A new nonlinear geometric curved-beam finite element is developed for three dimensional space systems by using the principal of potential energy and polynomial functions. The element is assumed to be curved in one plane only, but deformations in the three-dimensional space is considered. The element geometry is defined by a second order polynomial. In deriving the linear stiffness matrix, k, the displacement functions are approximated by cubic polynomials. In deriving the incremental stiffness matrices, ni and 1,2, however, while the transverse displacements are still approximated by cubic polynomials, the longitudinal displacements and twist are approximated by linear polynomials. A major improvement in the accuracy of the element is obtained by averaging the nonlinear part of the axial strain. The method of solution used is that of the fixed Lagrange coordinates and the NewtonRaphson procedure. Comparisons of numerical results with those of various other methods indicate that, in terms of the number of elements or degrees of freedom needed for convergence, the method seems significantly more effective than most. Non of the others seen to be more effective. The problems considered included shallow and deep arches, extremely thin arches, and arches of various profiles
