• Structural Engineering and Mechanics
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• v.48 no.1
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• pp.125-150
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• 2013

This paper intends to present an application of isogeometric analysis in crack problems. An isogeometric formula is developed based on NURBS basis functions - enriched and adopted via X-FEM enrichment functions. The proposed method which is represented by the combination of the two above-mentioned methods, first by using NURBS functions models the geometry exactly and then by defining level set function on domain, identifies available discontinuity in elements. Additional DOFs are allocated to elements containing the crack and X-FEM enrichment functions enrich approximate solution. Moreover, a subelement refinement technique is used to improve the accuracy of integration by the Gauss quadrature rule. Finally, several numerical examples are illustrated to demonstrate the effectiveness, robustness and accuracy of the proposed method during calculation of crack parameters.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.365-372
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• 2004

A new finite element model will be presented to analyze the nonlinear behavior of not only RC beams and slabs, but also RC beams strengthened by a patch repair. The numerical approach is based on the p-version degenerate shell element including theory of anisotropic laminated composites, theory of materially and geometrically nonlinear plates. In the nonlinear formulation of this model, the total Lagrangian formulation is adopted with large deflections and moderate rotations being accounted for in the sense of von Karman hypothesis. The material model is based on hardening rule, crushing condition, plate-end debonding strength model and so on. The Gauss-Lobatto numerical quadrature is applied to calculate the stresses at the nodal points instead of Gauss points. The validity of the proposed p-version finite element model is demonstrated through several numerical examples for the load-deflection curves, the ultimate loads, and the failure modes of reinforced connote slabs and RC beams bonded with steel plates or FRP plates compared with available experimental and numerical results.

• Advances in materials Research
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• v.8 no.4
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• pp.259-274
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• 2019

Flexoelectric effect has a major role on mechanical responses of piezoelectric materials when their dimensions become submicron. Applying differential quadrature (DQ) method, the present article studies dynamic characteristics of a small scale beam made of piezoelectric material considering flexoelectric effect. In order to capture scale-dependency of such piezoelectric beams, nonlocal elasticity theory is utilized and also surface effects are included for better structural modeling. Governing equations have been derived by utilizing Hamilton's rule with the assumption that the scale-dependent beam is subjected to thermal environment leading to uniform temperature variation across the thickness. Obtained results based on DQ method are in good agreement with previous data on pizo-flexoelectric beams. Finally, it would be indicated that dynamic response characteristics and vibration frequencies of the nano-size beam depends on the existence of flexoelectric influence and the magnitude of scale factors.

• Computers and Concrete
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• v.17 no.5
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• pp.567-578
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• 2016

As concrete is most usable material in construction industry it's been required to improve its quality. Nowadays, nanotechnology offers the possibility of great advances in construction. For the first time, the nonlinear buckling of straight concrete columns armed with single-walled carbon nanotubes (SWCNTs) resting on foundation is investigated in the present study. The column is modelled with Euler-Bernoulli and Timoshenko beam theories. The characteristics of the equivalent composite being determined using mixture rule. The foundation around the column is simulated with spring and shear layer. Employing nonlinear strains-displacements, energy methods and Hamilton's principal, the governing equations are derived. Differential quadrature method (DQM) is used in order to obtain the buckling load of structure. The influences of volume percent of SWCNTs, geometrical parameters, elastic foundation and boundary conditions on the buckling of column are investigated. Numerical results indicate that reinforcing the concrete column with SWCNTs, the structure becomes stiffer and the buckling load increases with respect to concrete column armed with steel.

• Wind and Structures
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• v.25 no.4
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• pp.381-395
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• 2017

Nonlinear vibration and instability of cylindrical shell conveying fluid-nanoparticles mixture flow are studied in this article. The surrounding elastic medium is modeled by Pasternak foundation. Mixture rule is used for obtaining the effective viscosity and density of the fluid-nanoparticles mixture flow. The material properties of the elastic medium and cylindrical shell are assumed temperature-dependent. Employing first order shear deformation theory (FSDT), the motion equations are derived using energy method and Hamilton's principal. Differential quadrature method (DQM) is used for obtaining the frequency and critical fluid velocity. The effects of different parameters such as volume percent of nanoparticles, boundary conditions, geometrical parameters of cylindrical shell, temperature change, elastic foundation and fluid velocity are shown on the frequency and critical fluid velocity of the structure. Results show that with increasing volume percent of nanoparticles in the fluid, the frequency and critical fluid velocity will be increases.

• Journal of Aerospace System Engineering
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• v.10 no.1
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• pp.8-14
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• 2016

The optimal estimation of a bearing only target tracking problem be achieved through the solution of the Fokker-Planck equation and the Bayesian update. Recently, a nonlinear filtering algorithm using a direct quadrature method of moments in which the associated Fokker-Planck equation can be propagated efficiently and accurately was proposed. Although this approach has demonstrated its promising in the field of nonlinear filtering in several examples, the "degeneracy" phenomenon, similar to that which exists in a typical particle filter, occasionally appears because only the weights are updated in the modified Bayesian rule in this algorithm. Therefore, in this paper to enhance the performance, a more stable measurement update process based upon the update equation in the Extended Kalman filters and a more accurate initialization and re-sampling strategy for weight and abscissas are proposed. Simulations are used to show the effectiveness of the proposed filter and the obtained results are promising.

• Steel and Composite Structures
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• v.28 no.3
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• pp.381-388
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• 2018

In this paper, forced vibration of micro cylindrical shell reinforced by functionally graded carbon nanotubes (FG-CNTs) is presented. The structure is subjected to transverse harmonic load and modeled by beam model. The size effects are considered based on strain gradient theory containing three small scale parameters. The mixture rule is used for obtaining the effective material properties of the structure. Based on sinusoidal shear deformation theory of beam, energy method and Hamilton's principle, the motion equations are derived. Applying differential quadrature method (DQM) and Newmark method, the frequency curves of the structure are plotted. The effect of different parameters including, CNTs volume percent and distribution type, boundary conditions, size effect and length to thickness ratio on the frequency curves of the structure is studied. Numerical results indicate that the dynamic deflection of the FGX-CNT-reinforced cylindrical is lower with respect to other type of CNT distribution.

• Journal of Mechanical Science and Technology
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• v.20 no.11
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• pp.1881-1890
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• 2006

In this paper, a Petrov-Galerkin natural element method (PG-NEM) based upon the natural neighbor concept is presented for the free vibration and dynamic response analyses of two-dimensional linear elastic structures. A problem domain is discretized with a finite number of nodes and the trial basis functions are defined with the help of the Voronoi diagram. Meanwhile, the test basis functions are supported by Delaunay triangles for the accurate and easy numerical integration with the conventional Gauss quadrature rule. The numerical accuracy and stability of the proposed method are verified through illustrative numerical tests.

• Advances in nano research
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• v.8 no.4
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• pp.283-292
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• 2020

In the present research, differential quadrature (DQ) method has been utilized for investigating free vibrations of porous functionally graded (FG) micro/nano beams in thermal environments. The exact location of neutral axis in FG material has been assumed where the material properties are described via porosity-dependent power-law functions. A scale factor related to couple stresses has been employed for describing size effect. The formulation of scale-dependent beam has been presented based upon a refined beam theory needless of shear correction factors. The governing equations and the associated boundary conditions have been established via Hamilton's rule and then they are solved implementing DQ method. Several graphs are provided which emphasis on the role of porosity dispersion type, porosity volume, temperature variation, scale factor and FG material index on free vibrational behavior of small scale beams.

• Smart Structures and Systems
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• v.20 no.5
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• pp.583-593
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• 2017

This research deals with the nonlocal temperature-dependent dynamic buckling analysis of embedded sandwich micro plates reinforced by functionally graded carbon nanotubes (FG-CNTs). The material properties of structure are assumed viscoelastic based on Kelvin-Voigt model. The effective material properties of structure are considered based on mixture rule. The elastic medium is simulated by orthotropic visco-Pasternak medium. The motion equations are derived applying Sinusoidal shear deformation theory (SSDT) in which the size effects are considered using Eringen's nonlocal theory. The differential quadrature (DQ) method in conjunction with the Bolotin's methods is applied for calculating resonance frequency and dynamic instability region (DIR) of structure. The effects of different parameters such as volume percent of CNTs, distribution type of CNTs, temperature, nonlocal parameter and structural damping on the dynamic instability of visco-system are shown. The results are compared with other published works in the literature. Results indicate that the CNTs have an important role in dynamic stability of structure and FGX distribution type is the better choice.