• Journal of Korea Game Society
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• v.7 no.2
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• pp.11-20
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• 2007

This paper proposes a real-time simulation technique for thin shells undergoing large deformation. Shells are thin objects such as leaves and papers that can be abstracted as 2D structures. Development of a satisfactory physical model that runs in real-time but produces visually convincing animation of thin shells has been remaining a challenge in computer graphics. Rather than resorting to shell theory which involves the most complex formulations in continuum mechanics, we adopt the energy functions from the discrete shells proposed by Grinspun et al. For real-time integration of the governing equation, we develop a modal warping technique for shells. This new simulation framework results from making extensions to the original modal warping technique which was developed for the simulation of 3D solids. We report experimental results, which show that the proposed method runs in real-time even for large meshes, and that it can simulate large bending and/or twisting deformations with acceptable realism.

• Smart Structures and Systems
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• v.21 no.3
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• pp.279-286
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• 2018

The free longitudinal vibration of a circular truncated nanocone is investigated based on the nonlocal elasticity theory. Exact analytical formulations for tapered nanostructures are derived and the nonlinear differential governing equation of motion is developed. The nonlocal small scale effect unavailable in classical continuum theory is addressed to reveal the long-range interaction of atoms implicated in nonlocal constitutive relation. Unlike most previous studies applying the truncation method to the infinite higher-order differential equation, this paper aims to consider all higher-order terms to show the overall nonlocality. The explicit solution of nonlocal stress for longitudinal deformation is determined and it is an infinite series incorporating the classical stress derived in classical mechanics of materials and the infinite higher-order derivative of longitudinal displacement. Subsequently, the first three modes natural frequencies are calculated numerically and the significant effects of nonlocal small scale and vertex angle on natural frequencies are examined. The coupling phenomenon of natural frequency is observed and it is induced by the combined effects of nonlocal small scale and vertex angle. The critical value of nonlocal small scale is defined, and after that a new proposal for determining the range of nonlocal small scale is put forward since the principle of choosing the nonlocal small scale is still unclear at present. Additionally, two different types of nonlocal effects, namely the nonlocal stiffness weakening and strengthening, reversed phenomena existing in nanostructures are observed and verified. Hence the opposite nonlocal effects are resolved again clearly. The nano-engineers dealing with a circular truncated nanocone-based sensors and oscillators may benefit from the present work.

• Bulletin of the Korean Chemical Society
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• v.21 no.9
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• pp.882-890
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• 2000

Ab initio calculations are carried out on protonation equilibria of 5-memberedheteroaromatic aldehydes (5MHAs;heteroatom Y = NH, O, PH,and S and substituentZ = NH2, OCH3, SCH3, CH3, H, Cl, CHO, CN,NO2) at the $MP2}6-31G*$ level. Naturalbond orbital (NBO) analyses show that the optimal localized natural Lewis structures of the protonated aldehydes,(P), are ortho (C3) protonated (for Y = O, PH and S) and N-pro-tonated (for Y = NH) forms in contrast to the standard structural Lewis formula for aldehydes, (R). The delo-calizability of ${\pilone}-pairon$ the heteroatom $(n{\pi}(Y))$ is in the order Y = NH > O > S > PH. The transmission efficiency of (Z) substituent effects to the carbonyl moiety run parallel to the delocalizability of $n{\pi}(Y)$ for R,but is dominantly influenced by the cationic charge on $C{\alpha}(C{\alpha}+)$ for P, which is in the reverse order of thede-localizability of $n{\pi}(Y).$ The Hammett ${\rho}values$ for variation of Z in the protonation are determined by the dif-ference in the transmission efficiencies between Pand R stateat simple interpretation of their magnitude is not warranted. However,the magnitude of the gas-phase ${\rho}z+$ values decreases as the level ofcomputation is raised from RHF/3-21G* to RHF/6-31G* and to $MP2}6-31G*$ but increases again at the MP4SDQ/6-31G* level. Further decrease occurs when solvent effect (water) is accounted for by the SCRF method. Comparison of the SCRF ${\rho}z+values$ with those determined in the aqueous acid solution for Y = S and CHCH shows inadequacy of accounting for the solvent effects on the ${\rho}values$ by a continuum model. It is noteworthy that semiempirical calculations, especially theAM1 method, give even lower magnitude of the gas-phase ${\rho}values.

• Smart Structures and Systems
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• v.19 no.1
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• pp.105-113
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• 2017

A microstructure-dependent dynamic model for silicon nanobeams with axial motion is developed by considering the effects of nonlocal elasticity and surface energy. The nanobeam is considered to subject to both transverse and longitudinal loads arising from nanostructural surface effect and all positive directions of physical quantities are defined clearly prior to modeling so as to clarify the confusions of sign in governing equations of previous work. The nonlocal and surface effects are taken into consideration in the dynamic behaviors of silicon nanobeams with axial motion including circular natural frequency, vibration mode, transverse displacement and critical speed. Various supporting conditions are presented to investigate the circular frequencies by a numerical method and the effects of many variables such as nonlocal nanoscale, axial velocity and external loads on non-dimensional circular frequencies are addressed. It is found that both nonlocal and surface effects play remarkable roles on the dynamics of nanobeams with axial motion and cause the frequencies and critical speed to decrease compared with the classical continuum results. The comparisons of the non-dimensional calculation values by present and previous studies validate the correctness of the present work. Additionally, numerical examples for silicon nanobeams with axial motion are addressed to show the nonlocal and surface effects on circular frequencies intuitively. Results obtained in this paper are helpful for the design and optimization of nanobeam-like microstructures based sensors and oscillators at nanoscale with desired dynamic mechanical properties.

• Advances in nano research
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• v.7 no.1
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• pp.39-49
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• 2019

This paper focuses on two main objectives. The first one is to exploit an energy equivalent model and finite element method to evaluate the equivalent Young's modulus of single walled carbon nanotubes (SWCNTs) at any orientation angle by using tensile test. The calculated Young's modulus is validated with published experimental results. The second target is to exploit the finite element simulation to investigate mechanical buckling and natural frequencies of SWCNTs. Energy equivalent model is presented to describe the atomic bonding interactions and their chemical energy with mechanical structural energies. A Program of Nanotube modeler is used to generate a geometry of SWCNTs structure by defining its chirality angle, overall length of nanotube and bond length between two adjacent nodes. SWCNTs are simulated as a frame like structure; the bonds between each two neighboring atoms are treated as isotropic beam members with a uniform circular cross section. Carbon bonds is simulated as a beam and the atoms as nodes. A finite element model using 3D beam elements is built under the environment of ANSYS MAPDL environment to simulate a tensile test and characterize equivalent Young's modulus of whole CNT structure. Numerical results are presented to show critical buckling loads, axial and transverse natural frequencies of SWCNTs with different orientation angles and lengths. The understanding of mechanical behaviors of CNTs are essential in developing such structures due to their great potential in wide range of engineering applications.

• Advances in nano research
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• v.14 no.3
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• pp.211-224
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• 2023

This work presents a modified analytical model for the bending behavior of axially functionally graded (AFG) carbon nanotubes reinforced composite (CNTRC) nanobeams. New higher order shear deformation beam theory is exploited to satisfy parabolic variation of shear through thickness direction and zero shears at the bottom and top surfaces.A Modified continuum nonlocal strain gradient theoryis employed to include the microstructure and the geometrical nano-size length scales. The extended rule of the mixture and the molecular dynamics simulations are exploited to evaluate the equivalent mechanical properties of FG-CNTRC beams. Carbon nanotubes reinforcements are distributed axially through the beam length direction with a new power graded function with two parameters. The equilibrium equations are derived with associated nonclassical boundary conditions, and Navier's procedure are used to solve the obtained differential equation and get the response of nanobeam under uniform, linear, or sinusoidal mechanical loadings. Numerical results are carried out to investigate the impact of inhomogeneity parameters, geometrical parameters, loadings type, nonlocal and length scale parameters on deflections and stresses of the AFG CNTRC nanobeams. The proposed model can be used in the design and analysis of MEMS and NEMS systems fabricated from carbon nanotubes reinforced composite nanobeam.

• Earthquakes and Structures
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• v.26 no.3
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• pp.239-249
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• 2024

A new layered shear continuum model box was developed to address the dynamic response issues of buried oil and gas pipelines under multi-point excitation. Vibration table tests were conducted to investigate the seismic response of buried pipelines and the surrounding soil under longitudinal multi-point excitation. A nonlinear model of the pipeline-soil interaction was established using ABAQUS finite element software for simulation and analysis. The seismic response characteristics of the pipeline and soil under longitudinal multi-point excitation were clarified through vibration table tests and simulation. The results showed good consistency between the simulation and tests. The acceleration of the soil and pipeline exhibited amplification effects at loading levels of 0.1 g and 0.2 g, which significantly reduced at loading levels of 0.4 g and 0.62 g. The peak acceleration increased with increasing loading levels, and the peak frequency was in the low-frequency range of 0 Hz to 10 Hz. The amplitude in the frequency range of 10 Hz to 50 Hz showed a significant decreasing trend. The displacement peak curve of the soil increased with the loading level, and the nonlinearity of the soil resulted in a slower growth rate of displacement. The strain curve of the pipeline exhibited a parabolic shape, with the strain in the middle of the pipeline about 3 to 3.5 times larger than that on both sides. This study provides an effective theoretical basis and test basis for improving the seismic resistance of buried oil and gas pipelines.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.37 no.1
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• pp.1-7
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• 2017

In general, the large loads which are applied from explosion, impact, earthquake and wind at a short time caused the materials of structures to large deformations, rotations and strains locally. If such phenomena will be analyzed, hydrocodes which can be considered fluid-structure interaction under computational continuum mechanics are inevitably needed. Also, the explosion mechanism is so complicated, it is reasonable that the behaviors of structure are predicted through explosion analyses and experiment at the same time. But, unfortunately, it is true that explosion experiments are limited to huge cost, large experiment facilities and safety problems. Therefore, in this study, it is shown that the results of explosion analyses using the AUTODYN are agreed with those of existing explosion experiments for reinforced concrete slabs within reasonable error limits. And the explosion damage of the same reinforced concrete slab are assessed for quite different reinforcement arrangement spacings, concrete cover depths, and vertical reinforcements. From the explosion analyses, it is known that the more the ratio of slab thickness to reinforcement arrangement spacing is increased, and small-diameter reinforcements are used than large-diameter reinforcements on the same reinforcement ratio, and vertical reinforcements are used, the more the anti-knock capacities are improved.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.1
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• pp.75-82
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• 2007

This paper addresses a method for shape optimization of a continuous elastic body considering stability, i.e., buckling behavior. The sensitivity formula for critical load is analytically derived and expressed in terms of shape variation, based on the continuum formulation of the stability problem. Unlike the conventional finite difference method (FDM), this method is efficient in that only a couple of analyses are required regardless of the number of design parameters. Commercial software such as ANSYS can be employed since the method requires only the result of the analysis in computation of the sensitivity. Though the buckling problem is more efficiently solved by structural elements such as a beam and shell, elastic solids have been chosen for the buckling analysis because solid elements can generally be used for any kind of structure whether it is thick or thin. Sensitivity is then computed by using the mathematical package MATLAB with the initial stress and buckling analysis of ANSYS. Several problems we chosen in order to illustrate the efficiency of the presented method. They are applied to the shape optimization problems to minimize weight under allowed critical loads and to maximize critical loads under same volume.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.24 no.1
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• pp.1-7
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• 2011

In this paper, based on an isogeometric approach, we have developed a shape design optimization method for plane elasticity problems subjected to design-dependent loads. The conventional shape optimization using the finite element method has some difficulties in the parameterization of geometry. In an isogeometric analysis, however, the geometric properties are already embedded in the B-spline basis functions and control points so that it has potential capability to overcome the aforementioned difficulties. The solution space for the response analysis can be represented in terms of the same NURBS basis functions to represent the geometry, which yields a precise analysis model that exactly represents the normal and curvature depending on the applied loads. A continuum-based isogeometric adjoint sensitivity is extensively derived for the plane elasticity problems under the design-dependent loads. Through some numerical examples, the developed isogeometric sensitivity analysis method is verified to show excellent agreement with finite difference sensitivity.