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Table 1 Boundary conditions of the computational model

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

Boundary Boundary conditions
Normal component Tangential component
Right Boundary \(\theta = \theta _{i}\) \(u_{r}(r,\theta _{i}) = 0\) \(u_{\theta } (r,\theta _{i}) = 0\)
Left Boundary \(\theta = \theta _{\max } = \theta _{i} + \theta _{e}\) \(u_{r}(r,\theta _{\max } ) = 0\) \(u_{\theta } (r,\theta _{\max } ) = 0\)
Inner Boundary \(r = r_{\mathrm{ib}}\) \(\sigma _{r}(r_{\mathrm{ib}},\theta ) = 0\) \(\tau _{r\theta } (r_{\mathrm{ib}},\theta ) = 0\)
Out Boundary \(r = r_{\mathrm{ob}}\), θ ≤ 90 \(\sigma _{r}(r_{\mathrm{ob}},\theta ) = - q(\lambda \cos \theta + \sin \theta )\) \(\tau _{r\theta } (r_{\mathrm{ob}},\theta ) = - q(\cos \theta - \lambda \sin \theta )\)
Out Boundary \(r = r_{\mathrm{ob}}\), θ>90 \(\sigma _{r}(r_{\mathrm{ob}},\theta ) = - q( - \lambda \cos \theta + \sin \theta )\) \(\tau _{r\theta } (r_{\mathrm{ob}},\theta ) = - q(\cos \theta + \lambda \sin \theta )\)