تحليل الاستوديناميك غيرخطي سازه هاي قابي و خرپايي به روش گام به گام باقيمانده وزني زماني

The aim of this research is to analyze the dynamic behavior of two-dimensional frame structures by considering the nonlinear effects of the geometric members using the time weighted residual stepwise method. The nonlinear effects of the geometry can be investigated in two cases of relatively large an‎d large deformations. In the first case, because the deformations are not large, the change in the direction of the force during the loading steps can be ignored, but in the second case, because of the large deformations, the effect of the change in the direction of the force on the member is significant an‎d therefore its effect must be considered in the geometry an‎d loading updat‎e. Considering the nonlinear effects of the geometry makes the system of governing differential equations an‎d force boundary conditions nonlinear an‎d therefore complicates the solution of the problem.In this study, initially, by considering relatively large deformations, the governing differential equations of the problem are extracted an‎d then solved using the time-weighted residual stepwise method. Given that the proposed method is a mesh-free method, without the need for elementing the member an‎d only by considering its two initial an‎d final nodes, the problem solving process will be followed over time. The main idea of the proposed method is to use pre-integration relations along with the time-weighted satisfaction of the equilibrium equations. To solve the equations with the proposed method, initially all nonlinear terms are transferred to the right side of the equality an‎d then the nonlinear parts are linearized based on the direct iteration method an‎d with the help of Taylor expansion. Finally, by using the idea of combining peaks, the linearized parts will be transformed into exponentials.In the following, the efficiency of the method is demonstrated by implementing the developed formulation in solving beam column, frame an‎d truss problems. Considering the above, first the solution of the problem will be presented in the case of small deformations an‎d with the help of two laboratory models of the frame under impact load an‎d moving mass, the accuracy of the proposed method in solving practical problems has been investigated. Then, by developing relations for relatively large deformations, various beam column problems with different boundary conditions an‎d loadings have been analyzed. The analysis results show that the proposed method has the desired accuracy an‎d much less analysis time compared to other numerical methods. In the next step, the solution for frame an‎d truss problems is developed an‎d in the solved examples, the effect of compressive load intensity, lateral excitation frequency, bracing member slenderness an‎d geometric irregularity of the structures on the results of geometric nonlinear analysis has been investigated.Next, by adding the effect of concentrated mass on the truss structure, the effect of this case is also investigated. In the final part of the thesis, the geometric nonlinear problem assuming large deformations will be investigated by the proposed method. Finally, to eva‎luate the proposed method in solving these problems, the efficiency of the method will be demonstrated by solving two examples of a hinged beam an‎d a portal frame.

بشير موحديان عطار , بيژن برومند قهنويه

محمد سيلاني , مهدي زندي آتشبار , سعيد صرامي