Numerical transfer-method with boundary conditions for arbitrary curved beam elements

A novel numerical transfer-method is presented to solve a system of linear ordinary differential equations with boundary conditions. It is applied to determine the structural behaviour of the classical problem of an arbitrary curved beam element. The approach of this boundary value problem yields a unique system of differential equations. A Runge–Kutta scheme is chosen to obtain the incremental transfer expression. The use of a recurrence strategy in this equation permits to relate both ends in the domain where boundary conditions are defined. Semicircular arch, semicircular balcony and elliptic–helical beam examples are provided for validation.