Computational Methods in Engineering

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This paper presents a new super-element with twelve degrees of freedom for latticed columns. This elements is developed such that it behaves, with an acceptable approximation, in the same manner as a reference model does. The reference model is constructed by using many Solid elements. The cross section area, moments of inertia, shear coefficient and torsoinal rigidity of the developed new element are derived. Since the reference model has a large number of degrees of freedom (especially for nonlinear cases), computation of the equivalent essential parameters of the proposed element is very time consuming, so, a model using only beam elements is also presented. For the super element, a general purpose program is developed that is capable of performing linear and nonlinear analysis of 3D-frames with latticed columns. In order to derive the essential parameters of the proposed super-element, many latticed columns are analyzed while shear deformations are taken into consideration. Using these essential equivalent parameters approximate relations are proposed for the compution of parameters of any latticed column based on geometric characteristics. Finally, to show the accuracy of the proposed element, several examples are presented. Keywords: Finite elements, Super-element, Latticed column, Shear deformations, 3D-frames

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The stored deformation energy in the dislocation structures in a polycrystalline metal can provide a sufficient  driving force to move grain boundaries during annealing. In this paper, a thermodynamically-consistent three-dimensional, finite-strain and dislocation density-based crystal viscoplasticity constitutive theory has been developed to describe the distribution of stored energy and dislocation density in a polycrystalline metal. The developed constitutive equations have been numerically implemented into the Abaqus finite element package via writing a user material subroutine. The simulations have been performed using both the simple Taylor model and the full micromechanical finite element model. The theory and its numerical implementation are then verified using the available data in literature regarding the physical experiments of the single crystal aluminum. As an application of the developed constitutive model, the relationship between the stored energy and the strain induced grain boundary migration in aluminum polycrystals has been investigated by the Taylor model and also, the full finite element model. The obtained numerical results indicated that the Taylor model could not precisely simulate the distribution of the stored deformation energy within the polycrystalline microstructure; consequently, the strain induced grain boundary migration.  This is due to the fact that the strain induced grain boundary migration in a plastically deformed polycrystalline microstructure is principally dependent on the spatial distribution of the stored deformation energy rather than the overall stored energy value.