Stiffness matrix of thin-walled curved beam for spatially coupled stability analysis

The exact stiffness matrix for the spatially coupled stability analysis of thin-walled curved beam with non-symmetric cross-section subjected to uniform compression is newly presented. For this, the elastic strain energy including the axially/flexurally/torsionally coupled terms and the potential energy due to the initial stress resultant are introduced. Then, equilibrium equations and force–deformation relationship are derived from the energy principle and explicit expressions for displacement parameters are derived based on power series expansions of displacement components. Next, the exact element stiffness matrix is determined using force–deformation relationships. In order to verify the accuracy of this study, the numerical solutions are presented and compared with the finite element solutions using the Hermitian curved beam elements. In addition, the coupling of symmetric and anti-symmetric modes at the buckling load crossover with change in curvature of beam is investigated.