الفهرس 
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Abstract
The aim of this study is to compose a corotational finite element formulation for space frames with geometrically nonlinear behavior under static and dynamic loads. Using a moving frame through three successive rotations similar to Euler angles is one of the oldest techniques, however, there are still some gaps that require attention, mainly due to singularity. Hence, alternative techniques had been developed, sometimes elusive and computationally expensive. In this thesis we went back to the old technique and filled the gaps. Three coordinate systems are used, the fixed global coordinate system, the fixed local coordinate system that is attached individually to every element, and the corotational local frame for each element that moves and rotates with the element. Due to the nature of the element corotational frame, the deformational motion is always small relative to this frame. Hence, this formulation can easily separate the rigid body motion from the total deformation. The successive rotations between different coordinate systems are expressed using Tait-Bryan angles. In static analysis, the stiffness matrices obtained using Euler-Bernoulli beam model, and the equilibrium equation is derived using the virtual work principle. An incremental iterative procedure based on the full Newton-Raphson method is employed to solve this equation. A MATLAB code is developed for this purpose. Furthermore, in dynamic analysis, stiffness matrices and mass matrices are determined based on Euler-Bernoulli beam model, and Lagrange’s equation is used to derive the equation of motion. An incremental iterative procedure is used to solve the equation of motion based on the full Newton-Raphson method and the Newmark direct-time integration method. A MATLAB code is developed for this purpose. The developed codes involve a relatively rapid convergence rate due to avoiding storing the joint orientation matrices and parametrizing finite rotations which are usually associated with the parametrized formulations. The transformation procedure is based on the Tait-Bryan angles successive rotations. This procedure is employed in two main stages to transform vectors and matrices from the fixed global frame to the moving corotational frame. The first stage is the transformation from the fixed global frame to the fixed local frame, and the second stage is the transformation from the fixed local frame to the moving corotational local frame. Transformation procedure also depends upon updating the coordinates with every equilibrium configuration during the analysis. In traditional techniques, singularity is attained when any rotation angle in the fixed local frame approaches π/2 and when any is greater than π/2, the techniques could fail to specify the location of the element. In this thesis, each case is treated with a proper procedure, and special handling of trigonometric formulations prevents singularity and correctly specify the location of elements in all situations. Different examples of beams and frames subjected to various static and dynamic loads are analyzed and compared to published results. While the method is not intricate, it is timesaving, highly effective, provides more stable and robust analysis, and gives sufficiently iv accurate results. Compared to the parametrization of finite rotations technique, the method has a significant reduction in the convergence rate because it avoids the storage of joint orientation matrices. This formulation is also extended to include the analysis of electrical transmission towers using a simplified formulation. This simplified formulation is based on using equivalent spatial beam elements. This extension does not include straight towers only, but tapered towers as well. The resistance of the tower’s diagonal members is provided in the analysis. The present results are compared to the results of the detailed model and to results of other simplified formulations of the towers to show the efficiency and flexibility of the proposed method.