The Haar wavelet method is applied for solving different problems of buckling of elastic beams. Solutions are given for the following problems: (i) beams with intermediate supports, (ii) crack simulation, (iii) beams with variable cross-section, (iv) buckling and vibrations of beams on an elastic foundation. Numerical results for seven test examples are presented. It follows from the calculations that the accuracy of the results is high even in the case of a small number of calculation points. In most cases the proposed method is mathematically simpler in comparison with the conventional approaches.
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