This study presents a geometrically exact formulation for curved beams, accounting for large displacements, finite rotations, and finite strains. To this aim, the position-based finite element approach developed by [1] is extended to add rotational degrees of freedom into the unknown vector. Specifically, a two-node curved Kirchhoff rod finite element is formulated adopting an interpolation scheme based on Hermite polynomials, as first suggested by [2]. Our finite element exhibits the same advantages of the latter in terms of accuracy and frame invariance, while avoiding the problem of membrane locking. Further, the adopted positional formulation allows us to obtain simpler analytical expressions for all the quantities of interest (strain, curvature, stiffness matrices, etc.). Geometrical nonlinearities are considered by using the Green-Lagrange measure of axial strain and the change in geometric curvature between the refer- ence and current configurations, thus allowing any hyper-elastic constitutive law implementation. The governing nonlinear equilibrium equations are obtained through the principle of stationary total potential energy and numerically solved using incremental-iterative procedures based on Newton-Raphson and arc-length methods. The optimization of the structural parameters is performed by applying quasiconvex optimization algorithms [3], first one by one and then jointly with the finite element method. A few design optimized results corroborate the proposed joint approach. [1] Valvo PS, “Symmetric stiffness matrices for isoparametric finite elements in nonlinear elasticity”, Comput Mech (2025) 75: 919-943. [2] Armero F, “A new Hermite finite element for nonlinear Kirchhoff rods: The plane case”, Int J Numer Methods Eng (2024) 125: e7448. [3] Boyd S, Vandenberghe L, “Convex Optimization”, Cambridge University Press (2004).