• Journal of the Computational Structural Engineering Institute of Korea
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• v.27 no.3
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• pp.155-162
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• 2014

Using an isogeometric approach, a continuum-based shape design optimization method is developed for steady state power flow problems at high frequencies. In case the isogeometric method is employed to the shape design optimization, the NURBS basis functions used in CAD geometric modeling are directly utilized to embed the exact geometry into the computational framework so that the design parameterization for shape optimization is much easier than that in the finite element method and consequently provides the enhanced smoothness of design perturbations. Thus, exact geometric models can be used in both the response and the shape sensitivity analyses, where normal vector and curvature are continuous over the whole design space so that enhanced shape sensitivity can be expected. Through numerical examples, the developed isogeometric sensitivity is compared with finite difference one to provide excellent agreement. Also, it turns out that the proposed method works very well in the shape optimization problems.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.55-60
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• 2011

In the present work, isogeometric analysis in linear elasticity problem is conducted using the basis functions from NURBS. The objectives of isogeometric analysis introduced is to integrate both geometric modeling(CAD) and computational analysis(CAE), and this can be accomplished from direct usage of geometric modeling by NURBS as the computational mesh. The merit of the isogeometry analysis is that NURBS surface are able to represent exact geometry from the control points and knot vectors, and also subsequent refinement is relatively simple relatively. In order to verify the computer codes developed in this study, it has been applied to two structural models of which geometry are simple ; 1) circular cylinder subjected to the constant internal pressure loading, 2) square plate with circular hole at center subjected to uniform tension. The exact solutions of these two models are available. Convergence of the approximate solutions by the present code for the isogeometry analysis are investigated by mesh refinement with inserting knots (h-refinement) and by mesh refinement with order elevation of the basis functions (p-refinement).

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.3
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• pp.155-163
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• 2018

One of the major disadvantages of isogeometric analysis(IGA) is that local refinement is nearly impossible in a conventional manner because of the tensor product nature in NURBS. In this research, we investigate a local refinement scheme for isogeometric analysis, named multi-resolution approach where different resolutions are employed at each subdomain, using h-refinement relation to endow displacement compatibility on an interface of subdomains. Then, we develop shape sensitivity analysis possessing same compatibility condition as in the analysis. Numerical examples are shown to demonstrate the computational efficiency of the method in analysis especially stress concentration problem and accurate sensitivity results which is also compatible on the interface.

• Steel and Composite Structures
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• v.34 no.2
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• pp.261-277
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• 2020

The main objective of this research paper is to consider vibration analysis of vacancy defected graphene sheet as a nonisotropic structure via molecular dynamic and continuum approaches. The influence of structural defects on the vibration of graphene sheets is considered by applying the mechanical properties of defected graphene sheets. Molecular dynamic simulations have been performed to estimate the mechanical properties of graphene as a nonisotropic structure with single- and double- vacancy defects using open source well-known software i.e., large-scale atomic/molecular massively parallel simulator (LAMMPS). The interactions between the carbon atoms are modelled using Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential. An isogeometric analysis (IGA) based upon non-uniform rational B-spline (NURBS) is employed for approximation of single-layered graphene sheets deflection field and the governing equations are derived using nonlocal elasticity theory. The dependence of small-scale effects, chirality and different defect types on vibrational characteristic of graphene sheets is investigated in this comprehensive research work. In addition, numerical results are validated and compared with those achieved using other analysis, where an excellent agreement is found. The interesting results indicate that increasing the number of missing atoms can lead to decrease the natural frequencies of graphene sheets. It is seen that the degree of the detrimental effects differ with defect type. The Young's and shear modulus of the graphene with SV defects are much smaller than graphene with DV defects. It is also observed that Single Vacancy (SV) clusters cause more reduction in the natural frequencies of SLGS than Double Vacancy (DV) clusters. The effectiveness and the accuracy of the present IGA approach have been demonstrated and it is shown that the IGA is efficient, robust and accurate in terms of nanoplate problems.

• Journal of computational fluids engineering
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• v.16 no.2
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• pp.49-55
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• 2011

Turbulent flows with wavy wall are simulated using Residual-based Variational Multiscale Method (RB-VMS) which is proposed by Bazilves et al(2007) as new Large Eddy Simulation methodology. Incompressible Navier-Stokes equations are integrated using Isogeometric analysis which adopt the basis function as NURBS. The Reynolds number is 6760 based on the bulk velocity and averaged channel height. And the amplitude (${\alpha}/{\lambda}$) of wavy wall is 0.05. The computational domain is $2{\lambda}{\times}1.05{\lambda}{\times}{\lambda}$ in the streamwise, wall normal and spanwise direction. Mean quantities and turbulent statistics near wavy wall are compared with DNS results of Cherukat et al.(1998). The predicted results show good agreement with reference data.

• Journal of the Society of Disaster Information
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• v.16 no.4
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• pp.832-841
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• 2020

Purpose: This study attempts at analyzing mechanical response of functionally graded material (FGM) plates in bending. An accurate and effective numerical approach based on isogeometric analysis (IGA) combined with higher-order shear deformation plate theory to predict the nonlinear flexural behavior is developed. Method: A higher-order shear deformation theory(HSDT) which accounts for the geometric nonlinearity in the von Karman sense is presented and used to derive the equilibrium and governing equations for FGM plate in bending. The nonlinear equations are solved by the modified Newton-Raphson iterative technique. Result: The volume fraction, plate length-to-thickness ratio and boundary condition have signifiant effects on the nonlinear flexural behavior of FGM plates. Conclusion: The proposed IGA method can be used as an accurate and effective numerical tool for analyzing the mechanical responses of FGM plates in flexure.

• Journal of the Society of Disaster Information
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• v.17 no.4
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• pp.839-847
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• 2021

Purpose: This study investigates mechanical behavior of functionally graded (FG) carbon nanotube-reinforced composite (CNTRC) plate in flexure. Isogeometric analysis (IGA) method coupled with shear deformable theory of higher-order (HSDT) to analyze the nonlinear bending response is presented. Method: Shear deformable plate theory into which a polynomial shear shape function and the von Karman type geometric nonlinearity are incorporated is used to derive the nonlinear equations of equilibrium for FG-CNTRC plate in bending. The modified Newton-Raphson iteration is adopted to solve the system equations. Result: The dispersion pattern of carbon nanotubes, plate geometric parameter and boundary condition have significant effects on the nonlinear flexural behavior of FG-CNTRC plate. Conclusion: The proposed IGA method coupled with the HSDT can successfully predict the flexural behavior of FG-CNTRC plate.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.71-78
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• 2018

This paper presents the assembling of multiple patches based on the single patch isogeometric formulation for the shear deformable shell element given in the previous study. The geometrically exact shell formulation has been accomplished with the shell theory based formulation and the generalized curvilinear coordinate system directly derived from the given NURBS geometry. For the knot elements matching across adjacent surfaces, the zero-th and first parametric continuity conditions are considered and the corresponding coupling constraints are implemented by a master-slave formulation between adjacent patches. The constraints are then enforced by a substitution method for condensation of the slave variables, thereby reducing the model size. Through numerical investigations, the important features of the first parametric continuity condition are confirmed. The performance of the multi-patch shell models is also examined comparing the rate of convergence of response coefficients for the zero and first order continuity conditions and continuity in coupling boundary between two patches is confirmed.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.4
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• pp.241-247
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• 2019

A band gap refers to a certain frequency range where the propagation of mechanical waves is prohibited. This work focuses on engineering three-dimensional Kelvin lattices having external band gaps at low audible frequency ranges using a gradient-based design optimization method. Elastic wave propagation in an infinite periodic lattice is investigated by employing the Bloch theorem. We model the ligaments using a shear-deformable beam model obtained by consistent linearization in a geometrically exact beam theory. For a given lattice topology, we enlarge band gap sizes by controlling the configuration of the beam neutral axis and cross-section thickness that are smoothly parameterized by B-spline basis functions within the isogeometric analysis framework.

• Steel and Composite Structures
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• v.30 no.6
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• pp.517-534
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• 2019

In this paper, the effects of inevitable out-of-plane defects on the postbuckling behavior of single-layered graphene sheets (SLGSs) under in-plane loadings are investigated based on nonlocal first order shear deformation theory (FSDT) and von-Karman nonlinear model. A generic imperfection function, which takes the form of the products of hyperbolic and trigonometric functions, is employed to model out-of-plane defects as initial geometrical imperfections of SLGSs. Nonlinear equilibrium equations are derived from the principle of virtual work and variational formulation. The postbuckling equilibrium paths of imperfect graphene sheets (GSs) are presented by solving the governing equations via isogeometric analysis (IGA) and Newton-Raphson iterative method. Finally, the sensitivity of the postbuckling behavior of GS to shape, amplitude, extension on the surface, and location of initial imperfection is studied. Results showed that the small scale and initial imperfection effects on the postbuckling behavior of defective SLGS are important and cannot be ignored.