In this thesis, a finite element based perturbation approach is presented for geometrically nonlinear analysis of thin-walled structures. Geometrically nonlinear static and dynamic analyses are essential for this class of structures. Nowadays nonlinear analysis of thin-walled shell structures is often done using finite element based incremental-iterative procedures. However standard finite element based nonlinear analysis of many practical structures is still computationally expensive and not suitable for repeated runs necessary for a design and optimization process, and also the interpretation of the results can be difficult. Koiter introduced a perturbation approach where a perturbation expansion for the load and the displacement field are made around a known state (e.g. a bifurcation buckling point) to capture the essential nonlinear behavior of the structure. The final outcome is a computationally inexpensive reduced order model providing a good insight into the structural behavior in terms of the postbuckling a and b coefficients and the first order (the buckling modes) and the second order modes. Therefore, application of Koiter’s perturbation approach within a finite element framework can support standard nonlinear analysis by providing an effective solution to the aforementioned problems. The main focus of the present research is on the extensions which are necessary for this application The aim of the present research is to show the feasibility of implementing the perturbation approach in a general purpose finite element code in order to handle practical shell structures. In accordance with this perspective, the implementation of the present work is done in the development environment of a general purpose finite element code (DIANA) so that practical problems can be addressed. A general framework for the finite element implementation of Koiter’s perturbation approach is already available in DIANA. The present implementation makes use of that framework and does the necessary extensions. Two key aspects in this research are the inclusion of the effect of prebuckling nonlinearity and consideration of composite shells. Inclusion of the effect of prebuckling nonlinearity makes it possible to handle an important class of problems consisting of axially loaded cylindrical and conical shells where the prebuckling nonlinearity has a large influence on the buckling and postbuckling behavior. The implementation of the perturbation approach is done for a class of Mindlin type curved beam and shell elements and a Kirchhoff type triangular flat shell element. The present thesis contains a part on static problems and a part on dynamic problems. In the part on static initial post-buckling problems, first the perturbation method is explained within the single mode context (considering one buckling mode), including prebuckling nonlinearity and its finite element implementation. The special case of a linear prebuckling state is also discussed. Various reference problems consisting of both isotropic and composite shells are considered. The postbuckling coefficients are compared with available results in literature and semi-analytical results. In all cases a reasonable agreement in the buckling and second order modes and the postbuckling coefficients is obtained. In case of the benchmark conical shell problem (representative of the 1/2 interstage of the Vega launcher) initial postbuckling response (based on single mode analysis) obtained using the present approach compares reasonably well with the full model analysis. A comparison of computational time with full model analysis shows the significant gain achieved in computational cost with the present approach. The locking problem in the determination of postbuckling b coefficient is an important issue in the implementation of the perturbation approach in a finite element context. It is found that the Mindlin type shell and beam elements that are used in this research (where both in-plane/axial and out-of-plane/lateral displacements are interpolated independently) do not show the locking problem with respect to convergence of the b coefficient. Next, in order to study modal interaction effects, the necessary extensions needed for multi mode analysis (in which more than one buckling mode is considered) are discussed. Considering a large number of modes in the perturbation analysis is computationally expensive. Therefore, a guideline is proposed for the selection of appropriate modes based on the minimum direction (the direction that leads to the steepest descent or the smallest ascent of the total potential energy in the buckling space) and uncoupled postbuckling coefficients (postbuckling coefficients associated with a single specific mode) and demonstrated using appropriate examples. Also, industrial benchmark problems consisting of a curved and a flat stiffened CFRP panel are considered. A reasonable agreement in the results is obtained in both cases. The efficiency of the reduced order model is also demonstrated by comparing the computational time with full model analysis. Finally, as a specific application, axially loaded, variable stiffness composite panels are considered and the potential of the perturbation approach in the optimization process for the improvement of postbuckling performance of such panels is demonstrated. The expressions for in-plane postbuckling stiffness for plates under axial compression is derived both for the single mode and the multi mode case. In a specific multi mode case where clustering of buckling modes appears, the minimum direction or the worst direction (in the buckling space) of the structure are determined for the initial postbuckling regime and the resulting postbuckling stiffness is computed. It is found that the panels considered having two nearly coincident buckling modes show the lowest postbuckling stiffness if they buckle in a shape with two half waves. This can be explained in terms of the second order stress distribution over the panel. It is an instance showing the type of insight one can gain about the structural behavior using the perturbation approach. It is also found that a compromise between buckling load and prebuckling stiffness may yield a better performance with respect to ultimate load (the failure load, in this case assumed to correspond with the onset of material degradation) and limit load (the maximum load that the structure can encounter during its operating life) compared to only buckling dominated design. Up to limit load level good agreement is obtained between the full model and the reduced order model analysis. In the part of the thesis about dynamic problems, the perturbation approach developed earlier for static postbuckling problems is extended for handling dynamic problems by taking inertial terms into account. Dynamic buckling and nonlinear free vibration problems are considered. A reasonable agreement in the prediction of the dynamic buckling load is achieved when compared with full model transient analysis. The gain in computational cost is shown for a representative case. In case of the nonlinear vibration problems, second order vibration modes, the dynamic b coefficients and the resulting backbone curves compare reasonably well with reference results.