• Bulletin of the Korean Chemical Society
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• 제20권11호
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• pp.1281-1287
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• 1999

The low-lying electronic states of diazirine and 3,3'-dimethyldiazirine have been studied by high level ab initio quantum chemical methods. The equilibrium geometries of the ground state and the first excited singlet and triplet states have been optimized using the Hartree-Fock (HF) and complete active space SCF (CASSCF) methods, as well as using the Møller-Plesset second order perturbation (MP2) theory and the single configuration interaction (CIS) theory. It was found that the first excited singlet state is of 1 B1 symmetry resulting from the n- π* transition, while the first excited triplet state is of 3 B2 symmetry resulting from the π- π* transition. The harmonic vibrational frequencies have been calculated at the optimized geometry of each electronic state, and the scaled frequencies have been compared with the experimental frequencies available. The adiabatic and vertical transition energies from the ground electronic state to the low-lying electronic states have been estimated by means of multireference methods based on the CASSCF wavefunctions, i.e., the multiconfigurational quasidegenerate second order perturbation (MCQDPT2) theory and the CASSCF second-order configuration interaction (CASSCF-SOCI) theory. The vertical transition energies have also been calculated by the CIS method for comparison. The computed transition energies, particularly by MCQDPT2, agree well with the experimental observations, and the electronic structures of the molecules have been discussed, particularly in light of the controversy over the existence of the so-called second electronic state.

• Advances in nano research
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• 제17권2호
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• pp.167-179
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• 2024

This study investigates the stability and performance of high-resistance badminton nets through the integration of reinforced lightweight materials. By focusing on the structural and economic impacts, the research aims to enhance both the durability and practicality of badminton nets in professional and recreational settings. Using a combination of advanced material engineering techniques and economic analysis, we explore the development of nets constructed from innovative composites. These composites offer improved resistance to environmental factors, such as weather conditions, while maintaining lightweight properties for ease of installation and use. The study employs high-order shear deformation theory and high-order nonlocal theory to assess the mechanical behavior and stability of the nets. Partial differential equations derived from energy-based methodologies are solved using the Generalized Differential Quadrature Method (GDQM), providing detailed insights into the thermal buckling characteristics and overall performance. The findings demonstrate significant improvements in net stability and longevity, highlighting the potential for broader applications in both the sports equipment industry and related economic sectors. By bridging the gap between material science and practical implementation, this research contributes to the advancement of high-performance sports equipment and supports the growth of the sport economy.

• Journal of Power System Engineering
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• 제16권5호
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• pp.40-46
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• 2012

For free surface flow problem, a high-order spectral/boundary element method is adapted as an efficient numerical tool. This method is one of the most efficient numerical methods by which the nonlinear gravity waves can be simulated and hydrodynamic forces also can be calculated in time domain. In this method, the velocity potential is expressed as the sum of surface potential and body potential. Then, surface potential is solved by using the high-order spectral method and body potential is solved by using the high-order boundary element method. Using the combination of these two methods, the free surface flow problems of a submerged moving body are solved in time domain. In the present study, lifting surface theory is added to the former work to include effects of lift force. Therefore, a new formulation for the basic mathematical theory is introduced to contain the lift body in calculation.

• Structural Engineering and Mechanics
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• 제74권4호
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• pp.547-557
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• 2020

In this paper, an automatic adaptive mesh refinement procedure is presented for two-dimensional problems on the basis of a new probabilistic error estimator. First-order perturbation theory is employed to determine the lower and upper bounds of the structural displacements and stresses considering uncertainties in geometric sizes, material properties and loading conditions. A new probabilistic error estimator is proposed to reduce the mesh dependency of the responses dispersion. The suggested error estimator neglects the refinement at the critical points with stress concentration. Therefore, the proposed strategy is combined with the classic adaptive mesh refinement to achieve an optimal mesh refined properly in regions with either high gradients or high dispersion of the responses. Several numerical examples are illustrated to demonstrate the efficiency, accuracy and robustness of the proposed computational algorithm and the results are compared with the classic adaptive mesh refinement strategy described in the literature.

• Structural Engineering and Mechanics
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• 제18권1호
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• pp.79-90
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• 2004

A high precision shear deformable triangular element has been proposed for bending analysis of triangular plate. The element has twelve nodes at the three sides and four nodes inside the element. Initially the element has thirty-five degrees of freedom, which has been reduced to thirty by eliminating the degrees of freedom of the internal nodes through static condensation. Plates having different boundary conditions, side ratios (b/a) and thickness ratios (h/a = 0.001, 0.1 and 0.2) have been analyzed using the proposed shear locking free element. Concentrated and uniformly distributed transverse loads have been used for the analysis. The formulation is made based on first order shear deformation theory. For validation of the present element and formulation few results of thin triangular plate have been compared with the analytical solutions. Results for thick plate have been presented as new results.

• Advances in concrete construction
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• 제15권1호
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• pp.47-61
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• 2023

This paper examines the dynamic response of rotating nanodevices under the external harmonic load. The spinning nanosystem is made of nanoscale tubes that rotate around the central nanomotor and is mathematically modeled via high-order beam theory as well as nonclassical nonlocal theory for the size impact. According to the Hamilton principle, the dynamic motion equations are derived, then the time-dependent results are obtained using the Newmark Beta technique along with the generalized differential quadratic method. The presented results are discussed dynamic deflection, resonant frequency, and natural frequency in response to the different applicable parameters, which help develop and produce nanoelectromechanical systems (NEMS) for various applications.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1114-1124
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• 2017

Acceleration/preconditioning strategies available in the SCEPTRE radiation transport code are described. A flexible transport synthetic acceleration (TSA) algorithm that uses a low-order discrete-ordinates ($S_N$) or spherical-harmonics ($P_N$) solve to accelerate convergence of a high-order $S_N$ source-iteration (SI) solve is described. Convergence of the low-order solves can be further accelerated by applying off-the-shelf incomplete-factorization or algebraic-multigrid methods. Also available is an algorithm that uses a generalized minimum residual (GMRES) iterative method rather than SI for convergence, using a parallel sweep-based solver to build up a Krylov subspace. TSA has been applied as a preconditioner to accelerate the convergence of the GMRES iterations. The methods are applied to several problems involving electron transport and problems with artificial cross sections with large scattering ratios. These methods were compared and evaluated by considering material discontinuities and scattering anisotropy. Observed accelerations obtained are highly problem dependent, but speedup factors around 10 have been observed in typical applications.

• Steel and Composite Structures
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• 제27권1호
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• pp.109-122
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• 2018

In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

• Earthquakes and Structures
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• 제16권5호
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• pp.547-561
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• 2019

In this work, a new analytical approach using a theory of a high order hyperbolic shear deformation theory (HSDT) has been developed to study the free vibration of plates of functionally graduated material (FGM). This theory takes into account the effect of stretching the thickness. In contrast to other conventional shear deformation theories, the present work includes a new displacement field that introduces indeterminate integral variables. During the manufacturing process of these plates defects can appear as porosity. The latter can question and modify the global behavior of such plates. The materials constituting the plate are assumed to be gradually variable in the direction of height according to a simple power law distribution in terms of the volume fractions of the constituents. The motion equations are derived by the Hamilton principle. Analytical solutions for free vibration analysis are obtained for simply supported plates. The effects of stretching, the porosity parameter, the power law index and the length / thickness ratio on the fundamental frequencies of the FGM plates are studied in detail.

• Structural Engineering and Mechanics
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• 제22권5호
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• pp.599-611
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• 2006

The theory with hierarchical warping functions had been used to analyze composite thin-walled structure, laminated beam and had good results. In the present paper, a series of hierarchical warping functions are developed to analyze the cylindrical bending problems of composite lamina. These warping functions which refine through-the-thickness variation of displacements were composed of basic and corrective functions by taking into account of anisotropic, material discontinues, and transverse shear and normal strain. Then the hierarchical finite element method was used to form a numerical algorithm. The distribution of the displacements, in-plane stresses, transverse shear stresses and transverse normal stress for composite laminate were analyzed with the present model. The results show that the present model has precise mechanical response compared with the first deformation transverse theory and the corrective order affects the accuracy of result.