مهندسی عمران شریف (Feb 2020)
MODIFIED APPLICATION OF MODIFIED ELEMENTAL ELEMENTS, BASED ON THE CONCEPT OF ENERGY, FOR ANALYZING STRUCTURES, IN THE RANGE OF SMALL DEFORMATIONS
Abstract
In this paper, applied element method for linear analysis of structures based on energy concept in the range of small deformations has been developed and introduced as modified applied element method. This method considers the structure as a set of rigid elements and connecting springs. Both elements of the structure are connected by a single spring with normal, shear and rotary stiffness. Springs stiffness can be calculate according to the properties of the materials. Considering principle of minimum total potential energy for the structure, deformation in the structure can be calculated. This method estimates the linear behavior of the structure with a very good accuracy and low analytical time in the range of small deformations. In this paper, first, the formulation of the modified applied elements method for the analysis of the behavior of linear structures in the small range of deformation is expressed, then, compare the accuracy and speed of this method with applied element method and theoretical values. The results show that in analyzing a cantilever beam with the proposed method, even with a model that includes the minimum number of elements, the error rate is less than 2 percent. This comparison was also used to analyze a one-story frame with simple supports, in this case the rate of error was less than 0.15 percent. However, solving this two problems by applied element method with the same dimensions of element, has more than 31\% and 32\% of the error rate in case of cantilever beam and one-span frame respectively. The calculation time of the proposed method is less than 40\% of the calculation time in the applied element method with 10 series of connection springs. Also, in this method, the value of the frame ductility was estimated with an error of about 3\%, while the corresponding error value in the applied element method was as much as 41\% in the same element size.
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