take only discrete values. To solve these non-linear optimization problems, the use of finite element methods is very time-consuming. The purpose of this study is to investigate the efficiency of the proposed hybrid algorithms for the mixed discrete-continuous optimization and compare it with the performance of genetic algorithms (GAs).
Design/methodology/approach
In this paper, the enhanced multipoint approximation method (MAM) is used to reduce the original nonlinear optimization problem to a sequence of approximations. Then, the sequential quadratic programing technique is applied to find the continuous solution. Following that, the implementation of discrete capability into the MAM is developed to solve the mixed discrete-continuous optimization problems.
Findings
The efficiency and rate of convergence of the developed hybrid algorithms outperforming GA are examined by six detailed case studies in the ten-bar planar truss problem, and the superiority of the Hooke–Jeeves assisted MAM algorithm over the other two hybrid algorithms and GAs is concluded.
Originality/value
The authors propose three efficient hybrid algorithms, the rounding-off, the coordinate search and the Hooke–Jeeves search-assisted MAMs, to solve nonlinear mixed discrete-continuous optimization problems. Implementations include the development of new procedures for sampling discrete points, the modification of the trust region adaptation strategy and strategies for solving mix optimization problems. To improve the efficiency and effectiveness of metamodel construction, regressors f defined in this paper can have the form in common with the empirical formulation of the problems in many engineering subjects.
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This paper evaluates a Successive Response Surface Method (SRSM) specifically developed for simulation‐based design optimization, e.g. that of explicit nonlinear dynamics in…
Abstract
This paper evaluates a Successive Response Surface Method (SRSM) specifically developed for simulation‐based design optimization, e.g. that of explicit nonlinear dynamics in crashworthiness design. Linear response surfaces are constructed in a subregion of the design space using a design of experiments approach with a D‐optimal experimental design. To converge to an optimum, a domain reduction scheme is utilized. The scheme requires only one user‐defined parameter, namely the size of the initial subregion. During optimization, the size of this region is adapted using a move reversal criterion to counter oscillation and a move distance criterion to gauge accuracy. To test its robustness, the results using the method are compared to SQP results of a selection of the well‐known Hock and Schittkowski problems. Although convergence to a small tolerance is slow when compared to SQP, the SRSM method does remarkably well for these sometimes pathological analytical problems. The second test concerns three engineering problems sampled from the nonlinear structural dynamics field to investigate the method's handling of numerical noise and non‐linearity. It is shown that, despite its simplicity, the SRSM method converges stably and is relatively insensitive to its only user‐required input parameter.
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Ping Jiang, Qi Zhou, Xinyu Shao, Ren Long and Hui Zhou
The purpose of this paper is to present a modified bi-level integrated system collaborative optimization (BLISCO) to avoid the non-separability of the original BLISCO. Besides, to…
Abstract
Purpose
The purpose of this paper is to present a modified bi-level integrated system collaborative optimization (BLISCO) to avoid the non-separability of the original BLISCO. Besides, to mitigate the computational burden caused by expensive simulation codes and employ both efficiently simplified and expensively detailed information in multidisciplinary design optimization (MDO), an effective framework combining variable fidelity metamodels (VFM) and modified BLISCO (MBLISCO) (VFM-MBLISCO) is proposed.
Design/methodology/approach
The concept of the quasi-separable MDO problems is introduced to limit range of applicability about the BLISCO method and then based on the quasi-separable MDO form, the modification of BLISCO method without any derivatives is presented to solve the problems of BLISCO. Besides, an effective framework combining VFM-MBLISCO is presented.
Findings
One mathematical problem conforms to the quasi-separable MDO form is tested and the overall results illustrate the feasibility and robustness of the MBLISCO. The design of a Small Waterplane Area Twin Hull catamaran demonstrates that the proposed VFM-MBLISCO framework is a feasible and efficient design methodology in support of design of engineering products.
Practical implications
The proposed approach exhibits great capability for MDO problems with tremendous computational costs.
Originality/value
A MBLISCO is proposed which can avoid the non-separability of the original BLISCO and an effective framework combining VFM-MBLISCO is presented to efficiently integrate the different fidelities information in MDO.
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Andrew Thelen, Leifur Leifsson, Anupam Sharma and Slawomir Koziel
Dual-rotor wind turbines (DRWTs) are a novel type of wind turbines that can capture more power than their single-rotor counterparts. Because their surrounding flow fields are…
Abstract
Purpose
Dual-rotor wind turbines (DRWTs) are a novel type of wind turbines that can capture more power than their single-rotor counterparts. Because their surrounding flow fields are complex, evaluating a DRWT design requires accurate predictive simulations, which incur high computational costs. Currently, there does not exist a design optimization framework for DRWTs. Since the design optimization of DRWTs requires numerous model evaluations, the purpose of this paper is to identify computationally efficient design approaches.
Design/methodology/approach
Several algorithms are compared for the design optimization of DRWTs. The algorithms vary widely in approaches and include a direct derivative-free method, as well as three surrogate-based optimization methods, two approximation-based approaches and one variable-fidelity approach with coarse discretization low-fidelity models.
Findings
The proposed variable-fidelity method required significantly lower computational cost than the derivative-free and approximation-based methods. Large computational savings come from using the time-consuming high-fidelity simulations sparingly and performing the majority of the design space search using the fast variable-fidelity models.
Originality/value
Due the complex simulations and the large number of designable parameters, the design of DRWTs require the use of numerical optimization algorithms. This work presents a novel and efficient design optimization framework for DRWTs using computationally intensive simulations and variable-fidelity optimization techniques.
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Andrew Thelen, Leifur Leifsson, Anupam Sharma and Slawomir Koziel
An improvement in the energy efficiency of wind turbines can be achieved using dual rotors. Because of complex flow physics, the design of dual-rotor wind turbines (DRWTs…
Abstract
Purpose
An improvement in the energy efficiency of wind turbines can be achieved using dual rotors. Because of complex flow physics, the design of dual-rotor wind turbines (DRWTs) requires repetitive evaluations of computationally expensive partial differential equation (PDE) simulation models. Approaches for solving design optimization of DRWTs constrained by PDE simulations are investigated. The purpose of this study is to determine design optimization algorithms which can find optimal designs at a low computational cost.
Design/methodology/approach
Several optimization approaches and algorithms are compared and contrasted for the design of DRWTs. More specifically, parametric sweeps, direct optimization using pattern search, surrogate-based optimization (SBO) using approximation-based models and SBO using kriging interpolation models with infill criteria are investigated for the DRWT design problem.
Findings
The approaches are applied to two example design cases where the DRWT fluid flow is simulated using the Reynolds-averaged Navier−Stokes (RANS) equations with a two-equation turbulence model on an axisymmetric computational grid. The main rotor geometry is kept fixed and the secondary rotor characteristics, using up to three variables, are optimized. The results show that the automated numerical optimization techniques were able to accurately find the optimal designs at a low cost. In particular, SBO algorithm with infill criteria configured for design space exploitation required the least computational cost. The widely adopted parametric sweep approach required more model evaluations than the optimization algorithms, as well as not being able to accurately find the optimal designs.
Originality/value
For low-dimensional PDE-constrained design of DRWTs, automated optimization algorithms are essential to find accurately and efficiently the optimal designs. More specifically, surrogate-based approaches seem to offer a computationally efficient way of solving such problems.
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Ibrahim T. Teke and Ahmet H. Ertas
The paper's goal is to examine and illustrate the useful uses of submodeling in finite element modeling for topology optimization and stress analysis. The goal of the study is to…
Abstract
Purpose
The paper's goal is to examine and illustrate the useful uses of submodeling in finite element modeling for topology optimization and stress analysis. The goal of the study is to demonstrate how submodeling – more especially, a 1D approach – can reliably and effectively produce ideal solutions for challenging structural issues. The paper aims to demonstrate the usefulness of submodeling in obtaining converged solutions for stress analysis and optimized geometry for improved fatigue life by studying a cantilever beam case and using beam formulations. In order to guarantee the precision and dependability of the optimization process, the developed approach will also be validated through experimental testing, such as 3-point bending tests and 3D printing. Using 3D finite element models, the 1D submodeling approach is further validated in the final step, showing a strong correlation with experimental data for deflection calculations.
Design/methodology/approach
The authors conducted a literature review to understand the existing research on submodeling and its practical applications in finite element modeling. They selected a cantilever beam case as a test subject to demonstrate stress analysis and topology optimization through submodeling. They developed a 1D submodeling approach to streamline the optimization process and ensure result validity. The authors utilized beam formulations to optimize and validate the outcomes of the submodeling approach. They 3D-printed the optimized models and subjected them to a 3-point bending test to confirm the accuracy of the developed approach. They employed 3D finite element models for submodeling to validate the 1D approach, focusing on specific finite elements for deflection calculations and analyzed the results to demonstrate a strong correlation between the theoretical models and experimental data, showcasing the effectiveness of the submodeling methodology in achieving optimal solutions efficiently and accurately.
Findings
The findings of the paper are as follows: 1. The use of submodeling, specifically a 1D submodeling approach, proved to be effective in achieving optimal solutions more efficiently and accurately in finite element modeling. 2. The study conducted on a cantilever beam case demonstrated successful stress analysis and topology optimization through submodeling, resulting in optimized geometry for enhanced fatigue life. 3. Beam formulations were utilized to optimize and validate the outcomes of the submodeling approach, leading to the successful 3D printing and testing of the optimized models through a 3-point bending test. 4. Experimental results confirmed the accuracy and validity of the developed submodeling approach in streamlining the optimization process. 5. The use of 3D finite element models for submodeling further validated the 1D approach, with specific finite elements showing a strong correlation with experimental data in deflection calculations. Overall, the findings highlight the effectiveness of submodeling techniques in achieving optimal solutions and validating results in finite element modeling, stress analysis and optimization processes.
Originality/value
The originality and value of the paper lie in its innovative approach to utilizing submodeling techniques in finite element modeling for structural analysis and optimization. By focusing on the reduction of finite element models and the creation of smaller, more manageable models through submodeling, the paper offers designers a more efficient and accurate way to achieve optimal solutions for complex problems. The study's use of a cantilever beam case to demonstrate stress analysis and topology optimization showcases the practical applications of submodeling in real-world scenarios. The development of a 1D submodeling approach, along with the utilization of beam formulations and 3D printing for experimental validation, adds a novel dimension to the research. Furthermore, the paper's integration of 1D and 3D submodeling techniques for deflection calculations and validation highlights the thoroughness and rigor of the study. The strong correlation between the finite element models and experimental data underscores the reliability and accuracy of the developed approach. Overall, the originality and value of this paper lie in its comprehensive exploration of submodeling techniques, its practical applications in structural analysis and optimization and its successful validation through experimental testing.