Yu, Qiang; Xu, Hang; Liao, Shijun Nonlinear analysis for extreme large bending deflection of a rectangular plate on non-uniform elastic foundations. (English) Zbl 1460.74056 Appl. Math. Modelling 61, 316-340 (2018). Summary: An analysis is presented for different bearing loadings of a plate resting on various linear and nonlinear foundations subjected to different boundary conditions such as the circled clamped, simply supported, and mixed boundary conditions. The highly accurate solutions of the plate deflection and the stress under different work conditions are obtained by the novel wavelet-homotopy technique, which are in full agreement with previous ones in literature. Different from previous studies, our solutions are also valid for the extra large plate bending cases, which are rarely considered before. Particularly, we consider the important case that the connection coefficients of various foundations are variational, which seems to be overlooked in previous studies owing to their extreme difficulties in mathematical treatments and programming. Besides, to overcome the limitation of existing wavelet technique of poor capability on handling complex boundary conditions, we reconstruct the boundary wavelet by the Coiflets so that it can be used to handle the governing partial differential equations subjected to nonhomogeneous boundary conditions. Moreover, we introduce the homotopy iteration technique so that the computational efficiency improves to a large extent as compared with the traditional Homotopy Analysis Method (HAM) technique. It is expected the proposed wavelet-homotopy method can be as a new generation of analytical tool for solving strong nonlinear problems subjected to complicated boundary conditions, especially for those with variable coefficients. Cited in 9 Documents MSC: 74K20 Plates 74S99 Numerical and other methods in solid mechanics Keywords:thin plate; wavelet-Galerkin method; closed wavelet method; wavelet homotopy method PDFBibTeX XMLCite \textit{Q. Yu} et al., Appl. Math. Modelling 61, 316--340 (2018; Zbl 1460.74056) Full Text: DOI References: [1] Timoshenko, S. P., Theory of plates and shells, Studies in Mathematics and Its Applications Elsevier Amsterdam, 6, 3760, 606 (1959) [2] Ventsel, E.; Krauthammer, T.; Carrera, E., Thin plates and shells: theory, analysis, and applications, Appl. Mech. Rev., 55, 4, 1813-1831 (2002) [3] Vlasov, V. Z., Beams, plates and shells on elastic foundations, Israel Program for Scientific Translations, Jerusalem (1966), https://ci.nii.ac.jp/naid/10005329921/en/ · Zbl 0214.24203 [4] Nath, Y.; Prithviraju, M.; Mufti, A. A., Nonlinear statics and dynamics of antisymmetric composite laminated square plates supported on nonlinear elastic subgrade, Commun. Nonlinear Sci. Numer. 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