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Based on aerodynamic analysis, an optimization method for the profiles of turbine blade is studied in this paper. This method is capable of addressing multiple objectives and constrains without relying on user input. A quintic polynomial is used to build the three‐dimensional blade model and a three dimensional Navier‐Stokes solver was used to solve the flow field around the turbine blade. The objective functions are the turbine aerodynamic efficiency and total pressure ratio. The optimization is completed with the K‐S function technique and accelerated by approximation technique. Finally, the proposed method is applied to optimizing a true blade to validate its accuracy and efficiency. The obtained result shows that the approximation method is more efficient and accurate than the conventional method.

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.

The purpose of this paper is to investigate the mechanical properties’ behaviors of woven composite cut-out structures with specific parameters. Because of the complexity of micro-scale and meso-scale structure, it is difficult to accurately predict the mechanical material behavior of woven composites. Numerical simulations are increasingly necessary for the design and optimization of test procedures for composite structures made by the woven composite. The results of the proposed method are well satisfied with the results obtained from the experiment and other studies. Moreover, parametric studies on different plates based on the stacking sequences are investigated.

A multi-scale modeling approach is suggested. Back-propagation neural networks (BPNN), radial basis function (RBF) and least square support vector regression are integrated with efficient global optimization (EGO) to reduce the weight of assigned structure. Optimization results are verified by finite element analysis.

Compared with other similar studies, the advantage of the suggested strategy uses homogenized properties behaviors with more complex analysis of woven composite structures. According to investigation results, it can be found that 450/−450 ply-orientation is the best buckling load value for all the cut-out shape requirements. According to the optimal results, the BPNN-EGO is the best candidate for the EGO to optimize the woven composite structures.

A multi-scale approach is used to investigate the mechanical properties of a complex woven composite material architecture. Buckling of different cut-out shapes with the same area is surveyed. According to investigation, 45°/−45° ply-orientation is the best for all cut-out shapes. Different surrogate models are integrated in EGO for optimization. The BPNN surrogate model is the best choice for EGO to optimization difficult problems of woven composite materials.

An existing two‐dimensional finite volume technique is modified by introducing a correction term to increase the accuracy of the method to second order. It is well known that the accuracy of the finite volume method strongly depends on the order of the approximation of the flux term at the control volume (CV) faces. For highly orthotropic and anisotropic media, first order approximations produce inaccurate simulation results, which motivates the need for better estimates of the flux expression. In this article, a new approach to approximate the flux term at the CV face is presented. The discretisation involves a decomposition of the flux and an improved least squares approximation technique to calculate the derivatives of the dependent function on the CV faces for estimating both the cross diffusion term and a correction for the primary flux term. The advantage of this method is that any arbitrary unstructured mesh can be used to implement the technique without considering the shapes of the mesh elements. It was found that the numerical results well matched the available exact solution for a representative transport equation in highly orthotropic media and the benchmark solutions obtained on a fine mesh for anisotropic media. Previously proposed CV techniques are compared with the new method to highlight its accuracy for different unstructured meshes.

A two‐step computational procedure is presented for reducing the size of the analysis model for an anisotropic symmetric structure to that of the corresponding orthotropic structure. The key elements of the procedure are: (a) decomposition of the stiffness matrix into the sum of an orthotropic and non‐orthotropic (anisotropic) parts; and (b) successive application of the finite element method and the classical Rayleigh—Ritz technique. The finite element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh—Ritz technique. The global approximation vectors are selected to be the solution corresponding to zero non‐orthotropic matrix and its various‐order derivatives with respect to an anisotropic tracing parameter (identifying the non‐orthotropic material coefficients). The size of the analysis model used in generating the global approximation vectors is identical to that of the corresponding orthotropic structure. The effectiveness of the proposed technique is demonstrated by means of numerical examples and its potential for solving other quasi‐symmetric problems is discussed.

The purpose of this paper is to report the implementation of an alternative time integration procedure for the dynamic non-linear analysis of structures.

The time integration algorithm discussed in this work corresponds to a spectral decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion. This is achieved by solving an eigenvalue problem in the time domain that only depends on the approximation basis being implemented. Complete sets of orthogonal Legendre polynomials are used to define the time approximation basis required by the model.

A classical example with known analytical solution is presented to validate the model, in linear and non-linear analysis. The efficiency of the numerical technique is assessed. Comparisons are made with the classical Newmark method applied to the solution of both linear and non-linear dynamics. The mixed time integration technique presents some interesting features making very attractive its application to the analysis of non-linear dynamic systems. It corresponds in essence to a modal decomposition technique implemented in the time domain. As in the case of the modal decomposition in space, the numerical efficiency of the resulting integration scheme depends on the possibility of uncoupling the equations of motion.

One of the main advantages of this technique is the possibility of considering relatively large time step increments which enhances the computational efficiency of the numerical procedure. Due to its characteristics, this method is well suited to parallel processing, one of the features that have to be conveniently explored in the near future.

The purpose of this paper is to present a new cubic B-spline (CBS) approximation technique for the numerical treatment of coupled viscous Burgers’ equations arising in the study of fluid dynamics, continuous stochastic processes, acoustic transmissions and aerofoil flow theory.

The system of partial differential equations is discretized in time direction using the finite difference formulation, and the new CBS approximations have been used to interpolate the solution curves in the spatial direction. The theoretical estimation of stability and uniform convergence of the proposed numerical algorithm has been derived rigorously.

A different scheme based on the new approximation in CBS functions is proposed which is quite different from the existing methods developed (Mittal and Jiwari, 2012; Mittal and Arora, 2011; Mittal and Tripathi, 2014; Raslan et al., 2017; Shallal et al., 2019). Some numerical examples are presented to validate the performance and accuracy of the proposed technique. The simulation results have guaranteed the superior performance of the presented algorithm over the existing numerical techniques on approximate solutions of coupled viscous Burgers’ equations.

The current approach based on new CBS approximations is novel for the numerical study of coupled Burgers’ equations, and as far as we are aware, it has never been used for this purpose before.

Many dynamic problems in economics are characterized by large state spaces which make both computing and estimating the model infeasible. We introduce a method for approximating the value function of high-dimensional dynamic models based on sieves and establish results for the (a) consistency, (b) rates of convergence, and (c) bounds on the error of approximation. We embed this method for approximating the solution to the dynamic problem within an estimation routine and prove that it provides consistent estimates of the modelik’s parameters. We provide Monte Carlo evidence that our method can successfully be used to approximate models that would otherwise be infeasible to compute, suggesting that these techniques may substantially broaden the class of models that can be solved and estimated.

The purpose of this paper is to develop a computational technique to couple finite element and meshfree methods for locking‐free analysis of shear deformable beams and plates, and to impose the boundary conditions directly when the matching field approach is adopted in the meshfree region.

Matching field approach eliminates shear‐locking which may occur due to inconsistencies in the approximations of the transverse displacement and rotation fields in shear‐deformable beams and plates. Continuous blending method is modified in order to be able to satisfy the constraint conditions of the matching field strategy.

For both transverse displacement and rotation fields, the developed technique produces approximation functions that satisfy the Kronecker delta property at the required nodes of the meshfree region when the matching field approach is adopted.

This approach allows for direct assembly of the stiffness matrices that are built for separate finite element and meshfree regions when the matching field approach is adopted. The boundary conditions can be directly applied, and the reaction forces can also be calculated directly from the structural stiffness matrix by using the developed technique.

The problem of determining a rational function whose magnitude characteristic approximates some arbitrary functions of frequency in an equiripple sense is discussed. A novel method that provides a rational all‐pole equiripple approximation to any arbitrary magnitude response in the frequency domain is described. The technique is applied to a typical example that serves to illustrate the effectiveness of the method.