Prof.
Marina Mozgaleva
(National Research Moscow State University of Civil Engineering)Prof.
Pavel Akimov
(Scientific Research Center “StaDyO”)

Numerical or semianalytical solution of problems of structural mechanics with immense number of unknowns is time-consuming process. High-accuracy solution at all points of the model is not required normally, it is necessary to find only the most accurate solution in some pre-known domains. The choice of these domains is a priori data with respect to the structure being modeled. Designers usually choose domains with the so-called edge effect (with the risk of significant stresses that could lead to destruction of structures) and regions which are subject to specific operational requirements. Stress-strain state in such domains is important. Wavelets provide effective and popular tool for local structural analysis.
Operational and variational formulations of problems of structural mechanics with the use of method of extended domain are presented. After discretization and obtaining of governing equations, problems are transformed to a multilevel space by multilevel wavelet transform. Discrete wavelet basis is used and corresponding direct and inverse algorithms of transformations are performed. Due to special algorithms of averaging, reduction of the problems is provided. Wavelet-based methods allows reducing the size of the problems and obtaining accurate results in selected domains simultaneously. These are rather efficient methods for evaluation of local phenomenon in structures.

### Short biography note

References:

1. Akimov P.A., Mozgaleva M.L. Correct Wavelet-based Multilevel Discrete-Continual Methods for Local Solution of Boundary Problems of Structural Analysis. // Applied Mechanics and Materials Vols. 353-356 (2013), pp. 3224-3227.

2. Akimov P.A., Mozgaleva M.L. Correct Wavelet-based Multilevel Numerical Method of Local Solution of Boundary Problems of Structural Analysis. // Applied Mechanics and Materials Vols. 166-169 (2012), pp. 3155-3158.

3. Akimov P.A., Mozgaleva M.L. Method of Extended Domain and General Principles of Mesh Approximation for Boundary Problems of Structural Analysis. // Applied Mechanics and Materials, Vols. 580-583 (2014), pp. 2898-2902.

4. Aslami M., Akimov P.A. Wavelet-based finite element method for multilevel local plate analysis. // Thin-Walled Structures, 98, 2016, pp. 392–402.

5. Mozgaleva M.L., Akimov P.A. Multilevel Wavelet-based Numerical Method of Local Structural Analysis for Three-dimensional Problem. // Procedia Engineering, 111 (2015), pp. 569-574.

6. Chui C.K. An introduction to wavelets. Academic Press, New York, 1992.

7. Burrus C.S., Gopinath R.A., Guo H. Introduction to Wavelets and Wavelet Transforms. A Primer, Prentice-Hall, Inc., Upper Saddle River, NJ, 1998.

Prof.
Marina Mozgaleva
(National Research Moscow State University of Civil Engineering)