• Advances in nano research
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• v.8 no.2
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• pp.157-167
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• 2020

This paper studies forced vibrational behavior of porous nanocrystalline silicon nanoshells under radial dynamic loads using strain gradient theory (SGT). This type of material contains many pores inside it and also there are nano-size grains which define the material character. The formulation for nanocrystalline nanoshell is provided by first order shell theory and a numerical approach is used in order to solve nanoshell equations. SGT gives a scale factor related to stiffness hardening provided by nano-grains. For more accurate description of size effects due to nano-grains or nano-pore, their surface energy influences have been introduced. Surface energy of inclusion exhibit extraordinary influence on dynamic response of the nanoshell. Also, dynamic response of the nanoshell is affected by the scale of nano-grain and nano-pore.

• Structural Engineering and Mechanics
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• v.71 no.3
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• pp.223-232
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• 2019

Since the actuators with small- scale structures may be exposed to external reciprocal actions lead to create undesirable loads causing instability, the buckling behaviors of them are interested to make reliable or accurate actions. Therefore, the purpose of this paper is to analyze plastic buckling behavior of the micro beam structures by adopting a Conventional Mechanism-based Strain Gradient plasticity (CMSG) theory. The effect of length scale on critical force is considered for three types of boundary conditions, i.e. the simply supported, cantilever and clamped - simply supported micro beams. For each case, the stability equations of the buckling are calculated to obtain related critical forces. The constitutive equation involves work hardening phenomenon through defining an index of multiple plastic hardening exponent. In addition, the Euler-Bernoulli hypothesis is used for kinematic of deflection. Corresponding to each length scale and index of the plastic work hardening, the critical forces are determined to compare them together.

• Coupled systems mechanics
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• v.8 no.3
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• pp.247-257
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• 2019

Fee vibrational characteristics of porous steel double-coupled nanoplate system in thermo-elastic medium is studied via a refined plate model. Different pore dispersions called uniform, symmetric and asymmetric have been defined. Nonlocal strain gradient theory (NSGT) containing two scale parameters has been adopted to stablish size-dependent modeling of the system. Hamilton's principle has been adopted to stablish the governing equations. Obtained results from Galerkin's method are verified with those provided in the literature. The effects of nonlocal parameter, strain gradient, foundation parameters, porosity distributions and porosity coefficient on vibration frequencies of metal foam nanoscale plates have been examined.

• Advances in nano research
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• v.12 no.3
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• pp.231-251
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• 2022

Dynamic behavior of temperature-dependent Reddy functionally graded (RFG) nanobeam subjected to thermomagnetic effects under the action of moving point load is carried out in the present work. Both symmetric and sigmoid functionally graded material distributions throughout the beam thickness are considered. To consider the significance of strain-stress gradient field, a material length scale parameter (LSP) is introduced while the significance of nonlocal elastic stress field is considered by introducing a nonlocal parameter (NP). In the framework of the nonlocal strain gradient theory (NSGT), the dynamic equations of motion are derived through Hamilton's principle. Navier approach is employed to solve the resulting equations of motion of the functionally graded (FG) nanoscale beam. The developed model is verified and compared with the available previous results and good agreement is observed. Effects of through-thickness variation of FG material distribution, beam aspect ratio, temperature variation, and magnetic field as well as the size-dependent parameters on the dynamic behavior are investigated. Introduction of the magnetic effect creates a hardening effect; therefore, higher values of natural frequencies are obtained while smaller values of the transverse deflections are produced. The obtained results can be useful as reference solutions for future dynamic and control analysis of FG nanobeams reinforced nanocomposites under thermomagnetic effects.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2011.11a
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• pp.528-535
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• 2011

In the present, the formation of shear band under a simple shear deformation is investigated using a rate-independent elastic-plastic constitutive relations. Moreover, the strain gradient terms are incorporated to obtain a non-local plastic constitutive relation, which in turn represented using combined two-back stress hardening model. Then, the continuum damage model is also included to the proposed model. The post-localization behavior are studied by introducing a small imperfection in a work piece. The strain gradient affects the shear localization significantly such that the intensity of shear band decreases as the strain gradient coefficient increases when the J2 flow theory is employed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.11
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• pp.1685-1696
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• 2001

A novel indentation theory is proposed by examining the data from the incremental plasticity theory based finite element analyses. First the optimal data acquisition location is selected, where the strain gradient is the least and the effect of friction is negligible. This data acquisition point increases the strain range by a factor of five. Numerical regressions of obtained data exhibit that strain hardening exponent and yield strain are the two main parameters which govern the subindenter deformation characteristics. The new indentation theory successfully provides the stress-strain curve with an average error less than 5%.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.35 no.9
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• pp.1041-1050
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• 2011

An elasto-plastic finite element method using the theory of strain gradient plasticity is proposed to evaluate the size dependency of structural plasticity that occurs when the configuration size decreases to micron scale. For this method, we suggest a low-order plane and three-dimensional displacement-based elements, eliminating the need for a high order, many degrees of freedom, a mixed element, or super elements, which have been considered necessary in previous researches. The proposed method can be performed in the framework of nonlinear incremental analysis in which plastic strains are calculated and averaged at nodes. These strains are then interpolated and differentiated for gradient calculation. We adopted a strain-gradient-hardening constitutive equation from the Taylor dislocation model, which requires the plastic strain gradient. The developed finite elements are tested numerically on the basis of typical size-effect problems such as micro-bending, micro-torsion, and micro-voids. With respect to the strain gradient plasticity, i.e., the size effects, the results obtained by using the proposed method, which are simple in their calculation, are in good agreement with the experimental results cited in previously published papers.

• Advances in Computational Design
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• v.5 no.4
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• pp.349-362
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• 2020

Dynamic characteristics of a scale-dependent porous metal foam cylindrical shell under a traveling load have been explored within this article based on a numerical approach. Within the material texture of the metal foams, uniform and non-uniform porosities may be dispersed. Based upon differential quadrature method (DQM) and Laplace transforms, the equations of motion for a shear deformable scale-dependent shell may be solved numerically. Scale-dependent shell modeling has been provided based upon strain gradient elasticity. Solving the equations will give the shell deflection as a function of load speed. Also, it is reported that shell deflection relies on the porosity dispersion and strain gradient influences.

• Advances in nano research
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• v.8 no.1
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• pp.49-58
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• 2020

This paper investigates the vibration characteristics of flexoelectric nanobeams resting on viscoelastic foundation and subjected to magneto-electro-viscoelastic-hygro-thermal (MEVHT) loading. In this regard, the Nonlocal strain gradient elasticity theory (NSGET) is employed. The proposed formulation accommodates the nonlocal stress and strain gradient parameter along with the flexoelectric coefficient to accurately predict the frequencies. Further, with the aid of Hamilton's principle the governing differential equations are derived which are then solved through Galerkin-based approach. The variation of the natural frequency of MEVHT nanobeams under the influence of various parameters such as the nonlocal strain gradient parameter, different field loads, power-law exponent and slenderness ratio are also investigated.

• Steel and Composite Structures
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• v.36 no.6
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• pp.643-656
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• 2020

This article presents a comprehensive static analysis of simply supported cross-ply carbon nanotubes reinforced composite (CNTRC) laminated nanobeams under various loading profiles. The nonlocal strain gradient constitutive relation is exploited to present the size-dependence of nano-scale. New higher shear deformation beam theory with hyperbolic function is proposed to satisfy the zero-shear effect at boundaries and parabolic variation through the thickness. Carbon nanotubes (CNTs), as the reinforced elements, are distributed through the beam thickness with different distribution functions, which are, uniform distribution (UD-CNTRC), V- distribution (FG-V CNTRC), O- distribution (FG-O CNTRC) and X- distribution (FG-X CNTRC). The equilibrium equations are derived, and Fourier series function are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear or sinusoidal mechanical loadings. Numerical results are obtained to present influences of CNTs reinforcement patterns, composite laminate structure, nonlocal parameter, length scale parameter, geometric parameters on center deflection ad stresses of CNTRC laminated nanobeams. The proposed model is effective in analysis and design of composite structure ranging from macro-scale to nano-scale.