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A displacement function suitable for plane curved beam in polar coordinates is introduced, and a partial differential governing equation of plane curved beam is obtained by theoretical analysis. Then, the formulation of displacement components and stress components is expressed by the displacement function. On this basis, a finite difference scheme of the partial differential governing equation, displacement components, and stress components of an elastic body in polar coordinates is presented. Finally, the finite difference equations of theoretical formulation are applied to analyze the stress distribution of curved rock, which will provide scientific basis and reference for coal mining engineering.

Curved beam elasticity theory based on the displacement function method using a finite difference scheme