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Showing 12 results for Finite Element Method

S. M. Tavakkoli, B. Hassani , H. Ghasemnejad ,
Volume 3, Issue 2 (6-2013)

The Isogeometric Analysis (IA) method is applied for structural topology optimization instead of the finite element method. For this purpose, the material density is considered as a continuous function throughout the design domain and approximated by the Non-Uniform Rational B-Spline (NURBS) basis functions. The coordinates of control points which are also used for constructing the density function, are considered as design variables of the optimization problem. In order to change the design variables towards optimum, the Method of Moving Asymptotes (MMA) is used. To alleviate the formation of layouts with porous media, the density function is penalized during the optimization process. A few examples are presented to demonstrate the performance of the method.
P. A. A. Magalhaes Junior, I. G. Rios, T. S. Ferreira, A. C. de Andrade Junior, O. A. de Carvalho Filho, C. A. Magalhaes,
Volume 4, Issue 3 (9-2014)

This article aims to study the self-supporting truss towers used to support large wind turbines. The goal is to evaluate and validate numerically by finite element method the structural analysis when the lattice structures of the towers of wind turbines are subjected to static loads and these from common usage. With this, it is expected to minimize the cost of transportation and installation of the tower and maximize the generation of electricity, considering technical standards and restrictions of structural integrity and safety, making vibration analysis and the required static and dynamic loads, thereby preventing failures by fractures or mechanical fatigue. Practical examples of towers will be designed by the system and will be tested in structural simulation programs using the Finite Element Method. This analysis is performed on the entire region coupling action of the turbine, with variable sensitivity to vibration levels. The results obtained for freestanding lattice tower are compared with the information of a tubular one designed to support the generator with the same characteristics. At the end of this work it was possible to observe the feasibility of using lattice towers that proved better as its structural performance but with caveats about its dynamic performance since the appearance of several other modes natural frequency thus reducing the intervals between them in low frequency and theoretically increase the risk of resonance.
H. Fathnejat, P. Torkzadeh, E. Salajegheh, R. Ghiasi,
Volume 4, Issue 4 (11-2014)

Vibration based techniques of structural damage detection using model updating method, are computationally expensive for large-scale structures. In this study, after locating precisely the eventual damage of a structure using modal strain energy based index (MSEBI), To efficiently reduce the computational cost of model updating during the optimization process of damage severity detection, the MSEBI of structural elements is evaluated using properly trained cascade feed-forward neural network (CFNN). In order to achieve an appropriate artificial neural network (ANN) model for MSEBI evaluation, a set of feed-forward artificial neural networks which are more suitable for non-linear approximation, are trained. All of these neural networks are tested and the results demonstrate that the CFNN model with log-sigmoid hidden layer transfer function is the most suitable ANN model among these selected ANNs. Moreover, to increase damage severity detection accuracy, the optimization process of damage severity detection is carried out by particle swarm optimization (PSO) whose cost function is constructed based on MSEBI. To validate the proposed solution method, two structural examples with different number of members are presented. The results indicate that after determining the damage location, the proposed solution method for damage severity detection leads to significant reduction of computational time compared to finite element method. Furthermore, engaging PSO algorithm by efficient approximation mechanism of finite element (FE) model, maintains the acceptable accuracy of damage severity detection.
S. Shojaee, A. Mohaghegh, A. Haeri,
Volume 5, Issue 4 (7-2015)

In this paper the piecewise level set method is combined with phase field method to solve the shape and topology optimization problem. First, the optimization problem is formed based on piecewise constant level set method then is updated using the energy term of phase field equations. The resulting diffusion equation which updates the level set function and optimization problem is solved through finite element method. The proposed method enhances the convergence rate and solution efficiency. Various two-dimensional examples are solved to verify the performance of proposed method.
M. Roodsarabi, M. Khatibinia , S. R. Sarafrazi,
Volume 6, Issue 3 (9-2016)

This study focuses on the topology optimization of structures using a hybrid of level set method (LSM) incorporating sensitivity analysis and isogeometric analysis (IGA). First, the topology optimization problem is formulated using the LSM based on the shape gradient. The shape gradient easily handles boundary propagation with topological changes. In the LSM, the topological gradient method as sensitivity analysis is also utilized to precisely design new holes in the interior domain. The hybrid of these gradients can yield an efficient algorithm which has more flexibility in changing topology of structure and escape from local optimal in the optimization process. Finally, instead of the conventional finite element method (FEM) a Non–Uniform Rational B–Splines (NURBS)–based IGA is applied to describe the field variables as the geometry of the domain. In IGA approach, control points play the same role with nodes in FEM, and B–Spline functions are utilized as shape functions of FEM for analysis of structure. To demonstrate the performance of the proposed method, three benchmark examples widely used in topology optimization are presented. Numerical results show that the proposed method outperform other LSMs.

M. Rezaiee-Pajand, H. Afsharimoghadam,
Volume 7, Issue 1 (1-2017)

In this paper, the effect of angle between predictor and corrector surfaces on the structural analysis is investigated. Two objective functions are formulated based on this angle and also the load factor. Optimizing these functions, and using the structural equilibrium path’s geometry, lead to two new constraints for the nonlinear solver. Besides, one more formula is achieved, which was previously found by other researchers, via a different mathematical process. Several benchmark structures, which have geometric nonlinear behavior, are analyzed with the proposed methods. The finite element method is utilized to analyze these problems. The abilities of suggested schemes are evaluated in tracing the complex equilibrium paths. Moreover, comparison study for the required number of increments and iterations is performed. Results reflect the robustness of the authors’ formulations.

P. Hamidi, T. Akhlaghi, M. Hajialilou Bonab,
Volume 7, Issue 2 (3-2017)

Calculation of lateral earth pressure on retaining walls is one of the main issues in geotechnics. The upper and lower bound theorems of plasticity are used to analyze the stability of geotechnical structures include bearing capacity of foundations, lateral earth pressure on retaining walls and factor of safety of slopes. In this paper formulation of finite element limit analysis is introduced to determine plastic limit load in the perfect plastic materials. Elements with linear strain rates, which are used in the formulation, cause to eliminate the necessity of velocity discontinuities between the elements. Using non-linear programming based on second order cone programming (SOCP), which has good conformity with cone yield functions such as Mohr-Coulomb and Drucker-Prager, is another important advantage that remove the problem of using ordinary linear programming algorithms for yield functions such as divergent in the apexes. Finally, the optimization problem will be solved by mathematical method. The proposed method is used for calculating active earth pressure on retaining walls in cohesive-frictional soils. According to results of analysis, active earth force on retaining wall is decreased by increasing soil cohesion, wall inclination friction angle between backfill and wall and friction angle of soil wherein the force is increased by increasing surcharge on the backfill and the backfill slope. Mathematical method is used for obtaining accurate results in this research, however, heuristic methods are used when approximate solutions are sufficient.

M. Rezaiee-Pajand, R. Naserian,
Volume 7, Issue 2 (3-2017)

By minimizing the total potential energy function and deploying the virtual work principle, a higher-order stiffness matrix is achieved. This new tangent stiffness matrix is used to solve the frame with geometric nonlinear behavior. Since authors’ formulation takes into account the higher-order terms of the strain vector, the convergence speed of the solution process will increase. In fact, both linear and nonlinear parts of the frame axial strains are included in the presented formulation. These higher-order terms affect the resulting unbalanced force and also frame tangent stiffness. Moreover, the finite element method, updated Lagrangian description, and arc length scheme are employed in this study. To check the efficiency of the proposed strategy, several numerical examples are solved. The findings indicate that the authors’ technique can accurately trace the structural equilibrium paths having the limit points.

M. Khatibinia, M. Roodsarabi, M. Barati,
Volume 8, Issue 2 (8-2018)

This paper presents the topology optimization of plane structures using a binary level set (BLS) approach and isogeometric analysis (IGA). In the standard level set method, the domain boundary is descripted as an isocountour of a scalar function of a higher dimensionality. The evolution of this boundary is governed by Hamilton–Jacobi equation. In the BLS method, the interfaces of subdomains are implicitly represented by the discontinuities of BLS functions taking two values 1 or −1. The subdomains interfaces are represented by discontinuities of these functions. Using a two–phase approximation and the BLS approach the original structural optimization problem is reformulated as an equivalent constrained optimization problem in terms of this level set function. For solving drawbacks of the conventional finite element method (FEM), IGA based on a Non–Uniform Rational B–Splines (NURBS) is adopted to describe the field variables as the geometry of the domain. For this purpose, the B–Spline functions are utilized as the shape functions of FEM for analysis of structure and the control points are considered the same role with nodes in FEM. Three benchmark examples are presented to investigate the performance the topology optimization based on the proposed method. Numerical results demonstrate that the BLS method with IGA can be utilized in this field.
H. Mazaheri, H. Rahami, A. Kheyroddin,
Volume 8, Issue 3 (10-2018)

Structural damage detection is a field that has attracted a great interest in the scientific community in recent years. Most of these studies use dynamic analysis data of the beams as a diagnostic tool for damage. In this paper, a massless rotational spring was used to represent the cracked sections of beams and the natural frequencies and mode shape were obtained. For calculation of rotational spring stiffness equivalent of uncracked and cracked sections, finite element models and experimental test were used. The damage identification problem was addressed with two optimization techniques of different philosophers: ECBO, PSO and SQP methods. The objective functions used in the optimization process are based on the dynamic analysis data such as natural frequencies and mode shapes. This data was obtained by developing a software that performs the dynamic analysis of structures using the Finite Element Method (FEM). Comparison between the detected cracks using optimization method and real beam shows an acceptable agreement.
A. Kaveh, M.r. Seddighian, E. Ghanadpour,
Volume 9, Issue 3 (6-2019)

Despite widespread application of grillage structures in many engineering fields such as civil, architecture, mechanics, their analysis and design make them more complex than other type of skeletal structures. This intricacy becomes more laborious when the corresponding
analysis and design are based on plastic concepts.
In this paper, Finite Element Method is utilized to find the lower and the upper bounds solutions of rectangular planner grids and this method is compared with analogues Finite Difference Method to indicate the efficiency of proposed approach.

R. Kamgar, Y. Askari Dolatabad, M. R. Babadaei Samani,
Volume 9, Issue 4 (9-2019)

Nowadays, steel shear walls are used as efficient lateral-load-resistant systems due to their high lateral stiffness and carrying capacity. In this paper, the effect of substituting a shape memory alloy (SMA) material is investigated instead of using conventional steel in the shear wall. A numerical study is conducted using finite element method (FEM) by OpenSees software. For this purpose, at first, to verify the numerical simulation, the results of the experimental data are compared with those obtained from the numerical phase. Finally, the behavior of a one-bay three-story steel frame equipped with shear walls made of conventional steel, shape memory alloy and a combination of these two materials are studied when the structure is subjected to cyclic and seismic loadings. Results indicate that the use of shape memory alloy increases the maximum deformation, the yield displacement, and also the loading capacity of the structure. Also, it decreases the residual deformation of the structure and its initial stiffness. In general, using composite materials of conventional steel and shape memory alloy can reduce the maximum value of compression axial load of the column and, as a result, increase maximum rotation at the connections. In addition, the minimum and maximum values of base shear occurred in the model with 50% and 25% of Ni-Ti SMA material, respectively.

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