Finite deformation of 2-D laminated curved beams with variable curvatures

In this research, both Lagrangian and Eulerian description are used to derive the finite deformation analysis. By choosing the deformed radius of curvature and deformed angle of tangent slope as parameters, the governing equations of laminated curved beam under static loading are transformed into a set of equations in terms of angle of tangent slope. All the quantities of axial force, shear force, radial and tangential displacements of laminated curved beam are expressed as functions of angle of tangent slope. The analytical solutions of laminated curved beams of circular and spiral are presented. The analytical solutions of circular beam under a pair of forces are presented as well. The results are also compared with the results using ANSYS. It shows good consistency.

► In research both un-deformed or Lagrangian state and deformed or Eulerian states are used for set deformation analysis.
► The analytical solutions of laminated curved beams of circular and spiral under bending moment are presented.
► The analytical solutions of circular beam under a pair of forces are presented as well.
► The results are also compared with the results using ANSYS. It shows good consistency.