• 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.

• 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.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.

• 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.15 no.2
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• pp.225-238
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• 2003

In the present study, the finite strip analysis of a box girder to simulate a ship's hull model is carried out to investigate its inelastic post-buckling behavior and to predict its ultimate flexural strength. Residual stresses and initial geometrical imperfections are both considered in the combined material and geometrical nonlinear analysis. The von-Mises yield criterion and the Prandtl-Reuss flow theory of plasticity are applied in modeling the elasto-plastic behavior of material. The Newton-Raphson iterative process is also employed in the analysis to achieve convergence. The numerical results agree well with the experimental data. The effects of some material and geometrical parameters on the ultimate strength of the structure are also investigated.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.767-782
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• 2022

In this paper, the nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells exposed to the thermal environment and a uniformly distributed harmonic loading using a semi-analytical method is investigated. The cylindrical shell is surrounded by a nonlinear viscoelastic foundation consisting of a two-parameter Winkler-Pasternak foundation augmented by a Kelvin-Voigt viscoelastic model with a nonlinear cubic stiffness. The distribution of temperature and material constitutive of the stiffeners are continuously changed through the thickness direction. The cylindrical shell has three layers consisting of metal, FGM, and ceramic. The interior layer of the cylindrical shell is rich in metal, while the exterior layer is rich in ceramic, and the FG material is located between two layers. The nonlinear vibration problem utilizing the smeared stiffeners technique, the von Kármán equations, and the Galerkin method has been solved. The multiple scales method is utilized to examine the nonlinear vibration behavior of SSMFG cylindrical shells. The considered resonant case is 1:3:9 internal resonance and subharmonic resonance of order 1/3. The influences of different material and geometrical parameters on the vibration behavior of SSMFG cylindrical shells are examined. The results show that the angles of stiffeners, temperature, and elastic foundation parameters have a strong effect on the vibration behaviors of the SSMFG cylindrical shells.

• 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.49 no.6
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• pp.727-743
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• 2014

Geometrically nonlinear analysis of planar beam and frame structures made of functionally graded material (FGM) by using the finite element method is presented. The material property of the structures is assumed to be graded in the thickness direction by a power law distribution. A nonlinear beam element based on Bernoulli beam theory, taking the shift of the neutral axis position into account, is formulated in the context of the co-rotational formulation. The nonlinear equilibrium equations are solved by using the incremental/iterative procedure in a combination with the arc-length control method. Numerical examples show that the formulated element is capable to give accurate results by using just several elements. The influence of the material inhomogeneity in the geometrically nonlinear behavior of the FGM beam and frame structures is examined and highlighted.

• Steel and Composite Structures
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• v.33 no.2
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• pp.307-318
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• 2019

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

• 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.