Showing 29 results for Finite Element
B. Sadeghian, M. Ataapour, A. Taherizadeh,
Volume 36, Issue 2 (3-2018)
Abstract
Friction stir welding is of the most applicable methods to join dissimilar metals. In this study, the thermal distribution during the joining of 304 stainless steel and 5083 aluminum alloy by friction stir welding method was simulated by the finite element method. Both, transient and stationary thermal solutions were used in the simulations and the two methods were compared correspondingly. To verify the model, two sheets of stainless steel and aluminum were prepared and the friction stir welding was applied. Additionally, by using thermocouples temperature, the history of points on the sheets was obtained during welding. Then, the simulation and the experimental results were compared to validate the model. Finally, an artificial neural network model was created and the effect of different input parameters on the maximum temperature under the tool was investigated.
Aliakbar Taghipour, J. Parvizian, S. Heinze, A. Duester, E. Rank,
Volume 37, Issue 1 (9-2018)
Abstract
finite cell method, are employed to compute a series of benchmark problems in the finite strain von Mises or J2 theory of plasticity. The hierarchical (integrated Legendre) shape functions are used for the finite element approximation of incompressible plastic dominated deformations occurring in the finite strain plasticity of ductile metals. The computational examples include the necking under uniaxial tension with notched and un-notched samples and the compression of a perforated plate. These computations demonstrate that the high-order finite element methods can provide a locking-free behavior with a pure displacement-based formulation. They also provide high convergence rates and robustness against high mesh distortions. In addition, it is shown that the finite cell method, on the top of the aforementioned advantages, provides easy mesh generation capabilities for highly complex geometries. The computational results are verified in comparison with the results obtained using a standard low-order finite element method known as the F-bar method. The numerical investigations reveal that both methods are good candidates for the plasticity analysis of engineering materials and structures made up of ductile materials, particularly those involving complex geometries.
F. Shirmohammadi, M. M. Saadatpour,
Volume 37, Issue 1 (9-2018)
Abstract
In this article spectral modal method is developed for studying wave propagation in thin plates with constant or variable thickness. Theses plates are subjected to the impact forces and different boundary conditions. Spectral modal method can be considered as the combination of Dynamic Stiffness Method (DSM), Fourier Analysis Method (FAM) and Finite Stripe Method (FSM). Using modeling of continuous distribution of mass and an exact stiffness causes solutions in frequency domain. Unlike the most numerical methods, in this method refining meshes is no longer necessary in which the cost and computational time is decreased. In this paper the important parameters of the method and their effects on results are studied through different examples.
M. Jafari, M. Jamshidian, S. Ziaei-Rad,
Volume 37, Issue 2 (3-2019)
Abstract
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.
H. Arzani, E. Khoshbavar Rad,
Volume 37, Issue 2 (3-2019)
Abstract
In this paper, a method is proposed to improve the results of the standard finite element method. L2 norm is used to determine the nodal error. In the next step, the appropriate order of the interpolation cover is seclected to be proportional to the nodal error and the results are corrected. The error computation procedure and the use of covering enrichment functions will continue until the error reaches the specified value. Cover enrichment interpolation functions will consider the effects of the adjacent elements of each node, in addition to the values obtained from the standard interpolation for each element. Computation rules are programmed in the matlab program and considered for the same examples. Comparison of the results of the proposed method with the exact solutions and the results of the methods proposed by the other researchers in the field of linear elasticity indicates the efficiency and accuracy of the proposed method.
I. Ahmadi, D. Kouhbor, R. Taghiloo,
Volume 38, Issue 1 (8-2019)
Abstract
In this paper, a finite element model is presented for the transient analysis of low velocity impact, and the impact induced damage in the composite plate subjected to low velocity impact is studied. The failure criteria suggested by Choi and Chang and the Tsai-Hill failure criteria are used for the prediction of the damage in the composite plate; then the effect of various parameters on the impact induced damage is investigated. The first order shear deformation plate theory and the Ritz finite element method are employed for modeling the behavior of plate, and the modified Hertz contact low is used for the prediction of the contact force through the impact. In the numerical results, the time history of indentation, contact force and stress during the impact and the impact induced damage is investigated. The matrix cracking and delamination in the plies of the laminated composite plate subjected to low velocity impact are studied and the effects of various parameters are investigated.
S. A. Ghazi Mirsaeed, V. Kalatjari,
Volume 38, Issue 1 (8-2019)
Abstract
In this paper, finite element analysis of thin viscoelastic plates is performed by proposing new plate elements using complex Fourier shape functions. New discrete Kirchhoff Fourier Theory (DKFT) plate elements are constructed by the enrichment of quadratic function fields in a six-noded triangular plate element with complex Fourier radial basis functions. In order to illustrate the validity and accuracy of the presented approach and robustness of the proposed elements in viscoelasticity, finite element analysis of square and elliptical viscoelastic thin plates is performed and the results are compared to those of analytical solutions and with those obtained by discrete Kirchhoff Theory (DKT) elements and the commercial software ABAQUS. The results show that FE solutions using DKFT elements have an excellent agreement with the analytical solutions and ABAQUS solutions, even though noticeably fewer elements, in comparison to DKT and classic plate elements, are employed, which means that the computational costs are reduced effectively.
M. Jamei, H. R. Ghafouri,
Volume 38, Issue 2 (2-2020)
Abstract
In this study, we present a numerical solution for the two-phase incompressible flow in the porous media under isothermal condition using a hybrid of the linear lower-order nonconforming finite element and the interior penalty discontinuous Galerkin (DG) method. This hybridization is developed for the first time in the two-phase modeling and considered as the main novelty of this research.The pressure equation and convection dominant saturation equation are discretized using the nonconforming Crouziex-Raviart finite element (CR FEM) and the weighed interior penalty discontinuous Galerkin (SWIP) method, respectively. Utilizing the nonconforming finite element method for solving the flow equation made the pressure and velocity values be consistent with respect to the degrees of freedom arrangement at the midpoint of the neighboring element edges. The boundary condition governing the simulation is the Robin type at entrance boundaries, and the time marching discretization for the governing equations is the sequential solution scheme. An H (div) projection using Raviart-Thomas element is implemented to improve the results’ resolution and preserve the continuity of the normal component of the velocity field. At the end of each time step, the non-physical oscillation is omitted using a slope limiter, namely, modified Chavent-Jaffre limiter, in each element. Also, in this study, the developed algorithm is verified using some benchmark problems and the test cases are considered to demonstrate the efficiency of the developed model in capturing the shock front at the interface of fluid phases and discontinuities.
O. Bateniparvar, N. Noormohammadi, A. M. Salehi,
Volume 39, Issue 2 (2-2021)
Abstract
In this paper, Equilibrated Singular Basis Functions (EqSBFs) are implemented in the framework of the Finite Element Method (FEM), which can approximately satisfy the harmonic PDE in homogeneous and heterogeneous media. EqSBFs are able to automatically reproduce the terms consistent with the singularity order in the vicinity of the singular point. The newly made bases are used as the complimentary enriching part along with the polynomial bases of the FEM to construct a new set of shape functions in the elements adjacent to the singular point. It will be shown that the use of the combined bases leads to the quality improvement of the solution function as well as its derivatives, especially in the vicinity of the singularity.
