• Structural Engineering and Mechanics
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• v.83 no.2
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• pp.135-151
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• 2022

The generalized displacement method is a nonlinear solution scheme that follows the equilibrium path of the structure based on the development of the generalized displacement. This method traces the path uniformly with a constant amount of generalized displacement. In this article, we first develop higher-order generalized displacement methods based on multi-point techniques. According to the concept of generalized stiffness, a relation is proposed to adjust the generalized displacement during the path-following. This formulation provides the possibility to change the amount of generalized displacement along the path due to changes in generalized stiffness. We, then, introduce higher-order algorithms of variable generalized displacement method using multi-point methods. Finally, we demonstrate with numerical examples that the presented algorithms, including multi-point generalized displacement methods and multi-point variable generalized displacement methods, are capable of following the equilibrium path. A comparison with the arc length method, generalized displacement method, and multi-point arc-length methods illustrates that the adjustment of generalized displacement significantly reduces the number of steps during the path-following. We also demonstrate that the application of multi-point methods reduces the number of iterations.

• Computers and Concrete
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• v.23 no.5
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• pp.303-309
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• 2019

This study investigates axisymmetric fractional vibration of an isotropic hyperelastic semi-linear thin disc with a view to examine effects of finite deformation associated with the material of the disc and effects of fractional vibration associated with the motion of the disc. The generalized three-dimensional equation of motion is reduced to an equivalent time fraction one-dimensional vibration equation. Using the method of variable separable, the resulting equation is further decomposed into second-order ordinary differential equation in spatial variable and fractional differential equation in temporal variable. The obtained solution of the fractional vibration problem under consideration is described by product of one-parameter Mittag-Leffler and Bessel functions in temporal and spatial variables respectively. The obtained solution reduces to the solution of the free vibration problem in literature. Finally, and amongst other things, the Cauchy's stress distribution in thin disc under finite deformation exhibits nonlinearity with respect to the displacement fields whereas in infinitesimal deformation hypothesis, these stresses exhibit linear relation with the displacement field.

• Ocean Systems Engineering
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• v.6 no.4
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• pp.363-375
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• 2016

Large numbers of submarine pipelines are laid as the world now is attaching great importance to offshore oil exploitation. Free spanning of submarine pipelines may be caused by seabed unevenness, change of topology, artificial supports, etc. By combining Iwan's wake oscillator model with the differential equation which describes the vibration behavior of free-span submarine pipelines, the pipe-fluid coupling equation is developed and solved in order to study the effect of both internal and external fluid on the vibration behavior of free-span submarine pipelines. Through generalized integral transform technique (GITT), the governing equation describing the transverse displacement is transformed into a system of second-order ordinary differential equations (ODEs) in temporal variable, eliminating the spatial variable. The MATHEMATICA built-in function NDSolve is then used to numerically solve the transformed ODE system. The good convergence of the eigenfunction expansions proved that this method is applicable for predicting the dynamic response of free-span pipelines subjected to both internal flow and external current.

• Steel and Composite Structures
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• v.26 no.4
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• pp.473-484
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• 2018

Free vibration of cross-ply laminated plates using a higher-order shear deformation theory is studied. The arbitrary number of layers is oriented in symmetric and anti-symmetric manners. The plate kinematics are based on higher-order shear deformation theory (HSDT) and the vibrational behaviour of multi-layered plates are analysed under simply supported boundary conditions. The differential equations are obtained in terms of displacement and rotational functions by substituting the stress-strain relations and strain-displacement relations in the governing equations and separable method is adopted for these functions to get a set of ordinary differential equations in term of single variable, which are coupled. These displacement and rotational functions are approximated using cubic and quantic splines which results in to the system of algebraic equations with unknown spline coefficients. Incurring the boundary conditions with the algebraic equations, a generalized eigen value problem is obtained. This eigen value problem is solved numerically to find the eigen frequency parameter and associated eigenvectors which are the spline coefficients.The material properties of Kevlar-49/epoxy, Graphite/Epoxy and E-glass epoxy are used to show the parametric effects of the plates aspect ratio, side-to-thickness ratio, stacking sequence, number of lamina and ply orientations on the frequency parameter of the plate. The current results are verified with those results obtained in the previous work and the new results are presented in tables and graphs.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.1
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• pp.37-49
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• 2000

This paper is for the first essential study on the development of unified finite element formulations for solving problems related to the dynamics/thermoelastics behavior of solids. In the first part of formulations, the finite element method is based on the introduction of a new quantity defined as heat displacement, which allows the heat conduction equations to be written in a form equivalent to the equation of motion, and the equations of coupled thermoelasticity to be written in a unified form. The equations obtained are used to express a variational formulation which, together with the concept of generalized coordinates, yields a set of differential equations with the time as an independent variable. Using the Laplace transform, the resulting finite element equations are described in the transform domain. In the second, the Laplace transform is applied to both the equation of heat conduction derived in the first part and the equations of motions and their corresponding boundary conditions, which is referred to the transformed equation. Selections of interpolation functions dependent on only the space variable and an application of the weighted residual method to the coupled equation result in the necessary finite element matrices in the transformed domain. Finally, to prove the validity of two approaches, a comparison with one finite element equation and the other is made term by term.