آناليز ديناميكي تاريخچه زماني قاب هاي شيب دار با مقطع متغير به روش باقيمانده وزني زماني

Nowadays, due to the importance of economic an‎d environmental issues in the design of structures, it is important to reduce the consumption of materials. The use of tapered members in sloped frames provides this possibility due to the use of the capacity of sections according to the needs of the structure. To optimize the design of frames, providing an efficient an‎d accurate method in the dynamic analysis of structures is effective. In this research, the dynamic behavior of frames with variable cross-section has been investigated. To achieve linear an‎d dynamic analysis, the mathematical model of the problem is usually expressed by a differential equation with partial derivatives. Among these equations, we can refer to scalar an‎d elastic wave equation. The closed solution of partial differential equations rarely exists; Therefore, many researchers have developed numerical methods to obtain approximate answers to the problem. In a part of the current research, the time-weighted residual step-by-step method is used for the dynamic time history analysis of sloped frames with variable cross section. First, this method has been implemented separately on variable cross-section elements under axial an‎d bending waves, considering Bernoulliʹs assumptions. Then by forming the stiffness matrix of the members an‎d forming the total stiffness matrix, all types of problems are solved. After formulating, programming an‎d validating this method for the mentioned differential equation, the obtained results do not have good stability; Therefore, more studies are conducted to provide a new method to solve axial an‎d bending wave propagation problems. The general idea of this method is to use the shape functions of the composite element method to estimate the displacement field with the dynamic stiffness approach. In the composite element method, the shape functions of the classical theory are combined with the shape functions of the finite element method, using Rayleigh-Ritz method, an‎d form the new shape function. This method is included in the category of boundary meshless methods. The new method for the mentioned differential equation is formulated an‎d implemented an‎d validated. The results obtained in the new method have very good accuracy, stability an‎d computational speed. Considering that many numerical methods cannot provide acceptable results on variable cross-sections, this research can take steps towards the optimal design of sloped variable cross-section frames.

بشير موحديان عطار , بيژن برومند قهنويه

مجتبي ازهري , مهدي زندي آتشبار