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  • An Advanced Time-Discontinuous Galerkin Finite Element Method for Structural Dynamics
  • Abstract This study presents a novel computational method for implementing the time finite element formulation for the equations of linear structural dynamics. The proposed method adopts the time-discontinuous Galerkin method, in which both the displacement and velocity variables are represented independently by second-order interpolation functions in the time domain. The solution algorithm derived utilizes a predictor/multi-corrector technique that can effectively obtain the solutions for the resulting system of coupled equations. The numerical implementation of the time-discontinuous Galerkin finite element method is verified through several benchmark problems. Numerical results are compared with exact and accepted solutions from previous literature. Since a fifth-order…
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  • On Finite Element Analysis of Fluid Flows Fully Coupled with Structural Interactions
  • Abstract The solution of fluid flows, modeled using the Navier-Stokes or Euler equations, fully coupled with structures/solids is considered. Simultaneous and partitioned solution procedures, used in the solution of the coupled equations, are briefly discussed, and advantages and disadvantages of their use are mentioned. In addition, a simplified stability analysis of the interface equations is presented, and unconditional stability for certain choices of time integration schemes is shown. Furthermore, the long-term dynamic stability of fluid-structure interaction systems is assessed by the use of Lyapunov characteristic exponents, which allow differentiating between a chaotic and a regular system behavior. Some state-of-the-art numerical solutions…
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  • A Naturally Parallelizable Computational Method for Inhomogeneous Parabolic Problems
  • Abstract A parallel numerical algorithm is introduced and analyzed for solving inhomogeneous initial-boundary value parabolic problems. The scheme is based on the method recently introduced in Sheen, Sloan, and Thomée (2000) for homogeneous problems. We give a method based on a suitable choice of multiple parameters. Our scheme allows one to compute solutions in a wide range of time. Instead of using a standard time-marching method, which is not easily parallelizable, we take the Laplace transform in time of the parabolic problems. The resulting elliptic problems can be solved in parallel. Solutions are then computed by a discrete inverse Laplace transformation.…
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  • Coupling of BEM/FEM for Time Domain Structural-Acoustic Interaction Problems
  • Abstract The BEM/FEM coupling procedure is applied to 2-D time domain structural-acoustic interaction problems. The acoustic domain for fluid or air is modeled by BEM scheme that is suitable for both finite and infinite domains, while the structure is modeled by FEM scheme. The input impact, which can be either plane waves or non-plane waves, can either be forces acting directly on the structural-acoustic system or be explosion sources. The far field or near field explosion sources which are difficult to be simulated by finite element modeling, can be simulated exactly by boundary element modeling as internal sources. In order to…
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  • Three-dimensional Numerical Simulation of Unsteady Marangoni Convection in the CZ Method using GSMAC-FEM
  • Abstract Three-dimensional (3D) unsteady numerical simulations are carried out by means of the finite element method (FEM) with the generalized simplified marker and cell (GSMAC) method in silicon melt with a non-deformable free surface with Prandtl number Pr = 1.8534 × 10-2, Marangoni number Ma = 0.0 - 6.2067 × 102, Grashof number Gr = 7.1104 × 106, and the aspect ratio As = 1.0 in the Czochralski (CZ) method. The flow state becomes unstable earlier by increasing the absolute value of the thermal coefficient of surface tension in the range of σT =0.0 - 1.5 × 10-5N/mK. Although the velocity…
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  • Molecular Dynamics Simulation of Crack Propagation in Polycrystalline Material
  • Abstract In this paper, we present a classical molecular dynamics algorithm and its implementation on Cray C90 and Fujitsu VPP700. The characters of this algorithm consist in a grid based on the block division of the atomic system and a neighbor list based on the use of a short range potential. The computer program is used for large scale simulations on a Cray C90 and a 32-node VPP700, and measurements of computational performance are reported. Then, we examine the interaction between a crack propagating and a tilt grain boundary under uniaxial tension using this computer program. The Johnson potential for α-Fe…
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  • The Meshless Local Petrov-Galerkin (MLPG) Method for Solving Incompressible Navier-Stokes Equations
  • Abstract The truly Meshless Local Petrov-Galerkin (MLPG) method is extended to solve the incompressible Navier-Stokes equations. The local weak form is modified in a very careful way so as to ovecome the so-called Babus~ka-Brezzi conditions. In addition, The upwinding scheme as developed in Lin and Atluri (2000a) and Lin and Atluri (2000b) is used to stabilize the convection operator in the streamline direction. Numerical results for benchmark problems show that the MLPG method is very promising to solve the convection dominated fluid mechanics problems.
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  • To Generate Good Triangular Meshes, Conforming to Control Spacing Requirements
  • Abstract To conduct numerical simulations by finite element methods, we often need to generate a high quality mesh, yet with a smaller number of elements. Moreover, the size of each of the elements in the mesh should be approximately equal to a given size requirement. Li et al. recently proposed a new method, named biting, which combines the strengths of advancing front and sphere packing. It generates high quality meshes with a theoretical guarantee. In this paper, we show that biting squares instead of circles not only generates high quality meshes but also has the following advantages. It is easier to…
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  • An Efficient Mesh-Free Method for Nonlinear Reaction-Diffusion Equations
  • Abstract The purpose of this paper is to develop a highly efficient mesh-free method for solving nonlinear diffusion-reaction equations in Rd, d=2, 3. Using various time difference schemes, a given time-dependent problem can be reduced to solving a series of inhomogeneous Helmholtz-type equations. The solution of these problems can then be further reduced to evaluating particular solutions and the solution of related homogeneous equations. Recently, radial basis functions have been successfully implemented to evaluate particular solutions for Possion-type equations. A more general approach has been developed in extending this capability to obtain particular solutions for Helmholtz-type equations by using polyharmonic spline…
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  • Determining the Unknown Traction of a Cracked Elastic Body Using the Inverse Technique with the Dual Boundary Element Method
  • Abstract The two-dimensional elasticity problem of an isotropic material, containing a centered-crack with unknown boundary traction is studied by the inverse procedure. The dual boundary integral equations are used to analyze the problem. While solving the ill-posed inverse problem, both of the conjugate gradient method and the regularization method are used. A scaling factor depending upon the material constant μ is introduced into the sensitivity matrix in order to keep the order of magnitude the same throughout the formulation. The result by using the displacement measurement will be compared with those by stress measurement, and an extensive discussion will be given.…
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