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Theory and Modern Applications

Table 2 Boundary conditions at four corners

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

Angular point

Given boundary conditions

Used boundary conditions

Boundary conditions of angular points

A

\(\{ u_{r},u_{\theta },\sigma _{r},\tau _{r\theta } \}\)

\(\{ u_{r},u_{\theta },\tau _{r\theta } \}\)

\(u_{r} = 0\); \(u_{\theta } = 0\); \(\tau _{r\theta } = 0\)

B

\(\{ u_{r},u_{\theta },\sigma _{r},\tau _{r\theta } \}\)

\(\{ u_{r},u_{\theta },\tau _{r\theta } \}\)

\(u_{r} = 0\); \(u_{\theta } = 0\); \(\tau _{r\theta } = 0\)

C

\(\{ u_{r},u_{\theta },\sigma _{r},\tau _{r\theta } \}\)

\(\{ u_{r},u_{\theta },\tau _{r\theta } \}\)

\(u_{r} = 0\); \(u_{\theta } = 0\); \(\tau _{r\theta } = 0\)

D

\(\{ u_{r},u_{\theta },\sigma _{r},\tau _{r\theta } \}\)

\(\{ u_{r},u_{\theta },\tau _{r\theta } \}\)

\(u_{r} = 0\); \(u_{\theta } = 0\); \(\tau _{r\theta } = 0\)