Stability of Non-prismatic Frames with Flexible Connections and Elastic Supports

M. Rezaiee-Pajand,F. Shahabian,M. Bambaeechee 대한토목학회 2016 KSCE JOURNAL OF CIVIL ENGINEERING Vol.20 No.2

An accurate formulation is obtained to determine critical load, and corresponding equivalent effective length factor of a simple frame. The presented methodology is based on the exact solutions of the governing differential equations for buckling of a frame with tapered and/or prismatic columns. Accordingly, the influences of taper ratio, shape factor, flexibility of connections, and elastic supports on the critical load, and corresponding equivalent efficient length factor of the frame will be investigated. The authors' findings can be easily applied to the stability design of general non-prismatic frames. Moreover, comparing the results with the accessible outcomes demonstrate the accuracy, efficiency and capabilities of the proposed formulation.

A new higher-order triangular plate bending element for the analysis of laminated composite and sandwich plates

M. Rezaiee-Pajand,F. Shahabian,F.H. Tavakoli 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.43 No.2

To analyze the bending and transverse shear effects of laminated composite plates, a thirteen nodes triangular element will be presented. The suggested formulations consider a parabolic variation of the transverse shear strains through the thickness. As a result, there is no need to use shear correction coefficients in computing the shear stresses. The proposed element can model both thin and thick plates without any problems, such as shear locking and spurious modes. Moreover, the effectiveness of w, n, as an independent degree of freedom, is concluded by the present study. To perform the accuracy tests, several examples will be solved. Numerical results for the orthotropic materials with different boundary conditions, shapes, number of layers, thickness ratios and fiber orientations will be presented. The suggested element calculates the deflections and stresses more accurate than those available in the literature.

Comprehensive evaluation of structural geometrical nonlinear solution techniques Part II: Comparing efficiencies of the methods

M. Rezaiee-Pajand,M. Ghalishooyan,M. Salehi-Ahmadabad 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.6

In part I of the article, formulation and characteristics of the several well-known structural geometrical nonlinear solution techniques were studied. In the present paper, the efficiencies and capabilities of residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control and modified normal flow will be evaluated. To achieve this goal, a comprehensive comparison of these solution methods will be performed. Due to limit page of the article, only the findings of 17 numerical problems, including 2-D and 3-D trusses, 2-D and 3-D frames, and shells, will be presented. Performance of the solution strategies will be considered by doing more than 12500 nonlinear analyses, and conclusions will be drawn based on the outcomes. Most of the mentioned structures have complex nonlinear behavior, including load limit and snap-back points. In this investigation, criteria like number of diverged and complete analyses, the ability of passing load limit and snap-back points, the total number of steps and analysis iterations, the analysis running time and divergence points will be examined. Numerical properties of each problem, like, maximum allowed iteration, divergence tolerance, maximum and minimum size of the load factor, load increment changes and the target point will be selected in such a way that comparison result to be highly reliable. Following this, capabilities and deficiencies of each solution technique will be surveyed in comparison with the other ones, and superior solution schemes will be introduced.

Damage identification of 2D and 3D trusses by using complete and incomplete noisy measurements

M. Rezaiee-Pajand,M.S. Kazemiyan 국제구조공학회 2014 Structural Engineering and Mechanics, An Int'l Jou Vol.52 No.1

Four algorithms for damage detection of trusses are presented in this paper. These approaches can detect damage by using both complete and incomplete measurements. The suggested methods are based on the minimization of the difference between the measured and analytical static responses of structures. A non-linear constrained optimization problem is established to estimate the severity and location of damage. To reach the responses, the successive quadratic method is used. Based on the objective function, thestiffness matrix of the truss should be estimated and inverted in the optimization procedure. The differences of the proposed techniques are rooted in the strategy utilized for inverting the stiffness matrix of the damaged structure. Additionally, for separating the probable damaged members, a new formulation is proposed. This scheme is employed prior to the outset of the optimization process. Furthermore, a new tactic is presented to select the appropriate load pattern. To investigate the robustness and efficiency of the authors’ method, several numerical tests are performed. Moreover, Monte Carlo simulation is carried out to assess the effect of noisy measurements on the estimated parameters.

The dynamic relaxation method using new formulation for fictitious mass and damping

M. Rezaiee-pajand,J. Alamatian 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.34 No.1

This paper addresses the modified Dynamic Relaxation algorithm, called mdDR by minimizing displacement error between two successive iterations. In the mdDR method, new relationships for fictitious mass and damping are presented. The results obtained from linear and nonlinear structural analysis, either by finite element or finite difference techniques; demonstrate the potential ability of the proposed scheme compared to the conventional DR algorithm. It is shown that the mdDR improves the convergence rate of Dynamic Relaxation method without any additional calculations, so that, the cost and computational time are decreased. Simplicity, high efficiency and automatic operations are the main merits of the proposed technique.

Estimating the Region of Attraction via collocation for autonomous nonlinear systems

M. Rezaiee-Pajand,B. Moghaddasie 국제구조공학회 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.2

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov’s partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.

Comprehensive evaluation of structural geometrical nonlinear solution techniques Part I: Formulation and characteristics of the methods

M. Rezaiee-Pajand,M. Ghalishooyan,M. Salehi-Ahmadabad 국제구조공학회 2013 Structural Engineering and Mechanics, An Int'l Jou Vol.48 No.6

This paper consists of two parts, which broadly examines solution techniques abilities for the structures with geometrical nonlinear behavior. In part I of the article, formulations of several well-known approaches will be presented. These solution strategies include different groups, such as: residual load minimization, normal plane, updated normal plane, cylindrical arc length, work control, residual displacement minimization, generalized displacement control, modified normal flow, and three-parameter ellipsoidal, hyperbolic, and polynomial schemes. For better understanding and easier application of the solution techniques, a consistent mathematical notation is employed in all formulations for correction and predictor steps. Moreover, other features of these approaches and their algorithms will be investigated. Common methods of determining the amount and sign of load factor increment in the predictor step and choosing the correct root in predictor and corrector step will be reviewed. The way that these features are determined is very important for tracing of the structural equilibrium path. In the second part of article, robustness and efficiency of the solution schemes will be comprehensively evaluated by performing numerical analyses.

The dynamic relaxation method using new formulation for fictitious mass and damping

Rezaiee-Pajand, M.,Alamatian, J. Techno-Press 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.34 No.1

This paper addresses the modified Dynamic Relaxation algorithm, called mdDR by minimizing displacement error between two successive iterations. In the mdDR method, new relationships for fictitious mass and damping are presented. The results obtained from linear and nonlinear structural analysis, either by finite element or finite difference techniques; demonstrate the potential ability of the proposed scheme compared to the conventional DR algorithm. It is shown that the mdDR improves the convergence rate of Dynamic Relaxation method without any additional calculations, so that, the cost and computational time are decreased. Simplicity, high efficiency and automatic operations are the main merits of the proposed technique.

Nonlinear dynamic analysis by Dynamic Relaxation method

M. Rezaiee-Pajand,J. Alamatian 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.5

Numerical integration is an efficient approach for nonlinear dynamic analysis. In this paper, general category of the implicit integration errors will be discussed. In order to decrease the errors, Dynamic Relaxation method with modified time step (MFT) will be used. This procedure leads to an alternative algorithm which is very general and can be utilized with any implicit integration scheme. For numerical verification of the proposed technique, some single and multi degrees of freedom nonlinear dynamic systems will be analyzed. Moreover, results are compared with both exact and other available solutions. Suitable accuracy, high efficiency, simplicity, vector operations and automatic procedures are the main merits of the new algorithm in solving nonlinear dynamic problems.

Estimating the Region of Attraction via collocation for autonomous nonlinear systems

Rezaiee-Pajand, M.,Moghaddasie, B. Techno-Press 2012 Structural Engineering and Mechanics, An Int'l Jou Vol.41 No.2

This paper aims to propose a computational technique for estimating the region of attraction (RoA) for autonomous nonlinear systems. To achieve this, the collocation method is applied to approximate the Lyapunov function by satisfying the modified Zubov's partial differential equation around asymptotically stable equilibrium points. This method is formulated for n-scalar differential equations with two classes of basis functions. In order to show the efficiency of the suggested approach, some numerical examples are solved. Moreover, the estimated regions of attraction are compared with two similar methods. In most cases, the proposed scheme can estimate the region of attraction more efficient than the other techniques.