• Structural Engineering and Mechanics
• /
• v.70 no.5
• /
• pp.525-534
• /
• 2019

An analytical research on buckling of simply supported thin plate with variable thickness under bi-axial compression is presented in this paper. Combining the perturbation technique, Fourier series expansion and Galerkin methods, the linear governing differential equation of the plate with arbitrary thickness variation under bi-axial compression is solved and the analytical expression of the critical buckling load is obtained. Based on that, numerical analysis is carried out for the plates with different thickness variation forms and aspect ratios under different bi-axial compressions. Four different thickness variation forms including linear, parabolic, stepped and trigonometric have been considered in this paper. The calculated critical buckling loads and buckling modes are presented and compared with the published results in the tables and figures. It shows that the analytical expressions derived by the theoretical method in this paper can be effectively used for buckling analysis of simply supported thin plates with arbitrary thickness variation, especially for the stepped thickness that used in engineering widely.

• Nuclear Engineering and Technology
• /
• v.41 no.5
• /
• pp.649-654
• /
• 2009

The finite element based lattice Boltzmann method (FELBM) has been developed to model complex fluid domain shapes, which is essential for studying fluid-structure interaction problems in commercial nuclear power systems, for example. The present study addresses a new finite element formulation of the lattice Boltzmann equation using a general weighted residual technique. Among the weighted residual formulations, the collocation method, Galerkin method, and method of moments are used for finite element based Lattice Boltzmann solutions. Different finite element geometries, such as triangular, quadrilateral, and general six-sided solids, were used in this work. Some examples using the FELBM are studied. The results were compared with both analytical and computational fluid dynamics solutions.

• Coupled systems mechanics
• /
• v.2 no.2
• /
• pp.159-174
• /
• 2013

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.04a
• /
• pp.341-348
• /
• 2004

This paper presents a modeling technique of cracks by combined extended and superposed finite element method (XSFEM) which is a combination of the extended finite element method (XFEM) and the mesh superposition method (sversion FEM). In the proposed method, the near-tip field is modeled by a superimposed patch consisting of quarter point elements and the rest of the discontinuity is treated by the XFEM. The actual crack opening in this method is measured by the sum of the crack openings of XFEM and SFEM in transition region. This method retains the strong point of the XFEM so it can avoid remeshing in crack evolution and trace the crack growth by translation or rotation of the overlaid mesh and the update of the nodes to be enriched by step functions. Moreover, the quadrature of the Galerkin weak form becomes simpler. Numerical experiments are provided to demonstrate the effectiveness and robustness of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.1
• /
• pp.17-35
• /
• 2016

In this study, the dynamic behaviour of a rotating Timoshenko beam when under the actions of a variable magnitude load moving at non-uniform speed is carried out. The effect of cross-sectional dimension and damping on the flexural motions of the elastic beam was neglected. The coupled second order partial differential equations incorporating the effects of rotary and gyroscopic moment describing the motions of the beam was scrutinized in order to obtain the expression for the dynamic deflection and rotation of the vibrating system using an elegant technique called Galerkin's Method. Analyses of the solutions obtained were carried out and various results were displayed in plotted curve. It was found that the response amplitude of the simply supported beam increases with an increase in the value of the foundation reaction modulus. Effects of other vital structural parameters were also established.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2006.05a
• /
• pp.1721-1725
• /
• 2006

유한요소법으로 공학적 문제를 해결할 때에는 적절한 모델링을 통하여 가장 빠르고 정확한 해를 얻도록 해야 한다. 유체 흐름의 기본 변수인 속도는 그 공간 도함수가 요소간에 불연속을 이루게 된다. 속도의 공간 도함수는 기본적으로 유체에서의 응력, 압력, 및 와도 등과 밀접한 관련이 있다. 또한 이러한 요소간의 속도의 공간 도함수에서 발생하는 불연속의 크기는 요소망이 세분화되어 감에 따라 감소하면서 정확한 해에 수렴하게 된다. 즉 속도의 공간 도함수를 대상으로 오차에 정도를 판단하는 것이 기존의 유한요소 모델의 타당성을 판단하는 기준으로 적합함을 알 수 있다.

• Korea-Australia Rheology Journal
• /
• v.11 no.3
• /
• pp.247-253
• /
• 1999

The growth of a spherical vapor bubble contained in a large body of upper convected Maxwell fluid is theoretically analyzed under the devolatilization condition of polymer by using a Galerkin FEM in the Lagrangian frame. Using the finite element technique, a fully explicit numerical scheme is developed both for the calculation of pressure distribution and for the tracking of bubble surface. Oscillatory behavior in bubble radius is observed during growth and the oscillatory behavior is found to be due to the interaction of mass transfer resistance and elasticity. It is found that the elasticity of fluid accelerates the growth and removal of volatile component. It is also found that the bubble growth in the devolatilization of polymers is affected by both mass transfer resistance and viscoelasticity of fluids.

• Water Engineering Research
• /
• v.2 no.3
• /
• pp.161-169
• /
• 2001

Present study deals with the development of a numerical model for the estimation of net annual recharge by coupling the Galerkin's finite element flow simulationl model with the Gauss-Newton-Marquardt optimization technique. The developed coupled numerical model is applied for estimating net annual recharge for Mahi Right Bank Canal (MRBC) project the norms of Groundwater Resources Estimation committee (1984, 1997) and Indian Agricultural research Institute(1983). It is observed that the estimated net recharge by inverse modeling is closer to the net recharge estimated using the water balance approach. Further it is observed that the computed head distribution from the estimated recharge agree closely with the observed head distribution. The study concludes that the developed model for inverse modeling can be successfully applied to large groundwater system involving regional aquifers where reliable recharge estimation always requires considerable time and financial resources.

• Structural Engineering and Mechanics
• /
• v.56 no.1
• /
• pp.85-106
• /
• 2015

Postbuckling of thick plates made of functionally graded material (FGM) subjected to in-plane compressive, thermal and thermomechanical loads is investigated in this work. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation. Thermomechanical non-homogeneous properties are considered to be temperature independent, and graded smoothly by the distribution of power law across the thickness in the thickness in terms of the volume fractions of constituents. By employing the higher order shear deformation plate theory together the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect FGM plates are derived. The Galerkin technique is used to determine the buckling loads and postbuckling equilibrium paths for simply supported plates. Numerical examples are presented to show the influences of power law index, foundation stiffness and imperfection on the buckling and postbuckling loading capacity of the plates.

• Steel and Composite Structures
• /
• v.15 no.1
• /
• pp.57-79
• /
• 2013

This paper studies the dynamic instability of laminated composite plates under thermal and arbitrary in-plane periodic loads using first-order shear deformation plate theory. The governing partial differential equations of motion are established by a perturbation technique. Then, the Galerkin method is applied to reduce the partial differential equations to ordinary differential equations. Based on Bolotin's method, the system equations of Mathieu-type are formulated and used to determine dynamic instability regions of laminated plates in the thermal environment. The effects of temperature, layer number, modulus ratio and load parameters on the dynamic instability of laminated plates are investigated. The results reveal that static and dynamic load, layer number, modulus ratio and uniform temperature rise have a significant influence on the thermal dynamic behavior of laminated plates.