Showing papers by "Mohammad Rezaiee-Pajand published in 2016"
TL;DR: In this article, free vibration analysis of two different double-beam systems is presented, where the ends of the beams are elastically restrained against translation and rotation by a mass-spring system.
43 citations
TL;DR: In this article, an explicit time integration algorithm with second-order accuracy and unconditional stability is presented for dynamic analysis, where the current displacement and velocity relations are defined in terms of the accelerations of two previous time steps.
Abstract: Complex structural dynamic problems are normally analyzed by finite element and numerical integration techniques. An explicit time integration algorithm with second-order accuracy and unconditional stability is presented for dynamic analysis. Utilizing weighted factors, the current displacement and velocity relations are defined in terms of the accelerations of two previous time steps. The concept of discrete transfer function and the pole mapping rule from the control theory are exploited to develop the new algorithm. Several linear and nonlinear dynamic analyses are performed to verify the efficiency of the method compared with the well-known Newmark method.
26 citations
TL;DR: In this article, an explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived.
Abstract: An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central difference method as a special case, while damping is shown to exert no effect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for specific values of the parameters; (ii) the numerical dissipation contained can help filter out spurious high-frequency components; and (iii) the crucial lower modes are generally unaffected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central difference method.
22 citations
TL;DR: In this paper, a new variable load factor is proposed for dynamic relaxation method, which is based on the minimizing of the unbalanced displacement, and several numerical tests are performed to prove the capability and efficiency of the presented scheme.
20 citations
TL;DR: In this article, a dynamic relaxation (DR) method is proposed to estimate the buckling limit load of non-linear structures in order to investigate the structural stability behavior of nonlinear structures.
Abstract: The numerical structural analysis schemes are extensively developed by progress of modern computer processing power. One of these approximate approaches is called "dynamic relaxation (DR) method." This technique explicitly solves the simultaneous system of equations. For analyzing the static structures, the DR strategy transfers the governing equations to the dynamic space. By adding the fictitious damping and mass to the static equilibrium equations, the corresponding artificial dynamic system is achieved. The static equilibrium path is required in order to investigate the structural stability behavior. This path shows the relationship between the loads and the displacements. In this way, the critical points and buckling loads of the non-linear structures can be obtained. The corresponding load to the first limit point is known as buckling limit load. For estimating the buckling load, the variable load factor is used in the DR process. A new procedure for finding the load factor is presented by imposing the work increment of the external forces to zero. The proposed formula only requires the fictitious parameters of the DR scheme. To prove the efficiency and robustness of the suggested algorithm, various geometric non-linear analyses are performed. The obtained results demonstrate that the new method can successfully estimate the buckling limit load of structures.
17 citations
TL;DR: In this article, the free vibration analysis of a double-beam system is investigated, which is formed by two beams with elastic restraints at one end and free at the other end.
Abstract: In this paper, the free vibration analysis of a double-beam system is investigated. This structure is formed by two beams with elastic restraints at one end and free at the other end. These beams a...
16 citations
TL;DR: In this article, a load factor is proposed to minimize the work increment of the external loads with respect to the load factor, which is only dependent on the fictitious parameters of the DR strategy.
14 citations
TL;DR: In this article, two triangular and rectangular elements with high accuracy were suggested to analyze thick orthotropic plates, two displacement fields are considered for inner and boundaries of the element, and its analytical solution is obtained.
12 citations
TL;DR: In this article, a 6-node triangular isoparametric element is formulated for geometrically nonlinear analysis of laminated shells to prevent the membrane and shear locking effects, the suggested scheme uses assumed strains for inplane and transverse shear strains.
12 citations
TL;DR: In this paper, a two-node beam with six different degrees of freedom is analyzed, and it is shown that by employing only a single beam, the LOCKING- FREE ANSWERS can be found.
Abstract: THIS STUDY IS DEVOTED TO STRAIN-BASED FORMULATION FOR A CURVED BEAM. ARCHES WITH PARABOLIC GEOMETRY, WHICH HAVE A VARIETY OF APPLICATIONS, BELONG TO THIS STRUCTURAL TYPE. DEPENDENCY OF THE CURVATURE RADIUS TO THE ARCH LENGTH CREATES SOME COMPLEXITIES IN THE SOLUTION PROCESS. TO ANALYZE THESE COMPLEX STRUCTURES, A TWO-NODE BEAM WITH SIX DEGREES OF FREEDOM IS SUGGESTED BY UTILIZING CLOSED-FORM SOLUTION AND THE STIFFNESS-BASED FINITE ELEMENT MET-HOD. CONSIDERING THE EFFECT OF SHEAR DEFORMATION, AND INCORPORA-TING EQUILIBRIUM CONDITIONS INTO THE FINITE ELEMENT MODEL, LEAD TO THE EXACT STRAINS. DISPLACEMENTS AND EXPLICIT STIFFNESS MATRIX ARE FOUND BASED ON THESE EXACT STRAINS. TO VALIDATE THE EFFICIENCY OF THE AUTHOR'S FORMULATION, SEVEN NUMERICAL TESTS ARE PERFORMED. THE OUTCOMES DEMONSTRATE THAT BY EMPLOYING ONLY A SINGLE ELEMENT, THE LOCKING-FREE ANSWERS CAN BE FOUND.
10 citations
TL;DR: In this paper, various dynamic relaxation methods are investigated for geometric nonlinear analysis of bending plates, including Underwood and Rezaiee-Pajand & Alamatian processes.
Abstract: In this paper, various dynamic relaxation methods are investigated for geometric nonlinear analysis of bending plates. Sixteen wellknown algorithms are employed. Dynamic relaxation fictitious parameters are the mass matrix, the damping matrix and the time step. The difference between the mentioned tactics is how to implement these parameters. To compare the efficiency of these strategies, several bending plates’ problems with large deflections are solved. Based on the number of iterations and analysis time, the scores of the different schemes are calculated. These scores determine the ranking of each technique. The numerical results indicate the appropriate efficiency of Underwood and Rezaiee-Pajand & Alamatian processes for the nonlinear analysis of bending plates.
TL;DR: In this paper, an exact solution of the governing differential equations for buckling of a simple non-prismatic frame with tapered and/or prismatic columns is presented.
Abstract: 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.
TL;DR: In this article, the free vibration of two-dimensional deformable rectangular tanks fully-filled with a compressible fluid is analytically investigated, and the exact solutions are derived, and numerical examples are performed to verify the presented closed-form relations.
TL;DR: In this paper, a quadrilateral four-node element with drilling degrees of freedom is proposed for the finite-element analysis, where the hybrid stress scheme is used in the local coordinates for small strains.
Abstract: This study deals with the geometric nonlinear analysis of the plane problem based on the corotational formulation. Both analytical solutions and hybrid stress functional will be utilized in the proposed technique. A quadrilateral four-node element with drilling degrees of freedom is proposed for the finite-element analysis. The corotational method is applied for the nonlinear behavior. In this way, small strains and rigid body motions can be separated. Based on analytical solution, the hybrid stress scheme is used in the local coordinates for small strains. By using Allman’s quadratic displacement, the boundary condition for this element is introduced. In this approach, added drilling degrees of freedom increase the accuracy and robustness of the element. Furthermore, the corotational formulas are written in the local and global coordinates system to derive the nonlinear relations. These equations were solved by using the arc-length algorithm. To investigate the accuracy and capability of the sugg...
TL;DR: In this article, two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations, and the results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.
Abstract: Two new elements with six degrees of freedom are proposed by applying the equilibrium conditions and strain-displacement equations. The first element is formulated for the infinite ratio of beam radius to thickness. In the second one, theory of the thick beam is used. Advantage of these elements is that by utilizing only one element, the exact solution will be obtained. Due to incorporating equilibrium conditions in the presented formulations, both proposed elements gave the precise internal forces. By solving some numerical tests, the high performance of the recommended formulations and also, interaction effects of the bending and axial forces will be demonstrated. While the second element has less error than the first one in thick regimes, the first element can be used for all regimes due to simplicity and good convergence. Based on static responses, it can be deduced that the first element is efficient for all the range of structural characteristics. The free vibration analysis will be performed using the first element. The results of static and dynamic tests show no deficiency, such as, shear and membrane locking and excessive stiff structural behavior.
TL;DR: In this article, two higher order triangular elements were formulated for inter-laminar stresses analysis in free edge of the laminated composite bending plates, and the analysis is based on a displacement model and includes the higher order shear deformation.
Abstract: Two higher order triangular elements will be formulated for inter-laminar stresses analysis in free edge of the laminated composite bending plates. The analysis is based on a displacement model and includes the higher order shear deformation. To demonstrate the validity and efficiency of the proposed method, the orthotropic laminated composite plates with arbitrary laminations and boundary conditions will be analyzed. In this paper, the effects of increasing the number of nodes and the degree of interpolation functions will be studied. It will be proven that by using particular higher order interpolation, more accurate stress resultants for plates can be predicted. Furthermore, a good rate of convergence will be found by utilizing only a very coarse mesh.