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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 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 study is to propose an improved design of PneuNets bending actuator which aims at obtaining larger deflection with the same magnitude of pressure. The PneuNets bending actuator shows potential application in the morphing trailing edge concept.

Finite element method is used to investigate the characteristics of the improved design bending actuator. Multiobjective optimal design of the PneuNets bending actuator is proposed based on the Gauss process regression models.

The maximum deflection is obtained when the height of the beams is smaller than half the height of the chambers. The spacing between chambers (beam length) has little effect on the deflection. Larger spacing could be used to reduce the actuator weight.

With the same pressure magnitude, the deflection of the improved design bending actuator is much larger than that of the baseline configuration. PneuNets bending actuator could increase the continuity of the aerodynamic surface compared to other actuators.

The purpose of this paper is to develop an efficient non-iterative model combining advanced numerical methods for solving buoyancy-driven flow problems.

The solution strategy is based on two independent numerical procedures. The Navier-Stokes equation is solved using the non-conforming Crouzeix-Raviart (CR) finite element method with an upstream approach for the non-linear convective term. The advection-diffusion heat equation is solved using a combination of Discontinuous Galerkin (DG) and Multi-Point Flux Approximation (MPFA) methods. To reduce the computational time due to the coupling, the authors use a non-iterative time stepping scheme where the time step length is controlled by the temporal truncation error.

Advanced numerical methods have been successfully combined to solve buoyancy-driven flow problems on unstructured triangular meshes. The accuracy of the results has been verified using three test problems: first, a synthetic problem for which the authors developed a semi-analytical solution; second, natural convection of air in a square cavity with different Rayleigh numbers (103-108); and third, a transient natural convection problem of low Prandtl fluid with horizontal temperature gradient in a rectangular cavity.

The proposed model is the first to combine advanced numerical methods (CR, DG, MPFA) for buoyancy-driven flow problems. It is also the first to use a non-iterative time stepping scheme based on local truncation error control for such coupled problems. The developed semi analytical solution based on Fourier series is also novel.

A finite volume scheme for diffusion equations on non-rectangular meshes is proposed in [Deyuan Li, Hongshou Shui, Minjun Tang, J. Numer. Meth. Comput. Appl., 1(4)(1980)217–224 (in Chinese)], which is the so-called nine point scheme on structured quadrilateral meshes. The scheme has both cell-centered unknowns and vertex unknowns which are usually expressed as a linear weighted interpolation of the cell-centered unknowns. The critical factor to obtain the optimal accuracy for the scheme is the reconstruction of vertex unknowns. However, when the mesh deformation is severe or the diffusion tensor is discontinuous, the accuracy of the scheme is not satisfactory, and the author hope to improve this scheme.

The authors propose an explicit weighted vertex interpolation algorithm which allows arbitrary diffusion tensors and does not depend on the location of discontinuity. Both the derivation of the scheme and that of vertex reconstruction algorithm satisfy the linearity preserving criterion which requires that a discretization scheme should be exact on linear solutions. The vertex interpolation algorithm can be easily extended to 3 D case.

Numerical results show that it maintain optimal convergence rates for the solution and flux on 2 D and 3 D meshes in case that the diffusion tensor is taken to be anisotropic, at times heterogeneous, and/or discontinuous.

This paper proposes a linearity preserving and explicit weighted vertex interpolation algorithm for cell-centered finite volume approximations of diffusion equations on general grids. The proposed finite volume scheme with the new interpolation algorithm allows arbitrary continuous or discontinuous diffusion tensors; the final scheme is applicable to arbitrary polygonal grids, which may have concave cells or degenerate ones with hanging nodes. The final scheme has second-order convergence rate for the approximate solution and higher than first-order accuracy for the flux on 2 D and 3 D meshes. The explicit weighted interpolation algorithm is easy to implement in three dimensions in case that the diffusion tensor is continuous or discontinuous.

The present contribution deals with the sensitivity analysis and optimization of structures for path‐dependent structural response. Geometrically as well as materially non‐linear behavior with hardening and softening is taken into account. Prandtl‐Reuss‐plasticity is adopted so that not only the state variables but also their sensitivities are path‐dependent. Because of this the variational direct approach is preferred for the sensitivity analysis. For accuracy reasons the sensitivity analysis has to be consistent with the analysis method evaluating the structural response. The proposed sensitivity analysis as well as its application in structural optimization is demonstrated by several examples.

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.

The purpose of the article is to construct a new class of higher-order iterative techniques for solving scalar nonlinear problems.

The scheme is generalized by using the power-mean notion. By applying Neville's interpolating technique, the methods are formulated into the derivative-free approaches. Further, to enhance the computational efficiency, the developed iterative methods have been extended to the methods with memory, with the aid of the self-accelerating parameter.

It is found that the presented family is optimal in terms of Kung and Traub conjecture as it evaluates only five functions in each iteration and attains convergence order sixteen. The proposed family is examined on some practical problems by modeling into nonlinear equations, such as chemical equilibrium problems, beam positioning problems, eigenvalue problems and fractional conversion in a chemical reactor. The obtained results confirm that the developed scheme works more adequately as compared to the existing methods from the literature. Furthermore, the basins of attraction of the different methods have been included to check the convergence in the complex plane.

The presented experiments show that the developed schemes are of great benefit to implement on real-life problems.

This paper's purpose is to deal with single point and multipoint optimization of an airfoil. The aim of the paper is to discuss optimization in several design points (multipoint optimization) and compare the results with those of optimization at a specified design point.

A gradient‐based method is adopted for optimization and the flow is governed by two dimensional, compressible Euler equations. A finite volume code based on unstructured grid is developed to solve the equations.

Two test cases are studied for an airfoil with initial profile of NACA0012, with two types of design variables. And at the end a multi‐point case is presented.

The advantage of this technique over the other gradient‐based methods is its high‐convergence rate.