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A hierarchical wavelet method for nonlinear bending of materially and geometrically anisotropic thin plate. (English) Zbl 1452.74074

Summary: The paper aims at the application of a hierarchical wavelet homotopy methodology for solving nonlinear bending of anisotropic thin plates. The newly mechanical models of materially anisotropic plate and geometrically orthotropic combined plate at ship double bottom in large deflection have been formulated. The dimensionless coupled and nonlinear governing equations have been derived and decomposed into linear differential terms, while the solutions are expanded in wavelet series as a requirement for implementing the Homotopy recursive system of algebra equations by Galerkin method. Highly accurate Coiflet-type solutions have been obtained with good computational efficiency in excellent agreement with other numerical results in published literatures. Materially and geometrically orthotropic analysis have been conducted with different ratios of elasticity modulus or inertia moment in orthogonal directions, which indicate both orthotropy play an important role in largely deformed anisotropic plate under extreme loads. Convergent solutions over wider bending range of isotropic or anisotropic plates subjected to different boundary conditions are given which reveals our proposed wavelet methodology performs good superiority and versatility dealing with strongly nonlinear problems.

MSC:

74K20 Plates
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74E10 Anisotropy in solid mechanics
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