• Structural Engineering and Mechanics
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• v.43 no.1
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• pp.105-126
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• 2012

Based on the first-order shear deformation theory (FSDT), and the virtual work principle, an elastic analysis for axisymmetric clamped-clamped Pressurized thick truncated conical shells made of functionally graded materials have been performed. The governing equations are a system of nonhomogeneous ordinary differential equations with variable coefficients. Using the matched asymptotic method (MAM) of the perturbation theory, these equations could be converted into a system of algebraic equations with variable coefficients and two systems of differential equations with constant coefficients. For different FGM conical angles, displacements and stresses along the radius and length have been calculated and plotted.

• Wind and Structures
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• v.22 no.3
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• pp.349-368
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• 2016

A preconditioning technique is presented for a simultaneous solution to wind-membrane interaction. In the simultaneous equations, a linear elastic model was employed to deal with the fluid-structure data transfer at the interface. A Lagrange multiplier was introduced to impose the specified boundary conditions at the interface and strongly coupled simultaneous equations are derived after space and time discretization. An initial linear elastic model preconditioner and modified one were derived by treating the linearized elastic model equation as a saddle point problem, respectively. Accordingly, initial and modified fluid-structure interaction (FSI) preconditioner for the simultaneous equations were derived based on the initial and modified linear elastic model preconditioners, respectively. Wind-membrane interaction analysis by the proposed preconditioners, for two and three dimensional membranous structures respectively, was performed. Comparison was made between the performance of initial and modified preconditioners by comparing parameters such as iteration numbers, relative residuals and convergence in FSI computation. The results show that the proposed preconditioning technique greatly improves calculation accuracy and efficiency. The priority of the modified FSI preconditioner is verified. The proposed preconditioning technique provides an efficient solution procedure and paves the way for practical application of simultaneous solution for wind-structure interaction computation.

• Structural Engineering and Mechanics
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• v.38 no.2
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• pp.157-169
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• 2011

In this paper the time-dependent closed-form static solution of the suspended pre-stressed biconcave and biconvex cable trusses with unmovable, movable and elastic or viscoelastic yielding supports subjected to various types of vertical load is presented. Irvine's forms of the deflections and the cable equations are modified because the effects of the rheological behaviour needed to be incorporated in them. The concrete cable equations in the form of the explicit relations are derived and presented. From a solution of a vertical equilibrium equation for a loaded cable truss with rheological properties, the additional vertical deflection as a time-function is determined. The time-dependent closed-form model serves to determine the time-dependent response, i.e., horizontal components of cable forces and deflection of the cable truss due to applied loading at the investigated time considering effects of elastic deformations, creep strains, temperature changes and elastic supports. Results obtained by the present closed-form solution are compared with those obtained by FEM. The derived time-dependent closed-form computational model is used for a time-dependent simulation-based reliability assessment of cable trusses as is described in the second part of this paper.

• Coupled systems mechanics
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• v.10 no.2
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• pp.123-142
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• 2021

The paper deals with the study of the dispersion of quasi-Lamb waves in a hydro-elastic system consisting of an elastic plate, barotropic compressible inviscid fluid, and rigid wall. The motion of the plate is described using the exact equations of elastodynamics, however, the flow of the fluid using the linearized equations and relations of the Navier-Stokes equations. The corresponding dispersion equation is obtained and this equation is solved numerically, as a result of which the corresponding dispersion curves are constructed. The main attention is focused on the effect of the presence of the fluid and the effect of the fluid layer thickness (i.e., the fluid depth) on the dispersion curves. The influence of the problem parameters on the dispersion curves related to the quasi-Scholte wave is also considered. As a result of the analyses of the numerical results, concrete conclusions are made about the influence of the fluid depth, the rigid wall restriction on the fluid motion, and the material properties of the constituents on the dispersion curves. During the analyses, the zeroth and the first four modes of the propagating waves are considered.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Journal of Mechanical Science and Technology
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• v.18 no.12
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• pp.2148-2157
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• 2004

The paper deals with the vibration and dynamic stability of cantilevered pipes conveying fluid on elastic foundations. The relationship between the eigenvalue branches and corresponding unstable modes associated with the flutter of the pipe is thoroughly investigated. Governing equations of motion are derived from the extended Hamilton's principle, and a numerical scheme using finite element methods is applied to obtain the discretized equations. The critical flow velocity and stability maps of the pipe are obtained for various elastic foundation parameters, mass ratios of the pipe, and structural damping coefficients. Especially critical mass ratios, at which the transference of the eigenvalue branches related to flutter takes place, are precisely determined. Finally, the flutter configuration of the pipe at the critical flow velocities is drawn graphically at every twelfth period to define the order of the quasi-mode of flutter configuration.

• Structural Engineering and Mechanics
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• v.38 no.6
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• pp.753-765
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• 2011

The radial vibration behaviors of a circular cylindrical composite piezoelectric transducer (CPT) are investigated. The CPT is composed of a piezoelectric ring polarized in the radial direction and an elastic ring graded in power-law variation form along the radial direction. The governing equations for plane stress state problem under the harmonic excitation are derived and the exact solutions for both piezoelectric and functionally graded elastic rings are obtained. The characteristic equations for resonant and anti-resonant frequencies are established. The presented methodology is fit to carry out the parametric investigation for composite piezoelectric transducers (CPTs) with arbitrary thickness in radial direction. With the aid of numerical analysis, the relationship between the radial vibration behaviors of the cylindrical CPT and the material inhomogeneity index of the functionally graded elastic ring as well as the geometric parameters of the CPTs are illustrated and some important features are reported.

• Structural Engineering and Mechanics
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• v.68 no.6
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• pp.713-720
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• 2018

In this paper a new numerical method to determine the elastic curve of the simply supported beams of variable cross-section is demonstrated. In general case it needs to solve linear or small nonlinear second order differential equations with prescribed boundary conditions. For numerical solution the initial values of the slope and the deflection of the end cross-section of the beam is necessary. For obtaining the initial values a lively procedure is developed: it is a special application of the shooting method because boundary value problems can be transformed into initial value problems. As a result of these transformations the initial values of the differential equations are obtained with high accuracy. Procedure is applied for calculating of elastic curve of a simply supported beam of variable cross-section. Results of these numerical procedures, analytical solution of the linearized version and finite element method are compared. It is proved that the suggested procedure yields technically accurate results.

• Steel and Composite Structures
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• v.44 no.1
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• pp.17-31
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• 2022

This investigation studies the characteristics of wave dispersion in sigmoid functionally graded (SFG) curved beams lying on an elastic substrate for the first time. Homogenization process was performed with the help of sigmoid function and two power laws. Moreover, various materials such as Zirconia, Alumina, Monel and Nickel steel were explored as curved beams materials. In addition, curved beams were rested on an elastic substrate which was modelled based on Winkler-Pasternak foundation. The SFG curved beams' governing equations were derived according to Euler-Bernoulli curved beam theory which is known as classic beam theory and Hamilton's principle. The resulted governing equations were solved via an analytical method. In order to validate the utilized method, the obtained outcomes were compared with other researches. Finally, the influences of various parameters, including wave number, opening angle, gradient index, Winkler coefficient and Pasternak coefficient were evaluated and indicated in the form of diagrams.

• Computers and Concrete
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• v.32 no.6
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• pp.543-551
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• 2023

In this article, thermal post-buckling and primary resonance of the porous functionally graded material (FGM) beams in thermal environment considering the geometric imperfection are studied, the material properties of FGM beams are assumed to vary along the thickness of the beam, meanwhile, the porosity volume fraction, geometric imperfection, temperature, and the elastic foundation are considered, using the Euler-Lagrange equation, the nonlinear vibration equations are derived, after the dimensionless processing, the dimensionless equations of motion can be obtained. Then, the two-step perturbation method is applied to solve the vibration problems, the resonance and thermal post-buckling response relations are obtained. Finally, the functionally graded index, the porosity volume fraction, temperature, geometric imperfection, and the elastic foundation on the resonance behaviors of the FGM beams are presented. It can be found that these parameters can influence the thermal post-buckling and primary resonance problems.