Computer Art Design Model Based on Nonlinear Fractional Differential Equations

Abstract

Abstract The influence of the environment will deform materials in computer art design. Based on nonlinear fractional differential equations, the paper constructs the change of material mechanical properties in computer art design. This paper uses the asymptotic expansion method to transform the higher-order partial differential equations into nonlinear fractional-order differential equations. In this paper, the equations are solved to obtain the stress function. Then the analytical formula of the high-order asymptotic field of the stress at the crack tip in the functionally graded material is obtained. In this paper, the separation method of variables is used to obtain the solution of the equation expressed in rectangular coordinates, and the expressions of displacement and stress are obtained. The study found that the order of the model can quantitatively describe the evolution of the mechanical properties of plastic metals in computer art.