Nonlinear Dynamic Analysis and Natural Frequencies of Gabled Frame Having Flexible Restraints and Connections

Amir R. Masoodi,Sina Heyrani Moghaddam 대한토목학회 2015 KSCE Journal of Civil Engineering Vol.19 No.6

Nonlinear dynamic and natural frequencies of a gabled frame with elastic restraints and semi-rigid connections are investigated by using a program in OpenSees software. Natural frequencies are obtained for two states, which are flexible connections and semi-rigid supports, separately. The mode shapes of structure are also obtained for the described states. Also, the effect of connection flexibility on the dynamic responses of the frame is obtained for different values of peak ground acceleration. The members of this structure are modeled as a nonlinear beam-column element. The members of structure are assumed to be prismatic. Two equal lumped masses at the head of two columns in horizontal and vertical directions are considered as the mass pattern of structure. Note that three degrees of freedom are allocated to all nodes. Furthermore, the mode shapes of frame are obtained. Conclusively, the effects of semi-rigid connections and supports on the natural frequencies and mode shapes of structure are investigated. As results, the top level displacement and base shear responses of frame are reported.

Elastoplastic nonlinear behavior of planar steel gabled frame

Moghaddam, Sina Heyrani,Masoodi, Amir R. Techno-Press 2019 Advances in computational design Vol.4 No.4

In this paper, static nonlinear analysis of gable frame is performed using OpenSees software. Both geometric and material nonlinearities are considered in analyses. To consider large displacements, co-rotational coordinate transformation is used in software. The effects of symmetric and asymmetric support conditions including clamped and simple supports are studied. On the other hand, the material nonlinearity is reflected on analyses using Giuffre-Menegotto-Pinto steel material. Note that strain hardening characteristics are also considered in this model. Moreover, I-shaped cross-section is assumed for all members. The results are provided for different geometry properties of gable frame including shallow and deep inclined roof. It should be added that buckling and post-buckling behaviors of gable frame are investigated using related equilibrium paths. A comparison study is also implemented on the responses of buckling loads obtained for different support and geometry conditions. To trace snap-through paths completely, a displacement control method entitled arc-length is utilized. Findings show the capability of proposed model in nonlinear analysis of gable frames.

Critical buckling moment of functionally graded tapered mono-symmetric I-beam

Mohammad Rezaiee-Pajand,Amir R. Masoodi,Ali Alepaighambar 국제구조공학회 2021 Steel and Composite Structures, An International J Vol.39 No.5

This study deals with the Lateral-Torsional Buckling (LTB) of a mono-symmetric tapered I-beam, in which the cross-section is varying longitudinally. To obtain the buckling moment, two concentrated bending moments should be applied at the two ends of the structure. This structure is made of Functionally Graded Material (FGM). The Young’s and shear modules change linearly along the longitudinal direction of the beam. It is considered that this tapered beam is laterally restrained continuously, by using torsional springs. Furthermore, two rotational bending springs are employed at the two structural ends. To achieve the buckling moment, Ritz solution method is utilized. The response of critical buckling moment of the beam is obtained by minimizing the total potential energy relation. The lateral and torsional displacement fields of the beam are interpolated by harmonic functions. These functions satisfy the boundary conditions. Two different support conditions are considered in this study. The obtained formulation is validated by solving benchmark problems. Moreover, some numerical studies are implemented to show the accuracy, efficiency and high performance of the proposed formulation.

Stability Analysis of Frame Having FG Tapered Beam–Column

M. Rezaiee-Pajand,Amir R. Masoodi 한국강구조학회 2019 International Journal of Steel Structures Vol.19 No.2

This study focuses on the analysis of the tapered beam–column having functionally graded section. By using two diff erent methods, the substantial eff ects of the coupling–extensional bending of this structure are considered. Both second-order eff ects and fl exibility of connections are considered in the analysis. The suggested exact stiff ness matrix is very general and suitable for analyzing any plane frame, which has non-prismatic members and various types of connections. By using this formulation, the frame stability analysis of the FG beam with power function will be performed. Furthermore, the eff ects of semi-rigid connections and supports on the buckling load of 2D frames will be studied. Finally, comparing the new responses with the available solutions shows the accuracy, effi ciency and capabilities of the proposed stiff ness matrix. In addition, some new problems, including 2D frame, especially gabled frame, are solved using authors’ schemes.

Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element

M. Rezaiee-Pajand,Amir R. Masoodi,E. Arabi 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.28 No.3

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

Static analysis of functionally graded non-prismatic sandwich beams

Rezaiee-Pajand, M.,Masoodi, Amir R.,Mokhtari, M. Techno-Press 2018 Advances in computational design Vol.3 No.2

In this article, the static behavior of non-prismatic sandwich beams composed of functionally graded (FG) materials is investigated for the first time. Two types of beams in which the variation of elastic modulus follows a power-law form are studied. The principle of minimum total potential energy is applied along with the Ritz method to derive and solve the governing equations. Considering conventional boundary conditions, Chebyshev polynomials of the first kind are used as auxiliary shape functions. The formulation is developed within the framework of well-known Timoshenko and Reddy beam theories (TBT, RBT). Since the beams are simultaneously tapered and functionally graded, bending and shear stress pushover curves are presented to get a profound insight into the variation of stresses along the beam. The proposed formulations and solution scheme are verified through benchmark problems. In this context, excellent agreement is observed. Numerical results are included considering beams with various cross sectional types to inspect the effects of taper ratio and gradient index on deflections and stresses. It is observed that the boundary conditions, taper ratio, gradient index value and core to the thickness ratio significantly influence the stress and deflection responses.

Lateral-torsional buckling of functionally graded tapered I-beams considering lateral bracing

Mohammad Rezaiee-Pajand,Amir R. Masoodi,Ali Alepaighambar 국제구조공학회 2018 Steel and Composite Structures, An International J Vol.28 No.4

In this paper, the lateral-torsional buckling of axially-transversally functionally graded tapered beam is investigated. The structure cross-section is assumed to be symmetric I-section, and it is continuously laterally supported by torsional springs through the length. In addition, the height of cross-section varies linearly throughout the length of structure. The proposed formulation is obtained for the case that the elastic and shear modulus change as a power function along the beam length and section height. This structure carries two concentrated moments at the ends. In this study, the lateral displacement and twisting angle relation of the beam are defined by sinusoidal series. After establishing the eigenvalue equation of unknown constants, the beam critical bending moment is found. To validate the accuracy and correctness of results, several numerical examples are solved.

Nonlinear vibration analysis of carbon nanotube reinforced composite plane structures

Mohammad Rezaiee-Pajand,Amir R. Masoodi,Niloofar Rajabzadeh-Safaei 국제구조공학회 2019 Steel and Composite Structures, An International J Vol.30 No.6

This paper is dedicated to nonlinear static and free vibration analysis of Uniform Distributed Carbon Nanotube Reinforced Composite (UD-CNTRC) structures under in-plane loading. The authors have suggested an efficient six-node triangular element. Mixed Interpolation of Tensorial Components (MITC) approach is employed to alleviate the membrane locking phenomena. Moreover, the behavior of the well-known LST element is considerably improved by applying an additional linear interpolation on the strain fields. Based on the rule of mixture, the properties of CNTRC are obtained. In this study, only the uniform distributed CNTs are employed through the thickness direction of element. To achieve the natural frequencies and shape modes, the eigenvalue problem is also solved. Using Total Lagrangian Principles, large amplitude free vibration is considered based on the first normalized mode shape of structure. Different well-known plane problem benchmarks and some proposed ones are studied to validate the accuracy and capability of authors‘ formulations. In addition, the effects of length to the height ratio of beam, CNT‘s characteristics, support conditions and normalized amplitude parameter on the linear and nonlinear vibration parameters are investigated.

Employing GDQ method for exploring undamped vibrational performance of CNT-reinforced porous coupled curved beam

Moein A. Ghandehari,Amir R. Masoodi Techno-Press 2023 Advances in nano research Vol.15 No.6

Coupled porous curved beams, due to their low weight and high flexibility, have many applications in engineering. This study investigates the vibration behavior of coupled porous curved beams in different boundary conditions. The system consists of two curved beams connected by a mid-layer of elastic springs. These beams are made of various materials, such as homogenous steel foam, and composite materials with PMMA (polymethyl methacrylate) and SWCNT (single-walled carbon nanotube) used as the matrix and nanofillers, respectively. To obtain equivalent material properties, the role of mixture (RoM) was employed, followed by the implementation of the porosity function. The system's governing equations were obtained by employing FSDT and Hamilton's law. To investigate thermal vibration, temperature was implemented as a load in the governing equations. The GDQ method was used to solve these equations. To demonstrate the applicability of the GDQ method in calculating the frequencies of the system and the correctness of the developed program, a validation study was conducted. After validation, numerous examples were presented to investigate the behavior of single and coupled curved beams in various material properties and boundary conditions. The results indicate that the frequencies of the curved beams and the system depend highly on the amount of porosity (n) and the distribution pattern. The system frequencies decreased with an increase in the porosity coefficient. The stiffness of the springs had no effect on the first mode frequency but increased frequencies of other modes in a specific range. The frequencies of the system decreased with an increase in environmental temperature.

Pushover analysis of gabled frames with semi-rigid connections

Ahmad Shooshtari,Sina Heyrani Moghaddam,Amir R. Masoodi 국제구조공학회 2015 Steel and Composite Structures, An International J Vol.18 No.6

The nonlinear static analysis of structure, which is under the effect of lateral loads and provides the capacity curve of the structure, is defined as a push-over analysis. Ordinarily, by using base shear and the lateral displacement of target point, the capacity curve is obtained. The speed and ease of results interpretation in this method is more than that of the NRHA responses. In this study, the nonlinear static analysis is applied on the semi-rigid steel gabled frames. It should be noted that the members of this structure are analyzed as a prismatic beam-column element in two states of semi-rigid connections and supports. The gabled frame is modeled in the OpenSees software and analyzed based on the displacement control at the target point. The lateral displacement results, calculated in the top level of columns, are reported. Furthermore, responses of the structure are obtained for various support conditions and the rigidity of nodal connections. Ultimately, the effect of semi-rigid connections and supports on the capacity and the performance point of the structure are presented in separated graphs.