In this paper, the nonlinear-non-elastic behavior of the braced frames of the SCBF Special Center is compared with the BRBF anti-arc bracing brackets. Different structures with different numbers of floors, which were previously designed according to the existing regulations and the recommended behavior coefficient, were non-linear static analysis by OPENSEES software and their load-bearing and cyclic behavior were determined for both types of braces. The effect of stiffness strain percentage and the degree of initial geometric defect of the brace on the behavior of the structures were also investigated. Comparison of results indicates more formable and stable behavior of anti-buckling brace than normal brace. Also, the effect of primary geometric defect is significant only in the initial steps of displacement and the higher the percentage of strain strain strain, the more stable behavior structure against larger forces. it shows.

In this paper, effects of initial geometric imperfection on free vibration analysis of multi-directional functionally graded nanoplates are studied using an isogeometric approach together with the quasi-3D shear deformation theory. Geometric imperfections may exist inherently in nanoplates or purposely created by researchers. These imperfections strongly affect the plates’ natural frequency. The initial geometric imperfection is considered as an initial curvature and modeled by an analytical function in the governing equations of the nanoplate. The effective material properties distribution is stated based on the Mori-Tanaka scheme, which in addition to the thickness of the plate, also changes in the in-plane directions. A four-variable quasi-3D theory with new distribution function is proposed. Based on Hamilton’s principle, a weak form of free vibration problem for nonlocal plates is derived. These discrete systems of equations are solved using an isogeometric approach. The accuracy of the present study was verified by comparing the results with those given in published papers. Present results indicate the importance of various parameters, especially imperfection amplitude, and material indexes in all directions, on the free vibration behavior of FG nanoplates.

In this research, the nonlinear buckling analysis of Functionally Graded (FG) nano-composite beam reinforced by various distributions of Boron Nitrid Nanotube (BNNT) is investigated under electro-thermodynamical loading with considering initial geometrical imperfection. The analysis is performed based on nonlocal elasticity theory and using the Finite Element Method (FEM). Various distributions of BNNT along the beam’s thickness are considered as uniform and decreasing-increasing functionally graded; and the extended mixture model is used to estimate the properties of nano-composite beam. The elastic medium around the smart nano-composite beam is modeled as elastic foundation. The governing equations of equilibrium are derived using energy method and nonlocal elasticity theory; and the critical buckling load is obtained for various boundary conditions such as simply-simply supported (S-S) and clamped-clamped (C-C) using the FEM. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of nano-composite beam increases and consequently the stability of the system increases. The effect of FG-X distribution type is more than uniform distributions. Also, the critical buckling load of nano-composite beam increases with an increase in the electric field and elastic foundation.

In this study, based on the third-order shear deformation theory the equations of motion are obtained to analyses the deformation of a long and slender composite beam. The beam has initial geometric imperfection and subjected to impact load. The impact procedures are applied by rigid body with a specific speed, off-center and at a certain distance from the beam's surface. Hamilton’s principle and the von-Karman nonlinear strain-displacement relationship are used to obtain the equations of motion that they are based on displacement and in a set of coupled nonlinear partial differential equations in dynamic mode. The generalized differential quadrature Method (GDQM) is used to discretize the obtained equations and convert them into a set of ordinary differential equations. Newton-Raphson iterative scheme is employed to solve the resulting system of nonlinear algebraic equations. Then, by solving the equations of the system, the effects of initial geometric imperfection on the beam’s deflection have been studied. Also the effects of mass and the initial velocity of the impactor on the beam’s deformation are investigated. The results of this research show that an increase in the amount of the initial velocity and mass of the impactor entail an increase in the beam deformation.

Exact and numerical solution of eccentrically stiffened panels in the industry is a major step forward in the design of these structures. This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FG cylindrical panels on elastic foundations subjected to hygro-thermo-mechanical loads. The stiffeners are assumed to be spiral-type. The panel has the initial geometrical imperfection. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. The elastic foundation is considered based on Winkler and Pasternak proposed model. Governing equations are derived basing on the Lekhnitsky smeared stiffeners technique and classical shell theory incorporating Von Karman-Donnell geometrical type nonlinearity. Explicit relations of load–deflection curves for FG cylindrical panels are determined by applying stress function and Galerkin method. The effects of angel of stiffener, different dimensional parameters, volume fraction index, initial geometrical imperfection, the stiffness of elastic foundation and moisture concentration on the postbuckling of FG panel are investigated. Also effects of temperature gradient through the thickness and effects of different boundary conditions are investigated for thermo-mechanical loading. The obtained results are validated by comparing with those in the literature.

Following the collapse of the World Trade Center towers, investigating the building resistance and providing the safety of residents in case of fire have attracted the attention of engineers more than ever. In this regard, similar to buildings, gas and liquid containment structures, vehicles, planes, and vessel fuselages are examples of engineering usage which need to be designed against fire. It was shown that inelastic or elastic buckling of steel plate webs, that experience plastic buckling at normal temperatures, is a possible phenomenon at elevated temperatures owing to the deterioration of mechanical properties, i.e., a change in the failure mode, is to be expected. Therefore, regarding the importance of the issue and its application in the industry, it is necessary to investigate the behavior of the I-shaped plate girders against fire. In this research, shear behaviors of long steel plate girder web panels subjected to pure shear loading are investigated at elevated temperatures by the nonlinear finite element method. Therefore, web panel shear design relationships mentioned in AISC360-16 specification is modified to be used in fire conditions. This is achieved by direct utilization of steel stress-strain reduction factors in EN1993-1-2 at elevated temperatures. It is observed that the adopted equation of AISC360-16 for fire situations yields values that are more non-conservative such that the difference reaches almost 18%. On the other hand, AISC equations are more accurate and in the safe region for compact plates. However, these equations lead to the unsafe condition at higher slenderness values. In this regard, nonlinear finite element analysis results were employed to modify the AISC 360-16 equation for predicting the ultimate shear strength of long steel plate girder web panels by considering the strength degradation caused by high slenderness, high temperature, and initial geometrical imperfections. Comparison of the results corroborated the appropriate accuracy of the proposed equations.

Effects of initial geometric imperfection and pre- & post-buckling deformations on vibration of isotropic rectangular plates under uniaxial compressive in-plane load have been studied. Vibration equations of a plate, using Mindlin theory and Von-Karman stressstrain relations for large deformations, have been extracted. The response of nonlinear differential equations was assumed as the summation of dynamic and static responses. Due to the large static deflection of a plate in comparison with its vibration amplitude, the differential equations have been solved in two steps. First, the static equations have been solved using the differential quadrature method and the Arc-length strategy. Next, considering small vibration amplitude about the deformed plate (the first step result) and eliminating nonlinear terms, natural frequencies have been calculated using the differential quadrature method and solving the obtained eigenvalue problem. The results for different initial geometric imperfection and different boundary conditions reflect the impact of the mentioned factors on the natural frequencies of plates.

Nowadays the use of FRP composites for strengthening steel structures has been considered by researchers. In present study, The maximum deformation of steel plates and structural sections before and after strengthening by GFRP plates was evaluated by modelling and static analysis using ABAQUS finite element software. The results indicated the amount of increasing rate in stiffness and load capacity of studied steel plates and I-shaped beams. In this strengthening method, better results would be achieved by installing GFRP plates to the flange of the beam in comparison with installing them to the web of the beam. The results for studied steel hollow sections and I-shaped columns, comparing axial and lateral behaviour of specimens before and after strengthening indicates the increasing rate in axial stiffness and therefore increase in load carrying capacity of columns in comparison with bare specimens. In this research, the influence of geometric imperfection on the reduction of the limit loads of the bare as well as the retrofitted steel plates was also evaluated. The results indicated that the strengthening of steel plates with GFRP plates could be decreased by the sensitivity of them due to presence of initial geometric imperfections, particularly for plates with higher width-to-thickness ratio.

Vibration of postbuckled cracked plate has been investigated using the differential quadrature element method. The crack modeled as an open crack using a no-mass linear spring. The governing equations of vibration of a buckled cracked plate are derived using the Mindlin theory and considering the effect of initial imperfection. The answer consist of static and dynamic parts. First, differential equations are discretized using the differential quadrature element method and then the resulting nonlinear algebraic equations are solved using the arc-length strategy. Then, assuming small amplitude vibrations of the plate about its buckled state and exploiting the static solution in the linearized vibration equations, the dynamic equations are converted to a non-standard eigenvalue problem. Finally, natural frequencies and mode shapes of the buckled cracked plate are obtained solving the eigenvalue problem. The accuracy of the proposed approach is verified using the results obtained by an experimental setup and those obtained by the finite element method. Moreover, several case studies of buckled cracked plates have been solved and effects of selected parameters have been studied.

In this study, an innovative method for crack identification in buckled plates using differential quadrature element method (DQEM) and sequential quadratic programming (SQP) method is proposed. This study consists of two steps. In first step, a numerical method is applied to calculate the frequencies of buckled cracked plates. Cracks are assumed to be open and modeled as linear rotational spring. Governing equations are extracted considering effects of shear deformations and initial geometric imperfection. Then, considering the solution as summation of static solution (postbuckling) and dynamic solution, the governing equations are converted into two different equation sets; postbuckling equations and vibration equations. The natural frequencies can be obtained solving these equation sets. In second step, SQP optimization method and the method used in first step combined to make a new method for identification of crack specification using natural frequencies. In this step, a weighted sum of square of differences between calculated frequencies and experimental frequencies considered as cost function and used to identify crack properties. Finally, the accuracy and precision of proposed method verified using some experimental and numerical case studies.