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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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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.

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.

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.

The proposed approach exhibits great capability for MDO problems with tremendous computational costs.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Various simplifications are introduced into the establishment of numerical models for problems with strong nonlinear interactions. The combustion of energetic materials in a chamber with moving boundaries is a typical example. This paper aims to establish a coupled numerical model for predicting the internal combustion in a launch process.

A two-fluid model is used to predict the fluid field induced by the propellant combustion. The moving boundary is located by using a finite element method. Based on a user subroutine interface in the commercial software ABAQUS, the development of the fluid field and the mechanical interactions is coupled with each other.

The paper is devoted to provide a coupled computational framework for predicting the propellant combustion in an expanding chamber. The coupling strategy is validated through predicting a pressure-driven piston system. Based on the validated computational framework, the two-phase reactive flows in a launch process is studied. The predicted parameters agree well with experimental measurements.

This paper provide a method to address the difficulties in realizing the dynamic interactions between multi-phase reactive flows and mechanical behaviors. The computational framework can be used as a research tool for investigating fluid field in a combustion chamber with moving boundaries.