Element Nodes (element + node)

Distribution by Scientific Domains


Selected Abstracts


Modelling and process optimization for functionally graded materials

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2005
Ravi S. Bellur-Ramaswamy
Abstract We optimize continuous quench process parameters to produce functionally graded aluminium alloy extrudates. To perform this task, an optimization problem is defined and solved using a standard non-linear programming algorithm. Ingredients of this algorithm include (1) the process parameters to be optimized, (2) a cost function: the weighted average of the precipitate number density distribution, (3) constraint functions to limit the temperature gradient (and hence distortion and residual stress) and exit temperature, and (4) their sensitivities with respect to the process parameters. The cost and constraint functions are dependent on the temperature and precipitate size which are obtained by balancing energy to determine the temperature distribution and by using a reaction-rate theory to determine the precipitate particle sizes and their distributions. Both the temperature and the precipitate models are solved via the discontinuous Galerkin finite element method. The energy balance incorporates non-linear boundary conditions and material properties. The temperature field is then used in the reaction rate model which has as many as 105 degrees-of-freedom per finite element node. After computing the temperature and precipitate size distributions we must compute their sensitivities. This seemingly intractable computational task is resolved thanks to the discontinuous Galerkin finite element formulation and the direct differentiation sensitivity method. A three-dimension example is provided to demonstrate the algorithm. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Finite element analysis of land subsidence above depleted reservoirs with pore pressure gradient and total stress formulations

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 4 2001
Giuseppe Gambolati
Abstract The solution of the poroelastic equations for predicting land subsidence above productive gas/oil fields may be addressed by the principle of virtual works using either the effective intergranular stress, with the pore pressure gradient regarded as a distributed body force, or the total stress incorporating the pore pressure. In the finite element (FE) method both approaches prove equivalent at the global assembled level. However, at the element level apparently the equivalence does not hold, and the strength source related to the pore pressure seems to generate different local forces on the element nodes. The two formulations are briefly reviewed and discussed for triangular and tetrahedral finite elements. They are shown to yield different results at the global level as well in a three-dimensional axisymmetric porous medium if the FE integration is performed using the average element-wise radius. A modification to both formulations is suggested which allows to correctly solve the problem of a finite reservoir with an infinite pressure gradient, i.e. with a pore pressure discontinuity on its boundary. Copyright © 2001 John Wiley & Sons, Ltd. [source]


Solution of non-linear dispersive wave problems using a moving finite element method

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2007
Abigail Wacher
Abstract The solution of the fully non-linear time-dependent two-dimensional shallow water equations is considered. Dispersive effects due to the Coriolis forces are taken into account. Such effects are of major importance in geophysical fluid dynamics applications. The recently proposed string gradient weighted moving finite element method is extended for this class of problems. This method simultaneously determines, at each time step, the solution of the governing partial differential equations and an optimal location of the finite element nodes. It has previously been applied to non-dispersive wave problems; here its performance under the demanding conditions of large Coriolis forces, inducing large mesh and field rotation, is studied. Optimal rates of convergence are obtained. Results for some example problems of water hump release are presented. Non-linear and linearized solutions are compared. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Hexahedral Mesh Matching: Converting non-conforming hexahedral-to-hexahedral interfaces into conforming interfaces

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2010
Matthew L. Staten
Abstract This paper presents a new method, called Mesh Matching, for handling non-conforming hexahedral-to-hexahedral interfaces for finite element analysis. Mesh Matching modifies the hexahedral element topology on one or both sides of the interface until there is a one-to-one pairing of finite element nodes, edges and quadrilaterals on the interface surfaces, allowing mesh entities to be merged into a single conforming mesh. Element topology is modified using hexahedral dual operations, including pillowing, sheet extraction, dicing and column collapsing. The primary motivation for this research is to simplify the generation of unstructured all-hexahedral finite element meshes. Mesh Matching relaxes global constraint propagation which currently hinders hexahedral meshing of large assemblies, and limits its extension to parallel processing. As a secondary benefit, by providing conforming mesh interfaces, Mesh Matching provides an alternative to artificial constraints such as tied contacts and multi-point constraints. The quality of the resultant conforming hexahedral mesh is high and the increase in number of elements is moderate. Copyright © 2009 John Wiley & Sons, Ltd. [source]