• Coupled systems mechanics
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• v.13 no.3
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• pp.247-275
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• 2024

The paper studies the influence of the fluid flow velocity and flow direction in the initial state on the dispersion of the axisymmetric waves propagating in the inhomogeneously pre-stressed hollow cylinder containing this fluid. The corresponding eigenvalue problem is formulated within the scope of the three-dimensional linearized theory of elastic waves in bodies with initial stresses, and with linearized Euler equations for the inviscid compressible fluid. The discrete-analytical solution method is employed, and analytical expressions of the sought values are derived from the solution to the corresponding field equations by employing the discrete-analytical method. The dispersion equation is obtained using these expressions and boundary and related compatibility conditions. Numerical results related to the action of the fluid flow velocity and flow direction on the influence of the inhomogeneous initial stresses on the dispersion curves in the zeroth and first modes are presented and discussed. As a result of the analyses of the numerical results, it is established how the fluid flow velocity and flow direction act on the magnitude of the influence of the initial inhomogeneous stresses on the wave propagation velocity in the cylinder containing the fluid.

• Interaction and multiscale mechanics
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• v.3 no.2
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• pp.123-143
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• 2010

The essential idea of the element-free Galerkin method (EFG) is that moving least-squares (MLS) approximation are used for the trial and test functions with the variational principle (weak form). By using the weighted orthogonal basis function to construct the MLS interpolants, we derive the formulae for an improved element-free Galerkin (IEFG) method for solving three-dimensional problems in linear elasticity. There are fewer coefficients in improved moving least-squares (IMLS) approximation than in MLS approximation. Also fewer nodes are selected in the entire domain with the IEFG method than is the case with the conventional EFG method. In this paper, we selected a few example problems to demonstrate the applicability of the method.

• Transactions of the Korean Society of Automotive Engineers
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• v.3 no.3
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• pp.19-28
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• 1995

The explicit scheme for finite element analysis of sheet metal forming problems has been widely used for providing practical solutions since it improves the convergency problem, memory size and computational time especially for the case of complicated geometry and large element number. The explicit schemes in general use are based on the elastic-plastic modelling of material requiring large computation time. In the present work, rigid-plastic explicit finite element method is introduced for analysis of sheet metal forming processes in which plane strain normal anisotropy condition can be assumed by dividing the whole piece into sections. The explicit scheme is in good agreement with the implicit scheme for numerical analysis and experimental results of auto-body panels. The proposed rigid-plastic explicit finite element method can be used as robust and efficient computational method for prediction of defects and forming severity.

• Structural Engineering and Mechanics
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• v.40 no.2
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• pp.257-277
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• 2011

In this paper the geometrically nonlinear continuum plate finite element model, hitherto not reported in the literature, is developed using the total Lagrange formulation. With the layerwise displacement field of Reddy, nonlinear Green-Lagrange small strain large displacements relations (in the von Karman sense) and linear elastic orthotropic material properties for each lamina, the 3D elasticity equations are reduced to 2D problem and the nonlinear equilibrium integral form is obtained. By performing the linearization on nonlinear integral form and then the discretization on linearized integral form, tangent stiffness matrix is obtained with less manipulation and in more consistent form, compared to the one obtained using laminated element approach. Symmetric tangent stiffness matrixes, together with internal force vector are then utilized in Newton Raphson's method for the numerical solution of nonlinear incremental finite element equilibrium equations. Despite of its complex layer dependent numerical nature, the present model has no shear locking problems, compared to ESL (Equivalent Single Layer) models, or aspect ratio problems, as the 3D finite element may have when analyzing thin plate behavior. The originally coded MATLAB computer program for the finite element solution is used to verify the accuracy of the numerical model, by calculating nonlinear response of plates with different mechanical properties, which are isotropic, orthotropic and anisotropic (cross ply and angle ply), different plate thickness, different boundary conditions and different load direction (unloading/loading). The obtained results are compared with available results from the literature and the linear solutions from the author's previous papers.

• Journal of Korean Society of Steel Construction
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• v.12 no.3 s.46
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• pp.303-315
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• 2000

The main object of this study is to analyze mechanical behaviors as anisotropic three-dimensional body under various static loads. This paper presents the applicability of the finite difference method to three dimensional problem of anisotropic body. The finite difference method as applied here is generalized to anisotropic three-dimensional problem of elastic body where the governing differential equations of equilibrium of such bodies are expressed in terms of the displacement u, v, and w in the coordinates axes x, y and z, care being taken to modify the finite difference expressions to satisfy the appropriate boundary conditions. By adopting a new three dimensional finite difference modelling including elimination of pivotal difference points in the case of free boundary condition, the three dimensional problem of anisotropic body was successfully completed. Several numerical results show quick convergence and numerical validity of finite difference technique in three dimensional problem.

• Structural Engineering and Mechanics
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• v.53 no.3
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• pp.411-427
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• 2015

Based on linear elastic theory of quasicrystals, various equations and solutions for quasicrystal beams are deduced systematically and directly from plane problem of two-dimensional quasicrystals. Without employing ad hoc stress or deformation assumptions, the refined theory of beams is explicitly established from the general solution of quasicrystals and the Lur'e symbolic method. In the case of homogeneous boundary conditions, the exact equations and exact solutions for beams are derived, which consist of the fourth-order part and transcendental part. In the case of non-homogeneous boundary conditions, the exact governing differential equations and solutions under normal loadings only and shear loadings only are derived directly from the refined beam theory, respectively. In two illustrative examples of quasicrystal beams, it is shown that the exact or accurate analytical solutions can be obtained in use of the refined theory.

• Geomechanics and Engineering
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• v.6 no.3
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• pp.213-233
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• 2014

The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

• Structural Engineering and Mechanics
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• v.78 no.3
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• pp.297-303
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• 2021

In this paper, a mathematical model is used to the evaluation of thermoelastic interactions in fiber-reinforced material with a spherical cavity. With the goal of establishing the generalized thermoelastic model with thermal relaxation time are exploited. inner surface of the spherical cavity is tractions free and loaded by the uniform step in temperature. The finite element scheme is used to get the problem numerical solutions. The numerical results have been discussed graphically to show the impacts of the presence and the absence of reinforcement.

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.581-609
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• 2012

In this paper a novel non-iterative approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.5
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• pp.567-573
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• 2010

In this study, we evaluated the structural integrity and weight of a rocket motor with a torispherical dome by size optimization. Size optimization was achieved by first-order and sub-problem methods, using the Ansys Parametric Design Language (APDL). For rapid design verification, a modified 2D axisymmetric finite-element model was used, and the bolt pre-tension load was expressed as function of the ratio of the cross-sectional area. The thickness of the dome and the cylindrical part of the rocket motor were selected as the design parameters. Our results showed that the weight and structural integrity of the rocket motor at the initial design stage could be determined more rapidly and accurately with the modified 2D axisymmetric finite-element model than with the 3D finite-element model; further, the weight of the rocket motor could be saved to maximum of 17.6% within safety limit.