جستجوی مقالات مرتبط با کلیدواژه "spline" در نشریات گروه "مکانیک"

The present study investigates the optimal design of the die shape in the metal forming process using extrusion. Due to the large deformations that occur during the forming process and the resulting entry into the plastic deformation zone, the finite element method is used to analyze the problem in this area, and the modeling is performed in the Eulerian system. The objective function of this study is to minimize the total energy required for deformation in the extrusion process. The design variable is the die shape, and spline curves with multiple control points are used to generate the die shape. Due to the nonlinear nature of the forming problem, the complexity, and the large amount of computation required during the analysis, a powerful combination of two metaheuristic optimization methods, the Imperialist Competitive Algorithm and Ant Colony Algorithm (ICACO), has been inspired for the optimal design of the die shape. To validate the obtained results for the die geometry, they are compared with the results presented in previous studies, The error was less than 2%, showing a good agreement. The results obtained have led to a significant reduction in the total energy consumption during deformation by approximately 12% compared to the conventional linear mode.

In this paper, the numerical distribution of residual stresses in the girth weld were determined in two (hoop an axial) direction. Two API X70 steel pipes of 56 inch outside diameter were girth welded first. Hole drilling strain gage test were conducted for strain measurement on the external surface of the pipes. The values of residual stresses were determined then from strain data using ASTM 837 standard. The values of residual stresses were determined. Next, distribution of residual stresses were assessed using spline and approximating polynomials. The well-behaved spline and polynomials, confirm the accuracy of residual stress results from experiment. The result showed lower-order polynomials have more suitable behavior in residual stress distribution. Noting to impossibility of using semi-destructive hole drilling strain gage test in project’s real situations, we can make use of these curves in assessing and estimating residual stresses distribution of similar welding. The most stable polynomial estimation curves for evaluating hoop and axial residual stress distribution are respectively third and second order. The closeness and uniformity of axial residual stress distribution curve compared to the hoop residual stress distribution curve is representative of more balanced behavior of these stresses distribution.

Grid dispersion is one of the criteria of validating the finite element method (FEM) in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA) is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS) functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.

Shape optimization of free form shell structures with different objective and constraint functions including the stress constraint is the subject of this article. To construct the geometry B-Splines are employed that allow generating smooth free form geometries with a small number of parameters which are considered as the design variables of the optimization problem. For analysis, the finite element method by using the Wilson’s quad shell element is employed. For shape optimization, in each step of the optimization process the mesh generation, finite element analysis, sensitivity analysis and geometry update steps are repeated until convergence. Maximization of the stiffness of structure with volume constraint and the minimization of the weight of structure with the von Misses stress constraint are the addressed problems of this article. In both kinds of problems, the applicates of the control points are considered as the design variables of the shape optimization problem and the sequential quadratic programming (SQP) is employed to solve the optimization problem. Since in this approach, the derivatives of the objective and constraint functions are needed, the sensitivity analysis is carried out in each step by the finite difference method. The quality and smoothness of the obtained results together with the convergence graphs of the presented examples are indicative of the usefulness and efficiency of the proposed approach for shape optimization of shell structures.