• Proceedings of the Computational Structural Engineering Institute Conference
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• 2001.10a
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• pp.435-442
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• 2001

Derivation procedures of exact dynamic element stiffness matrix of shear deformable nonsymmetric thin-walled straight beams are rigorously presented for the spatial free vibration analysis. An exact dynamic element stiffness matrix is established from governing equations for a uniform beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The natural frequencies are evaluated and compared with analytic solutions or results of the analysis using ABAQUS' shell elements for the thin-walled straight beam structure in order to demonstrate the validity of this study.

• Proceedings of the KSR Conference
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• 2004.10a
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• pp.906-915
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• 2004

Derivation procedures of exact dynamic stiffness matrices of thin-walled curved beams subjected to axial forces are rigorously presented for the spatial free vibration analysis. An exact dynamic stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. Firstly this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, displacement functions of dispalcement parameters are exactly derived and finally exact stiffness matrices are determined using clement force-displacement relationships. The natural frequencies of the nonsymmetric thin-walled curved beam are evaluated and compared with analytical solutions or results by ABAQUS's shell elements in order to demonstrate the validity of this study.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2002.04a
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• pp.385-392
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• 2002

Derivation procedures of exact elastic element stiffness matrix of thin-walled curved beams are rigorously presented for the static analysis. An exact elastic element stiffness matrix is established from governing equations for a uniform curved beam element with nonsymmetric thin-walled cross section. First this numerical technique is accomplished via a generalized linear eigenvalue problem by introducing 14 displacement parameters and a system of linear algebraic equations with complex matrices. Thus, the displacement functions of displacement parameters are exactly derived and finally exact stiffness matrices are determined using member force-displacement relationships. The displacement and normal stress of the section are evaluated and compared with thin-walled straight and curved beam element or results of the analysis using shell elements for the thin-walled curved beam structure in order to demonstrate the validity of this study.

• Structural Engineering and Mechanics
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• v.4 no.1
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• pp.9-23
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• 1996

The behaviour of elasto-plastic planar arches subjected to dynamic loads in presented. The governing equations are formulated through the dynamic equations and compatibility conditions. The latter is established by applying the generalized conjugate segment analogy. Bending moments at the nodes and axial forces in the members are considered as primary variables in the elastic regime. They are supplemented by the rotations at the nodes and dislocations in the elements when plastic hinges occur. Newmark-${\beta}$ method is adopted in the time marching process. The interaction diagram of each element is treated as the yield surface for the element and the associated flow rule is enforced as plastic flow occurs. The method provides good prediction of dynamic response of elasto-plastic arches while requiring small core storage and short computer time.

• Computers and Concrete
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• v.30 no.3
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• pp.185-196
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• 2022

In this paper, the dynamic characteristics of a composite cylindrical beam made of a mechanism of carbon dioxide absorption coated on the tube core are investigated based on the classical beam theory coupled with the modified couple stress theory. The composite tube structures are assumed to be uniform along the tube length, and the energy method regarding the Hamilton principle is utilized for generating the governing equations. A powerful numerical solution, the generalized differential quadrature method (GDQM), is employed to solve the differential equations. The carbon dioxide trapping mechanism is a composite consisting of a polyacrylonitrile substrate and a cross-link polydimethylsiloxane gutter layer. Methacrylate, poly (ethylene glycol), methyl ether methacrylate, and three pedant methacrylates are all taken into account as potential mechanisms for capturing carbon dioxide. The application of the present study is helpful in the design and production of microelectromechanical systems (MEMS) and the different valuable parameters, such as the length-scale parameter, rate of section change, aspect ratio, etc., are presented in detail.

• Steel and Composite Structures
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• v.50 no.4
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• pp.459-474
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• 2024

Classical and first-order nonlocal beam theory are employed in this study to assess the thermal buckling performance of a small-scale conical, cylindrical beam. The beam is constructed from functionally graded (FG) porosity-dependent material and operates under the thermal conditions of the environment. Imperfections within the non-uniform beam vary along both the radius and length direction, with continuous changes in thickness throughout its length. The resulting structure is functionally graded in both radial and axial directions, forming a bi-directional configuration. Utilizing the energy method, governing equations are derived to analyze the thermal stability and buckling characteristics of a nanobeam across different beam theories. Subsequently, the extracted partial differential equations (PDE) are numerically solved using the generalized differential quadratic method (GDQM), providing a comprehensive exploration of the thermal behavior of the system. The detailed discussion of the produced results is based on various applied effective parameters, with a focus on the potential application of nanotubes in enhancing sports bikes performance.

• Advances in concrete construction
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• v.17 no.4
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• pp.187-210
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• 2024

Cantilever structures demonstrate diverse nonlocal effects, resulting in either stiffness hardening or dynamic softening behaviors, as various studies have indicated. This research delves into the free and forced vibration analysis of rotating nanoscale cylindrical beams and tubes under external dynamic stress, aiming to thoroughly explore the nonlocal impact from both angles. Utilizing Euler-Bernoulli and Reddy beam theories, in conjunction with higher-order tube theory and Hamilton's principle, nonlocal governing equations are derived with precise boundary conditions for both local and nonlocal behaviors. The study specifically examines two-dimensional functionally graded materials (2D-FGM), characterized by axially functionally graded (AFG) and radial porosity distributions. The resulting partial differential equations are solved using the generalized differential quadrature element method (GDQEM) and Newmark-beta procedures to acquire time-dependent results. This investigation underscores the significant influence of boundary conditions when nonlocal forces act on cantilever structures.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.32 no.1B
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• pp.21-27
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• 2012

The HLLL scheme, proposed by T. Linde, determines all the wave speeds from the initial states because the middle wave is evaluated by the introduction of a generalized entropy function. The scheme is considered a genuine successor to the original HLL scheme because it is completely separated form the Roe's linearization scheme unlike the HLLE scheme and does not rely on the exact solution unlike the HLLC scheme. In this study, a numerical model was configured by the HLLL scheme with the total energy as a generalized entropy function to solve governing equations, which are the one-dimensional shallow water equations without source terms and with an additional conserved variable relating a concentration. Despite the limitations of the first order solutions, results to three cases with the exact solutions were generally accurate. The HLLL scheme appeared to be superior in comparison with the other HLL-type schemes. In particular, the scheme gave fairly accurate results in capturing the front of wetting and drying. However, it revealed shortcomings of more time-consuming calculations compared to the other schemes.

• Journal of the Korean GEO-environmental Society
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• v.15 no.3
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• pp.41-48
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• 2014

Experimental study of sedimentation and self-weight consolidation has been primary research area in dredged soil. However, good quality of the dredged soil and minimum water pollution caused by the pumping of reclaimed soil require intensive study of the flow characteristics of dredged material due to dumping. In this study, continuity and the equilibrium equations for mass flow assuming single phase was derived to simulate mass flow in dredged containment area. To optimize computation and modeling time for three dimensional geometry and boundary conditions, depth integration is applied to governing equations to consider three dimensional topography of the site. Petrov-Galerkin formulation is applied in spatial discretization of governing equations. Generalized trapezoidal rule is used for time integration, and Newton iteration process approximated the solution. DG and CDG technique were used for weighting matrix in discontinuous test function in dredged flow analysis, and numerical stability was evaluated by performed a square slump simulation. A comparative analysis for numerical methods showed that DG method applied to SU / PG formulation gives minimal pseudo oscillation and reliable numerical results.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.12
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• pp.2012-2018
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• 2004

The vibration of a semi-circular pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the geometric nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed from the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized-$\alpha$ method. From these results, we should consider the geometric nonlinearity to analyze dynamics of a semi-circular pipe conveying fluid more precisely.