Search results for: finite volume algorithm

Authors: A. Gherbi, L. Dahmani, A. Boudjemia

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This paper presents the Finite Element Method (FEM) for analyzing the failure pattern of rectangular slab with various edge conditions. Non-Linear static analysis is carried out using ANSYS 15 Software. Using SOLID65 solid elements, the compressive crushing of concrete is facilitated using plasticity algorithm, while the concrete cracking in tension zone is accommodated by the nonlinear material model. Smeared reinforcement is used and introduced as a percentage of steel embedded in concrete slab. The behavior of the analyzed concrete slab has been observed in terms of the crack pattern and displacement for various loading and boundary conditions. The finite element results are also compared with the experimental data. One of the other objectives of the present study is to show how similar the crack path found by ANSYS program to those observed for the yield line analysis. The smeared reinforcement method is found to be more practical especially for the layered elements like concrete slabs. The value of this method is that it does not require explicit modeling of the rebar, and thus a much coarser mesh can be defined.

Keywords: ANSYS, cracking pattern, displacements, reinforced concrete slab, smeared reinforcements

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Authors: S. Etaig, R. Hasan, N. Perera

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This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.

Keywords: computational fluid dynamics, natural convection, nanofluid and thermal conductivity

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Authors: Jamal Laaouine, Mohammed Elhassani Charkani

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Let p be a prime and let b be an integer. MDS b-symbol codes are a direct generalization of MDS codes. The γ-constacyclic codes of length pˢ over the finite commutative chain ring Fₚm [u]/ < u² > had been classified into four distinct types, where is a nonzero element of the field Fₚm. Let C₃ be a code of Type 3. In this paper, we obtain the b-symbol distance db(C₃) of the code C₃. Using this result, necessary and sufficient conditions under which C₃ is an MDS b-symbol code are given.

Keywords: constacyclic code, repeated-root code, maximum distance separable, MDS codes, b-symbol distance, finite chain rings

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Authors: Mojtaba Aghamiri Esfahani, Mohammad Karkon, Seyed Majid Hosseini Nezhad, Reza Hosseini-Ara

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In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.

Keywords: stochastic finite elements, plate bending, free vibration, Monte Carlo, Neumann expansion method.

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Authors: Hae-Yeoun Lee

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Quantification of cardiac function is performed by calculating blood volume and ejection fraction in routine clinical practice. However, these works have been performed by manual contouring,which requires computational costs and varies on the observer. In this paper, an automatic left ventricle segmentation algorithm on cardiac magnetic resonance images (MRI) is presented. Using knowledge on cardiac MRI, a K-mean clustering technique is applied to segment blood region on a coil-sensitivity corrected image. Then, a graph searching technique is used to correct segmentation errors from coil distortion and noises. Finally, blood volume and ejection fraction are calculated. Using cardiac MRI from 15 subjects, the presented algorithm is tested and compared with manual contouring by experts to show outstanding performance.

Keywords: cardiac MRI, graph searching, left ventricle segmentation, K-means clustering

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Authors: V. Tabrizi, A. Vali, R. GHasemi, V. Behnamgol

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In this article, a nonlinear model of an under actuated six degrees of freedom (6 DOF) quadrotor UAV is derived on the basis of the Newton-Euler formula. The derivation comprises determining equations of the motion of the quadrotor in three dimensions and approximating the actuation forces through the modeling of aerodynamic coefficients and electric motor dynamics. The robust nonlinear control strategy includes a smooth second order non-singular terminal sliding mode control which is applied to stabilizing this model. The control method is on the basis of super twisting algorithm for removing the chattering and producing smooth control signal. Also, nonsingular terminal sliding mode idea is used for introducing a nonlinear sliding variable that guarantees the finite time convergence in sliding phase. Simulation results show that the proposed algorithm is robust against uncertainty or disturbance and guarantees a fast and precise control signal.

Keywords: quadrotor UAV, nonsingular terminal sliding mode, second order sliding mode t, electronics, control, signal processing

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Authors: Meng-Hui Chen, Chiao-Wei Yu, Pei-Chann Chang

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Imperial competitive algorithm (ICA) simulates a multi-agent algorithm. Each agent is like a kingdom has its country, and the strongest country in each agent is called imperialist, others are colony. Countries are competitive with imperialist which in the same kingdom by evolving. So this country will move in the search space to find better solutions with higher fitness to be a new imperialist. The main idea in this paper is using the peculiarity of ICA to explore the search space to solve the kinds of combinational problems. Otherwise, we also study to use the greed search to increase the local search ability. To verify the proposed algorithm in this paper, the experimental results of traveling salesman problem (TSP) is according to the traveling salesman problem library (TSPLIB). The results show that the proposed algorithm has higher performance than the other known methods.

Keywords: traveling salesman problem, artificial chromosomes, greedy search, imperial competitive algorithm

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Authors: Mehrdad Shahrbanozadeh, Gholam Abbas Barani, Saeed Shojaee

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In this study, a finite element (Seep3D model) and an artificial neural network (ANN) model were developed to simulate flow through dam foundation. Seep3D model is capable of simulating three-dimensional flow through a heterogeneous and anisotropic, saturated and unsaturated porous media. Flow through the Shahid Abbaspour dam foundation has been used as a case study. The FEM with 24960 triangular elements and 28707 nodes applied to model flow through foundation of this dam. The FEM being made denser in the neighborhood of the curtain screen. The ANN model developed for Shahid Abbaspour dam is a feedforward four layer network employing the sigmoid function as an activator and the back-propagation algorithm for the network learning. The water level elevations of the upstream and downstream of the dam have been used as input variables and the piezometric heads as the target outputs in the ANN model. The two models are calibrated and verified using the Shahid Abbaspour’s dam piezometric data. Results of the models were compared with those measured by the piezometers which are in good agreement. The model results also revealed that the ANN model performed as good as and in some cases better than the FEM.

Keywords: seepage, dam foundation, finite element method, neural network, seep 3D model

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Authors: Abbas Mirakhorli

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A hub covering problem is a type of hub location problem that tries to maximize the coverage area with the least amount of installed hubs. There have not been many studies in the literature about multi-objective hubs covering location problems. Thus, in this paper, a bi-objective model for the hub covering problem is presented. The two objectives that are considered in this paper are the minimization of total transportation costs and the maximization of coverage of origin-destination nodes. A genetic algorithm is presented to solve the model when the number of nodes is increased. The genetic algorithm is capable of solving the model when the number of nodes increases by more than 20. Moreover, the genetic algorithm solves the model in less amount of time.

Keywords: facility location, hub covering, multi-objective optimization, genetic algorithm

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Authors: Masoumeh Ali Pouri, Hamid Haj Seyyed Javadi

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Nowadays, cloud processing is one of the important issues in information technology. Since scheduling of tasks graph is an NP-hard problem, considering approaches based on undeterminisitic methods such as evolutionary processing, mostly genetic and cuckoo algorithms, will be effective. Therefore, an efficient algorithm has been proposed for scheduling of tasks graph to obtain an appropriate scheduling with minimum time. In this algorithm, the new approach is based on making the length of the critical path shorter and reducing the cost of communication. Finally, the results obtained from the implementation of the presented method show that this algorithm acts the same as other algorithms when it faces graphs without communication cost. It performs quicker and better than some algorithms like DSC and MCP algorithms when it faces the graphs involving communication cost.

Keywords: cloud computing, scheduling, tasks graph, chakoos algorithm

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Authors: Hamidreza Saberkari, Mousa Shamsi, Hossein Ahmadi, Saeed Vaali, , MohammadHossein Sedaaghi

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In the recent years, using signal processing tools for accurate identification of the protein coding regions has become a challenge in bioinformatics. Most of the genomic signal processing methods is based on the period-3 characteristics of the nucleoids in DNA strands and consequently, spectral analysis is applied to the numerical sequences of DNA to find the location of periodical components. In this paper, a novel ensemble algorithm for gene selection in DNA sequences has been presented which is based on the combination of Goertzel algorithm and anti-notch filter (ANF). The proposed algorithm has many advantages when compared to other conventional methods. Firstly, it leads to identify the coding protein regions more accurate due to using the Goertzel algorithm which is tuned at the desired frequency. Secondly, faster detection time is achieved. The proposed algorithm is applied on several genes, including genes available in databases BG570 and HMR195 and their results are compared to other methods based on the nucleotide level evaluation criteria. Implementation results show the excellent performance of the proposed algorithm in identifying protein coding regions, specifically in identification of small-scale gene areas.

Keywords: protein coding regions, period-3, anti-notch filter, Goertzel algorithm

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Authors: Emad Askar, Eldesoky Elsoaly, Mohamed Kamel, Hisham Kamel

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The objective of this article is to improve the passive vibration damping of solar array (SA) used in space structures, by the effective application of numerical optimization. A case study of a SA is used for demonstration. A finite element (FE) model was created and verified by experimental testing. Optimization was then conducted by implementing the FE model with the genetic algorithm, to find the optimal placement of aluminum circular patches, to suppress the first two bending mode shapes. The results were verified using experimental testing. Finally, a parametric study was conducted using the FE model where patch locations, material type, and shape were varied one at a time, and the results were compared with the optimal ones. The results clearly show that through the proper application of FE modeling and numerical optimization, passive vibration damping of space structures has been successfully achieved.

Keywords: damping optimization, genetic algorithm optimization, passive vibration damping, solar array vibration damping

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Authors: Jingpeng Gao, Xinrui Mao, Zhibin Deng

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Aiming at the low recognition rate on the composite signal modulation in low signal to noise ratio (SNR), this paper proposes a modulation recognition algorithm based on ICanny-CNN. Firstly, the radar signal is transformed into the time-frequency image by Choi-Williams Distribution (CWD). Secondly, we propose an image processing algorithm using the Guided Filter and the threshold selection method, which is combined with the hole filling and the mask operation. Finally, the shallow convolutional neural network (CNN) is combined with the idea of the depth-wise convolution (Dw Conv) and the point-wise convolution (Pw Conv). The proposed CNN is designed to complete image classification and realize modulation recognition of radar signal. The simulation results show that the proposed algorithm can reach 90.83% at 0dB and 71.52% at -8dB. Therefore, the proposed algorithm has a good classification and anti-noise performance in radar signal modulation recognition and other fields.

Keywords: modulation recognition, image processing, composite signal, improved Canny algorithm

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

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In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, non-Newtonian power-law fluids, numerical simulation

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Authors: Amin H. Almasria, Rajai Z. Alrousanb, Al-Harith Manasrah

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The collapse of a light weight pedestrian bridges due to vehicle collision is investigated and studied in detail using a dynamic nonlinear finite element analysis. Typical bridge widely used in Jordan is studied and modeled under truck collision using one dimensional beam finite element in order to minimize analysis time due to the dynamic nature of the problem. Truck collision with the bridge is simulated at different speeds and locations of collisions using dynamic explicit finite element scheme with material nonlinearity taken into account. Energy absorption of bridge is investigated through principle of energy conservation, where truck kinetic energy is assumed to be stored in the bridge as strain energy. Weak failure points in the bridges were identified, and modifications are proposed in order to strengthen the bridge structure and prevent total collapse. The proposed design modifications on bridge structure were successful in allowing the bridge to fail locally rather than globally and expected to help in saving lives.

Keywords: finite element method, dynamic impact, pedestrian bridges, strain energy, collapse failure

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Authors: Partha P. Gopmandal, S. Bhattacharyya

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We investigate the thermal end effect on the pseudo-steady state behavior of the isotachophoretic transport of ionic species in a 2-D microchannel. Both ends of the channel are kept at a constant temperature which may lead to significant changes in electrophoretic migration speed. A mathematical model based on Nernst-Planck equations for transport of ions coupled with the equation for temperature field is considered. In addition, the charge conservation equations govern the potential field due to the external electric field. We have computed the equations for ion transport, potential and temperature in a coupled manner through the finite volume method. The diffusive terms are discretized via central difference scheme, while QUICK (Quadratic Upwind Interpolation Convection Kinematics) scheme is used to discretize the convective terms. We find that the thermal end effect has significant effect on the isotachophoretic (ITP) migration speed of the analyte. Our result shows that the ITP velocity for temperature dependent case no longer varies linearly with the applied electric field. A detailed analysis has been made to provide a range of the key parameters to minimize the Joule heating effect on ITP transport of analytes.

Keywords: finite volume method, isotachophoresis, QUICK scheme, thermal effect

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Authors: Arbnor Pajaziti, Hasan Cana

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In this paper, the structural genetic algorithm is used to optimize the neural network to control the joint movements of robotic arm. The robotic arm has also been modeled in 3D and simulated in real-time in MATLAB. It is found that Neural Networks provide a simple and effective way to control the robot tasks. Computer simulation examples are given to illustrate the significance of this method. By combining Genetic Algorithm optimization method and Neural Networks for the given robotic arm with 5 D.O.F. the obtained the results shown that the base joint movements overshooting time without controller was about 0.5 seconds, while with Neural Network controller (optimized with Genetic Algorithm) was about 0.2 seconds, and the population size of 150 gave best results.

Keywords: robotic arm, neural network, genetic algorithm, optimization

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA) is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: balanced truncation, clustering, dominant pole, Hankel norm, model reduction

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Authors: Gkolfo I. Smani, Vasileios Megalooikonomou

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Social influence and influence diffusion have been studied in social networks. However, most existing tasks on this subject focus on static networks. In this paper, the problem of maximizing influence diffusion in dynamic social networks, i.e., the case of networks that change over time, is studied. The DM algorithm is an extension of the MATI algorithm and solves the influence maximization (IM) problem in dynamic networks and is proposed under the linear threshold (LT) and independent cascade (IC) models. Experimental results show that our proposed algorithm achieves a diffusion performance better by 1.5 times than several state-of-the-art algorithms and comparable results in diffusion scale with the Greedy algorithm. Also, the proposed algorithm is 2.4 times faster than previous methods.

Keywords: influence maximization, dynamic social networks, diffusion, social influence, graphs

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Authors: Lee Feng Koo, Tze Jin Wong, Pang Hung Yiu, Nik Mohd Asri Nik Long

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Greater common divisor (GCD) attack is an attack that relies on the polynomial structure of the cryptosystem. This attack required two plaintexts differ from a fixed number and encrypted under same modulus. This paper reports a security reaction of Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field under GCD attack. Lucas Based El-Gamal Cryptosystem in the Elliptic Curve group over finite field was exposed mathematically to the GCD attack using GCD and Dickson polynomial. The result shows that the cryptanalyst is able to get the plaintext without decryption by using GCD attack. Thus, the study concluded that it is highly perilous when two plaintexts have a slight difference from a fixed number in the same Elliptic curve group over finite field.

Keywords: decryption, encryption, elliptic curve, greater common divisor

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Authors: Elham Alaee, Mousa Shamsi, Hossein Ahmadi, Soroosh Nazem, Mohammad Hossein Sedaaghi

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Human face has a fundamental role in the appearance of individuals. So the importance of facial surgeries is undeniable. Thus, there is a need for the appropriate and accurate facial skin segmentation in order to extract different features. Since Fuzzy C-Means (FCM) clustering algorithm doesn’t work appropriately for noisy images and outliers, in this paper we exploit Possibilistic C-Means (PCM) algorithm in order to segment the facial skin. For this purpose, first, we convert facial images from RGB to YCbCr color space. To evaluate performance of the proposed algorithm, the database of Sahand University of Technology, Tabriz, Iran was used. In order to have a better understanding from the proposed algorithm; FCM and Expectation-Maximization (EM) algorithms are also used for facial skin segmentation. The proposed method shows better results than the other segmentation methods. Results include misclassification error (0.032) and the region’s area error (0.045) for the proposed algorithm.

Keywords: facial image, segmentation, PCM, FCM, skin error, facial surgery

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Authors: Abdelhadi Lotfi, Abdelkader Benyettou

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In this work, a training algorithm for probabilistic neural networks (PNN) is presented. The algorithm addresses one of the major drawbacks of PNN, which is the size of the hidden layer in the network. By using a cross-validation training algorithm, the number of hidden neurons is shrunk to a smaller number consisting of the most representative samples of the training set. This is done without affecting the overall architecture of the network. Performance of the network is compared against performance of standard PNN for different databases from the UCI database repository. Results show an important gain in network size and performance.

Keywords: classification, probabilistic neural networks, network optimization, pattern recognition

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Authors: A. Boudjemai, A. Zafrane, R. Hocine

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Honeycomb sandwich panels are increasingly used in the construction of space vehicles because of their outstanding strength, stiffness and light weight properties. However, the use of honeycomb sandwich plates comes with difficulties in the design process as a result of the large number of design variables involved, including composite material design, shape and geometry. Hence, this work deals with the presentation of an optimal design of hexagonal honeycomb sandwich structures subjected to space environment. The optimization process is performed using a set of algorithms including the gravitational search algorithm (GSA). Numerical results are obtained and presented for a set of algorithms. The results obtained by the GSA algorithm are much better compared to other algorithms used in this study.

Keywords: optimization, gravitational search algorithm, genetic algorithm, honeycomb plate

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

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In this paper, first, we propose least support orthogonal matching pursuit (LS-OMP) algorithm to improve the performance, of the OMP (orthogonal matching pursuit) algorithm. LS-OMP algorithm adaptively chooses optimum L (least part of support), at each iteration. This modification helps to reduce the computational complexity significantly and performs better than OMP algorithm. Second, we give the procedure for the invisible image watermarking in the presence of compressive sampling. The image reconstruction based on a set of watermarked measurements is performed using LS-OMP.

Keywords: compressed sensing, orthogonal matching pursuit, restricted isometry property, signal reconstruction, least support orthogonal matching pursuit, watermark

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Authors: Kay Thi Yar, Khin Mar Lar Tun

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Nowadays, social networks are so popular and widely used in all over the world. In addition, searching personal information of each person and searching connection between them (peoples’ relation in real world) becomes interesting issue in our society. In this paper, we propose a framework with three portions for exploring peoples’ relations from their connected information. The first portion focuses on the Graph database structure to store the connected data of peoples’ information. The second one proposes the graph database searching algorithm, the Modified-SoS-ACO (Sense of Smell-Ant Colony Optimization). The last portion proposes the Deductive Reasoning Algorithm to define two persons’ relationship. This study reveals the proper storage structure for connected information, graph searching algorithm and deductive reasoning algorithm to predict and analyze the personnel relationship from peoples’ relation in their connected information.

Keywords: personnel information, graph storage structure, graph searching algorithm, deductive reasoning algorithm

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: Linyu Wang, Jiahui Ma, Jianhong Xiang, Hanyu Jiang

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the traditional greedy compressed sensing algorithm needs to know the signal sparsity when recovering the signal, but the signal sparsity in the practical application can not be obtained as a priori information, and the recovery accuracy is low, which does not meet the needs of practical application. To solve this problem, this paper puts forward Piecewise adaptive backtracking orthogonal least squares algorithm. The algorithm is divided into two stages. In the first stage, the sparsity pre-estimation strategy is adopted, which can quickly approach the real sparsity and reduce time consumption. In the second stage iteration, the correction strategy and adaptive step size are used to accurately estimate the sparsity, and the backtracking idea is introduced to improve the accuracy of signal recovery. Through experimental simulation, the algorithm can accurately recover the estimated signal with fewer iterations when the sparsity is unknown.

Keywords: compressed sensing, greedy algorithm, least square method, adaptive reconstruction

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Authors: Ahmad M. Awwad, Jehad Al-Sadi

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The star network is one of the promising interconnection networks for future high speed parallel computers, it is expected to be one of the future-generation networks. The star network is both edge and vertex symmetry, it was shown to have many gorgeous topological proprieties also it is owns hierarchical structure framework. Although much of the research work has been done on this promising network in literature, it still suffers from having enough algorithms for load balancing problem. In this paper we try to work on this issue by investigating and proposing an efficient algorithm for load balancing problem for the star network. The proposed algorithm is called Star Clustered Dimension Exchange Method SCDEM to be implemented on the star network. The proposed algorithm is based on the Clustered Dimension Exchange Method (CDEM). The SCDEM algorithm is shown to be efficient in redistributing the load balancing as evenly as possible among all nodes of different factor networks.

Keywords: load balancing, star network, interconnection networks, algorithm

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Authors: Kriangkrai Maneerat, Chutima Prommak

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Indoor wireless localization systems have played an important role to enhance context-aware services. Determining the position of mobile objects in complex indoor environments, such as those in multi-floor buildings, is very challenging problems. This paper presents an effective floor estimation algorithm, which can accurately determine the floor where mobile objects located. The proposed algorithm is based on the confidence interval of the summation of online Received Signal Strength (RSS) obtained from the IEEE 802.15.4 Wireless Sensor Networks (WSN). We compare the performance of the proposed algorithm with those of other floor estimation algorithms in literature by conducting a real implementation of WSN in our facility. The experimental results and analysis showed that the proposed floor estimation algorithm outperformed the other algorithms and provided highest percentage of floor accuracy up to 100% with 95-percent confidence interval.

Keywords: floor estimation algorithm, floor determination, multi-floor building, indoor wireless systems

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Authors: C. Juntarasaid, T. Pulngern, S. Chucheepsakul

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A formulation of postbuckling analysis of end supported rods under self-weight has been presented by the variational method. The variational formulation involving the strain energy due to bending and the potential energy of the self-weight, are expressed in terms of the intrinsic coordinates. The variational formulation is accomplished by introducing the Lagrange multiplier technique to impose the boundary conditions. The finite element method is used to derive a system of nonlinear equations resulting from the stationary of the total potential energy and then Newton-Raphson iterative procedure is applied to solve this system of equations. The numerical results demonstrate the postbluckled configurations of end supported rods under self-weight. This finite element method based on variational formulation expressed in term of intrinsic coordinate is highly recommended for postbuckling analysis of end-supported rods under self-weight.

Keywords: postbuckling, finite element method, variational method, intrinsic coordinate

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