A Fourier Series Method for Solving Ordinary Differential Equations with Non-Constant Coefficients Arising in Inverse Shape Design
نویسندگان
چکیده
An analytical method of integrating ordinary differential equations with non-constant coefficients arising from an elastic membrane concept for inverse shape design is presented utilizing Fourier series formulation. The non-homogeneous ordinary differential equation with non-constant coefficients mimics forced oscillations of a system of mass-damper-spring elements linked in parallel where coefficients of mass, damper and spring are non-constant. This elastic membrane concept for inverse shape design requires knowledge only of the surface field variables distribution on the body to perform a shape update. Thus, it can be implemented without modifying an existing field analysis code. The proposed formulation allows each segment of an evolving shape to move at its own optimal speed thus potentially significantly reducing the required number of shape updates until it matches the specified surface field data.
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