• Smart Structures and Systems
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• v.25 no.5
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• pp.619-630
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• 2020

This paper studies nonlinear free vibration characteristics of nonlocal magneto-electro-elastic (MEE) nanobeams resting on nonlinear elastic substrate having geometrical imperfection by considering piezoelectric reinforcement scheme. The piezoelectric reinforcement can cause an enhanced vibration behavior of smart nanobeams under magnetic field. All of previously reported studies on MEE nanobeams ignore the influences of geometric imperfections which are very substantial due to the reason that a nanobeam cannot be always perfect. Nonlinear governing equations of a smart nanobeam are derived based on classical beam theory and an analytical trend is provided to obtained nonlinear vibration frequency. This research shows that changing the volume fraction of piezoelectric constituent in the material has a great influence on vibration behavior of smart nanobeam under electric and magnetic fields. Also, it can be seen that nonlinear vibration behaviors of smart nanobeam are dependent on the magnitude of exerted electric voltage, magnetic potential, hardening elastic foundation and geometrical imperfection.

• Structural Engineering and Mechanics
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• v.71 no.5
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• pp.485-502
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• 2019

In this research, the nonlinear static, buckling and vibration analysis of viscoelastic micro-composite beam reinforced by various distributions of boron nitrid nanotube (BNNT) with initial geometrical imperfection by modified strain gradient theory (MSGT) using finite element method (FEM) are presented. The various distributions of BNNT are considered as UD, FG-V and FG-X and also, the extended rule of mixture is used to estimate the properties of micro-composite beam. The components of stress are dependent to mechanical, electrical and thermal terms and calculated using piezoelasticity theory. Then, the kinematic equations of micro-composite beam using the displacement fields are obtained. The governing equations of motion are derived using energy method and Hamilton's principle based on MSGT. Then, using FEM, these equations are solved. Finally the effects of different parameters such as initial geometrical imperfection, various distributions of nanotube, damping coefficient, piezoelectric constant, slenderness ratio, Winkler spring constant, Pasternak shear constant, various boundary conditions and three material length scale parameters on the behavior of nonlinear static, buckling and vibration of micro-composite beam are investigated. The results indicate that with an increase in the geometrical imperfection parameter, the stiffness of micro-composite beam increases and thus the non-dimensional nonlinear frequency of the micro structure reduces gradually.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.819-822
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• 2001

Fiber waviness is one of manufacturing defects encountered frequently in thick composite structures. It affects significantly on the behavior as well as strength of thick composites. Thick composites with fiber waviness have two kinds of nonliearity. One is material nonlinearity, and the other is geometrical nonliearity due to fiber waviness. There are only a few studies that have considered both material and geometrical nonlinearities. In this paper, a FEA model was proposed to predict nonlinear behavior and strength of thick composites with fiber waviness.

• Structural Engineering and Mechanics
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• v.47 no.1
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• pp.27-44
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• 2013

A finite element computational procedure for the accurate analysis of quasistatic thermorheological complex structures response is developed. The geometrical nonlinearity, arising from large displacements and rotations (but small strains), is accounted for by the total Lagrangian description of motion. The Schapery's nonlinear single-integral viscoelastic constitutive model is modified for a time-stress-temperature-dependent behavior. The nonlinear thermo-viscoelastic constitutive equations are incrementalized leading to a recursive relationship and thereby the resulting finite element equations necessitate data storage from the previous time step only, and not the entire deformation history. The Newton-Raphson iterative scheme is employed to obtain a converged solution for the non-linear finite element equations. The developed numerical model is verified with the previously published works and a good agreement with them is found. The applicability of the developed model is demonstrated by analyzing two examples with different thermal/mechanical loading histories.

• Structural Engineering and Mechanics
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• v.41 no.6
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• pp.735-750
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• 2012

This paper presents a comparison between two different procedures to deal with the geometric nonlinear analysis of space trusses, considering its structural stability aspects. The first nonlinear formulation, called positional, uses nodal positions rather than nodal displacements to describe the finite elements kinematics. The strains are computed directly from the proposed position concept, using a Cartesian coordinate system fixed in space. The second formulation, called corotational, is based on the explicit separation between rigid body motion and deformed motion. The numerical examples demonstrate the performances and the convergence of the responses for both analyzed formulations. Two numerical examples were compared, including a lattice beam with postcritical behavior. Despite the two completely different approaches to deal with the geometrical nonlinear problem, the results present good agreement.

• Structural Engineering and Mechanics
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• v.48 no.6
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• pp.879-914
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• 2013

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.

• Journal of Korean Society of Steel Construction
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• v.14 no.4
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• pp.489-497
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• 2002

Nonlinear behavior and large deformation cannot be analyzed using techniques based on linear theory. Nonetheless, they are emerging as gradually huge and complex structures. In addition, the optimum design of structure is necessary in the development of high-performance computation and numerical methods. as well as stricter design-criterion. Therefore, the structural problems in engineering that are limited to the linear region must be extended to the nonlinear region. Likewise, structural behavior must be accurately analyzed. In turn, this requires considering the expected problems beforehand. Only then can an efficient, economical, and optimized structure be designed. This paper presents the solution of the geometrical nonlinear problem of anisotropic cylindrical shell. The characteristics of the geometrical nonlinear behavior of anisotropic circular cylindrical shells may vary according to several causes. e.g., change of fibers, curvature in the circumferential direction, subtended angle, aspect, etc. Parametric studies were conducted to determine the effect of factors on the large deflection behavior of laminated shells, with interesting observations.

• Advances in nano research
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• v.9 no.3
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• pp.147-156
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• 2020

This research is related to nonlinear stability analysis of advanced microbeams reinforced by Graphene Platelets (GPLs) considering generic geometrical imperfections and thermal loading effect. Uniform, linear and nonlinear distributions of GPLs in transverse direction have been considered. Imperfection sensitivity of post-bucking behaviors of the microbeam to different kinds of geometric imperfections have been examined. Geometric imperfection is first considered to be identical as the first buckling mode, then a generic function is employed to consider sine-type, local-type and global-type imperfectness. Modified couple stress theory is adopted to incorporate size-dependent behaviors of the beam at micro scale. The post-buckling problem is solved analytically to derive load-amplitude curves. It is shown that post-buckling behavior of microbeam is dependent on the type geometric imperfection and its magnitude. Also, post-buckling load can be enhanced by adding more GPLs or selecting a suitable distribution for GPLs.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.701-711
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• 2020

This papers studies nonlinear stability and post-buckling behaviors of geometrically imperfect metal foam doubly-curved shells with eccentrically stiffeners resting on elastic foundation. Metal foam is considered as porous material with uniform and non-uniform models. The doubly-curved porous shell is subjected to in-plane compressive loads as well as a transverse pressure leading to post-critical stability in nonlinear regime. The nonlinear governing equations are analytically solved with the help of Airy stress function to obtain the post-buckling load-deflection curves of the geometrically imperfect metal foam doubly-curved shell. Obtained results indicate the significance of porosity distribution, geometrical imperfection, foundation factors, stiffeners and geometrical parameters on post-buckling characteristics of porous doubly-curved shells.

• Structural Engineering and Mechanics
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• v.58 no.6
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• pp.1109-1126
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• 2016

The present paper focuses on size optimization of double layer barrel vaults considering nonlinear behavior. In order to tackle the optimization problem an improved colliding bodies optimization (ICBO) algorithm is proposed. The important task that should be achieved before optimization of structural systems is to determine the best form having the least cost. In this study, an attempt is done to find the best form then it is optimized considering linear and non-linear behaviors. In the optimization process based on nonlinear behavior, the geometrical and material nonlinearity effects are included. A large-scale double layer barrel vault is presented as the numerical example of this study and the obtained results indicate that the proposed ICBO has better computational performance compared with other algorithms.