Large deformation analysis of composite spatial curved beams with arbitrary undeformed configurations described by Euler angles with discontinuities and singularities

Based on Kirchhoff theory, governing equations of a spatial curved beam with an arbitrary undeformed configuration that undergoes large deformation are established in an arc-length coordinate system and axial extension of the beam is considered. Modified Euler angles are defined to describe geometrical relations and overcome discontinuities of Euler angles. A novel three-layer coordinate system method is developed to overcome singularities of Euler angles associated with Gimbal lock and applied to a challenging composite spatial curved beam problem. A general differential quadrature element method (DQEM) is applied to discretize the nonlinear mathematical model. Connecting conditions are used in the DQEM to deal with discontinuities of composite beams, such as concentrated loads, rigid and hinged joints and so on. A new computing process that uses a trapezoidal integral method in conjunction with a bisection method is employed to obtain modified Euler angles of a spatial curved beam with an arbitrary undeformed configuration. Numerical results are given to assess its validity and effectiveness.