A homotopy-based wavelet approach for large deflection of a circular plate on nonlinear foundations with parameterized boundaries. (15th May 2021) - Yu, Qiang; Xu, Hang
Abstract: A Coiflet-type wavelet-homotopy approach is implemented to investigate the large deformation of a circular plate resting on different nonlinear foundations with various boundary parameters. A parameterized and continuous boundary model for circular plate with various constraints of rotation and translation has been proposed overlooked in previous studies. Parameterized wavelet approximation of arbitrary Robin-type boundary is reconstituted without variable substitution. Comprehensive analysis on the parameterized Robin-type boundaries is conducted by Linear Programming Approach, indicating the boundary singularities are actually false corresponding to the degenerated cases of Dirichlet-type and Neumann-type ones. Highly accurate Coiflet-type solutions of the coupled governing nonlinear differential equations with integration involving in extreme bending of circular plate have been obtained performing good computational efficiency in excellent agreement with other numerical results, which implies the wavelet scheme is a high precision computation method with great potential in giving highly accurate solutions of strongly nonlinear problems. Highlights: The new Coiflet-type wavelet approach for Robin boundary conditions is proposed. Extreme large bending of a circular plate resting nonlinear foundations is analyzed. Highly accurate solutions with integrations and singularities are obtained. Parameterized Robin-type boundaries are conducted by Linear Programming Approach. Validity and efficiency of the proposed technique is provided.