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.

实施了Coiflet型小波同伦方法，研究了具有不同边界参数的，位于不同非线性基础上的圆形板的大变形。在以前的研究中已经忽略了具有各种旋转和平移约束的圆形板的参数化连续边界模型。重构了任意Robin类型边界的参数化小波逼近，而无需进行变量替换。通过线性规划方法对参数化的Robin型边界进行了综合分析，表明对应于Dirichlet型和Neumann型退化情况的边界奇异点实际上是假的。