• Structural Engineering and Mechanics
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• 제83권2호
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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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• 제23권5호
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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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• 제6권4호
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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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• 제26권4호
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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.

• 한국전산구조공학회논문집
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• 제13권1호
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• pp.37-49
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• 2000

본 논문은 구조물의 동역학 및 열탄성 연성문제 해석을 위한 통합된 유한요소법을 개발하는데 초점을 두고있다. 첫째로, 열전도 방정식에 열변위라는 물리량을 도입하여 동역학의 운동 방정식과 유사하도록 유도한 후, 변분법과 일반좌표계를 이용하여 시간영역에서 정식화하였다. 둘째로, 두 방정식에 라플라스 변환을 동시에 도입하고, 공간변수만을 갖는 형상함수와 가중잔여법을 적용하여 유한요소식을 변환영역에서 표현하였다. 연성된 방정식을 문제의 특성에 따라서 분류하였고 정식화 과정을 검증하였다. 또한 수치해석 알고리듬이 갖는 수치 역 변환의 정성적인 경향에 대하여 검토하였다.