Mojtaba Aslami

Local High-Accuracy Plate Analysis Using Wavelet-Based Multilevel Discrete-Continual Finite Element Method

The distinctive paper is devoted to application of wavelet-based discrete-continual finite element method (WDCFEM), to analysis of plates with piecewise constant physical and geometrical parameters in so-called “basic” direction. Initial continual and discrete-continual formulations of the problem are presented. Due to special algorithms of averaging using wavelet basis within multigrid approach, reduction of the problem is provided. Resultant multipoint boundary problem for system of ordinary differential equations is given.

Theoretical Foundations of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

This paper is devoted to correct and efficient method of local static analysis of Bernoulli beam on elastic foundation. First of all, problem discretized by finite difference method, and then transformed to a localized one by using the Haar wavelets. Finally, imposing an optimal reduction in wavelet coefficients, the localized, reduced results can be obtained. It becomes clear after comparison with analytical solutions, that the localization of the problem by multiresolution wavelet approach gives exact solution in desired regions of beam even in high level of reduction in wavelet coefficients. This localization can be applied to any arbitrary region of the beam by choosing optimum reduction matrix and obtaining exact solutions with an acceptable reduced size of the problem.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 1: Continual and Discrete-Continual Formulations of the Problems

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Two-dimensional and three-dimensional problems of analysis of structures with piecewise constant physical and geometrical parameters along so-called “basic” direction are under consideration. High-accuracy solution of the corresponding problems at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known local domains. Wavelet analysis is a powerful and effective tool for corresponding researches. Initial continual and discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are presented.

Modified Wavelet-Based Multilevel Discrete-Continual Finite Element Method for Local Structural Analysis - Part 2: Reduced Formulations of the Problems in Haar Basis

The distinctive paper is devoted to wavelet-based discrete-continual finite element method (WDCFEM) of structural analysis. Discrete-continual formulations of multipoint boundary problems of two-dimensional and three-dimensional structural analysis are transformed to corresponding localized formulations by using the discrete Haar wavelet basis and finally, with the use of averaging and reduction algorithms, the localized and reduced governing equations are obtained. Special algorithms of localization with respect to each degree of freedom are presented.

About Verification of Correct Wavelet-Based Approach to Local Static Analysis of Bernoulli Beam

This paper is devoted to verification of correct and efficient wavelet-based method of local static analysis of Bernoulli beam on elastic foundation, proposed by authors. Corresponding results for sample problem have been compared with analytical solutions. Comparison shows that the localization of the problem with reducing its size by proposed method provide high-accuracy results for desired regions of the structure even in high level of reduction in wavelet coefficients. It should be noted that, the wavelet analysis can exactly decompose problem and the sources of the observed error between the analytical solution and numerical result, is based mainly on applied method for solving (in this case, finite difference method), and can be improved.