An efficient method for nonlinear dynamic analysis of 3D space structures /Hamidreza Hashamdar - Hamidreza, Hashamdar (2012)
The aim of this thesis is to develop an efficient method for the nonlinear analysis of space structures with high degree of freedom such as cable structures. Space structures can provide large uninterrupted covered areas such as sport centres, aircraft hangars, tensile cables, etc. The proposed theory for nonlinear analysis of 3D space structure is based on the minimization of the total potential dynamic work. The minimization of the total potential dynamic work is an indirect method which is based on the principle of the convergence of energy in structures. Conventional methods such as superposition methods are direct methods. The dynamic response analysis of a nonlinear system is based on the evaluation of response for a series of short time intervals using different types of time integration techniques. In dynamic problems, the differential equations arising from the equilibrium of the dynamic forces acting on the mass is solved by implicit or explicit methods. In order to verify the proposed theory, static and dynamic testing of the model is performed. The degree of error by elastic deformation of the frame and degree of symmetry of the model during the static test shows that the boundary condition of the frame is rigid and the frame is symmetric. The results of the dynamic test show that the theoretical and experimental values of the natural frequencies, mode shapes, and modal damping ratios are in good agreement. The dynamic responses calculated due to the exciting structure with various load intensities from different points are also in agreement with the finite element modelling. The influence of the magnitude of the damping ratios in different modes while using an orthogonal damping matrix is negligible. Finally, in comparison to conventional methods, the computational time taken by the proposed method is acceptable.In general, the reduction in time and cost as well as the highly accurate results obtained justify the use of indirect methods such as the optimization theory. The developed method is found to be a suitable technique for the minimization of the total potential energy function, especially in cases where the number of variables is large and the structure is highly nonlinear. The proposed method decreases computational time and the number of iterations required per time step.