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A new higher order Haar wavelet method (HOHWM) has been developed for solving differential and integro-differential equations. Generalized approach has been proposed for wavelet expansion allowing improvement of the accuracy and the rate of convergence of the solution. The sample problem considered shows, that applying the approach proposed allows to improve the order of convergence of the HWM from two to four and to reduce the absolute error by several orders of magnitude (depending on mesh). Furthermore, in the case of sample problem considered, the computational and implementation complexities are kept in the same range with widely used HWM. [ABSTRACT FROM AUTHOR]

Optimal design of the frontal protection system of a car is considered. The study is focused on design of the fastening components. A simple theoretical estimate on deformation energy is given. The car-pedestrian collision situation is analyzed by use of the LS-DYNA explicit solver. Corresponding stiffness analysis is performed by use of the LS-DYNA implicit solver. The approximation of the objective and constraint functions is modeled by use of artificial neural network (NN) and search for an optimal design is performed by use of a genetic algorithm (GA). The obtained numerical results are validated against experimental test results. [ABSTRACT FROM AUTHOR]

Abstract: The objective of the current study is the optimization of the structure and manufacturing processes of large composite plastic parts. The main attention is paid to strengthening of plastic preformed shell by adding variable thickness glass–fiber composite layers and optimizing the material concentrations of the reinforcement layer. The final properties of the part are determined by minimizing the cost and production time simultaneously. The multistage optimization procedure has been applied. According to this approach, the solution of the posed optimization problem has been decomposed into FEA (including free size optimization), meta-modeling and global optimization. Multiple criteria analysis (MCA) is used for evaluating decision options against multiple criteria. Search for global optimum has been performed using of genetic algorithm. The solution has been implemented in MATLAB code. The product family of the composite plastic bathtub, together with the derivate products and their production technologies, is designed using proposed methodology. [Copyright &y& Elsevier]

The Haar wavelet discretization technique for solving the elastic bending problems of orthotropic plates and shells is proposed. Free transverse vibrations of orthotropic rectangular plates with a variable thickness in one direction are considered as a model problem. In the case of constant plate thickness, the numerical results are validated by comparing them with an exact solution. The results obtained are found to be in good agreement with those available in the literature. [ABSTRACT FROM AUTHOR]

Current study contains adaption of Haar wavelet discretization method (HWDM) for FG beams and its accuracy estimates. The convergence analysis is performed for differential equations covering a wide class of composite and nanostructures. Corresponding error bound has been derived. It has been shown that the order of convergence of the HWDM can be increased from two to four by applying Richardson extrapolation method. The theoretical estimates are validated by numerical samples considering FGM beam as a model problem. The results obtained by applying HWDM are compared with the results of finite difference method (FDM). [ABSTRACT FROM AUTHOR]

The accuracy issues of Haar wavelet method are studied. The order of convergence as well as error bound of the Haar wavelet method is derived for general n th order ODE. The Richardson extrapolation method is utilized for improving the accuracy of the solution. A number of model problems are examined. The numerically estimated order of convergence has been found in agreement with convergence theorem results in the case of all model problems considered. [ABSTRACT FROM AUTHOR]