A 3-D mixed curved beam element satisfying equilibrium equations has been developed based on the Hellinger-Reissner principle. For the description of deformation and equilibrium, nodal displacements and resultant forces are taken as independent field variables. Nodal displacements are approximated linearly and resultant forces are approximated as constants. Accuracy of the element has been greatly enhanced by the satisfaction of point wise equilibrium of resultant forces along the element.
Various curved beam structures have been analyzed utilizing the element and the results have been compared with these using other elements. For more accurate results have been obtained for the problems of constant curvature or concentrated forces and less errors have been observed for problems of variable curvature or distributed forces.
Further research will be required for the improvement of user convenience in treating distributed forces, variable curvature and in the derivation of shapes and base vectors from curvature information. Extensions to the nonlinear problems would be also desirable.
