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This article investigates energy absorption capacity and plastic deformation trend of lateral flattening of an aluminum profile with H-shaped cross section under the quasi-static lateral loading by experimental, numerical and theoretical methods. Samples were prepared with different lengths and three different filling conditions including empty, core-filled and perfectly-filled by polyurethane foam. In addition, samples with the same geometry and filling conditions were laterally compressed with loading angles of 0 and 90 degree. Effect of some parameters such as length, three different filling conditions and loading angle were experimentally investigated on lateral force and specific absorbed energy (SAE). The results show that SAE is independent of samples length. At the loading angle of 90 degree, presence of the filler causes increment of SAE by the structure. Using the perfectly-filled profile under the loading angle of 90 degree is the most optimum condition. Based on two different energy absorption mechanisms, a theoretical equation was derived to estimate total absorbed energy (TAE) by empty sample with loading angle of zero; and predicted results were compared with the experimental samples. Due to present limitations in preparing the samples with different geometrical dimensions, nonlinear ABAQUS software was employed. Some samples with different wall thicknesses were modeled and influence of thickness was investigated on TAE. TAE is directly correlated to the second power of wall thickness; and this relationship can be clearly understood from the theoretical equation and numerical results. High correlation of experimental, numerical and theoretical results indicates precision and accuracy of the performed research.

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The method of fundamental solutions is a boundary-type mesh-free method, which is very suitable for problems with unknown or moving boundaries. In this paper, the method of fundamental solutions is employed for shape optimization in torsion problems. The objective of this work has been to find optimum corners radii of hollow cross-sections under torsion for minimizing the maximum stress. First, it is shown that for the optimum value of the corner radius, the maximum shearing stress on the outer boundary should be equal to the shearing stress at internal corner. Considering this fact, a suitable objective function is defined and then it is minimized using the Levenberg-Marquardt method, which is a gradient-based optimization method. The configuration of collocation and source points has a very important effect on the accuracy of the solution in the method of fundamental solutions. Here, a two-constraint method is used for proper configuration of source and collocation points. To verify the accuracy of the developed code for torsion analysis of hollow members using the method of fundamental solutions, an example with a hollow elliptical domain is presented. The obtained numerical results are compared with the results of exact solution, which show a very good agreement. The optimum values of corners radii for members with square, rectangle and trapezoid cross-sections and different thicknesses have been successfully found. Then, using the obtained results, a formula for the optimum value of the radius of internal corners of hollow rectangle cross sections is constructed.

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