چكيده به لاتين
Abstract
In the Finite Element method, the stress components are first included in the elements and then these components are restored to the node. Since the stress components are calculated from the displacement, They have less error and accuracy. There are methods for the recovery process, and in this research, two nodal stress recovery techniques are proposed. The first method is the colliding body optimization algorithm (CBO), which consists of three parts. The input contains the number of variables and limits of the function. The part of the solver, in this stage, the formulas of the algorithm include the coefficient of restitution, the calculation of the amount of mass, the mass before the collision, the mass after the collision, how to repeat the problem, categorize the data through minimization, and other steps that are defined for the algorithm. and is calculated. In the output stage, the variables of the problem, which are polynomial coefficients here, are calculated. A function f is introduced, which uses Khayam-Pascal triangle sentences in the function arrangement, but the coefficients of Khayam-Pascal sentences are not used, but the task of the algorithm is to obtain these coefficients. Enter the coordinates of the desired point and the algorithm calculates and outputs the polynomial coefficients and the value of the function f, which in this research is of the stress type. The second algorithm is particle mass optimization (PSO) which introduces the variables of the problem in the input part and defines the limits of the functions. Algorithm formulas are used in the solver part. The speed and position of the particle and the best position of the particle are determined in this step. The function f its sentences are removed from the Pascal-Khaiyam’s triangle regardless of its coefficients. The task of the algorithm is to calculate the coefficients of the sentences that ‘it gives us in the output of the algorithm. The value of the function f in this research is of stress type.
In the following, Abaqus software and MATLAB coding in the finite element method are used to model a beam with the dimensions introduced in the next sections. We calculate and compare the amount of stress and measure the amount of error and accuracy.
The method of finite elements has a shape function, stiffness matrix, derivative, integral, and complexity. We want to calculate the stress value of finite elements easily and with less cost and time without complexity using the two mentioned algorithms.
The stress value of finite elements and the value of f resulting from the algorithms we compare in this research on the type of stress. Their difference should be the smallest so that the obtained answers are acceptable.
Keywords
Finite Element Method, Error estimation, Metaheuristics, Optimization, Colliding
