A subdivision-based implementation of the hierarchical b-spline finite element method

A novel technique is presented to facilitate the implementation of hierarchical b-splines and their interfacing with conventional finite element implementations. The discrete interpretation of the two-scale relation, as common in subdivision schemes, is used to establish algebraic relations between the basis functions and their coefficients on different levels of the hierarchical b-spline basis. The subdivision projection technique introduced allows us first to compute all element matrices and vectors using a fixed number of same-level basis functions. Their subsequent multiplication with subdivision matrices projects them, during the assembly stage, to the correct levels of the hierarchical b-spline basis. The proposed technique is applied to convergence studies of linear and geometrically nonlinear problems in one, two and three space dimensions. © 2012 Elsevier B.V.

Finite element analysis of compressor disc heat transfer using the transient conduction method with sparse boundary collocation points

Surface temperature measurements from two discs of a gas turbine compressor rig are used as boundary conditions for the transient conduction solution (inverse heat transfer analysis). The disc geometry is complex, and so the finite element method is used. There are often large radial temperature gradients on the discs, and the equations are therefore solved taking into account the dependence of thermal conductivity on temperature. The solution technique also makes use of a multigrid algorithm to reduce the solution time. This is particularly important since a large amount of data must be analyzed to obtain correlations of the heat transfer. The finite element grid is also used for a network analysis to calculate the radiant heat transfer in the cavity formed between the two compressor discs. The work discussed here proved particularly challenging as the disc temperatures were only measured at four different radial locations. Four methods of surface temperature interpolation are examined, together with their effect on the local heat fluxes. It is found that the choice of interpolation method depends on the available number of data points. Bessel interpolation gives the best results for four data points, whereas cubic splines are preferred when there are considerably more data points. The results from the analysis of the compressor rig data show that the heat transfer near the disc inner radius appears to be influenced by the central throughflow. However, for larger radii, the heat transfer from the discs and peripheral shroud is found to be consistent with that of a buoyancy-induced flow.

Analysis of Si/GaAs Bonding Stresses with the Finite Element Method

In conjunction with ANSYS, we use the finite element method to analyze the bonding stresses of Si/GaAs. We also apply a numerical model to investigate a contour map and the distribution of normal stress,shearing stress,and peeling stress,taking into full consideration the thermal expansion coefficient as a function of temperature. Novel bonding structures are proposed for reducing the effect of thermal stress as compared with conventional structures. Calculations show the validity of this new structure.

Elastic Strain Field Distribution of a Self-Organized Growth Lensed-Shaped Quantum Dot by Finite Element Method

The stress and strain fields in self-organized growth coherent quantum dots (QD) structures are investigated in detail by two-dimension and three-dimension finite element analyses for lensed-shaped QDs. The nonobjective isolate quantum dot system is used. The calculated results can be directly used to evaluate the conductive band and valence band confinement potential and strain introduced by the effective mass of the charge carriers in strain QD.

Stress analysis of silica-based arrayed waveguide grating by a finite element method

The stress distribution in silica optical waveguides on silicon is calculated by using finite element method (FEM). The waveguides are mainly subjected to compressive stress along the x direction and the z direction, and it is accumulated near the interfaces between the core and cladding layers. The shift of central wavelength of silica arrayed waveguide grating (AWG) on silicon-substrate with the designed wavelength and the polarization dependence are caused by the stress in the silica waveguides.

U-transformation-finite element method in 3-dimensional analysis of orthotropic laminates

For an orthotropic laminate, an equivalent system with doubly cyclic periodicity is introduced. Then a 3-dimensional finite element model for the equivalent system is transformed into the unitary space, where the large finite element matrix equation is decoupled into some small matrix equations. Such a decoupling very efficiently reduces the computational effort. For an orthotropic laminate with four clamped edges, no exact elasticity solution is available, and the deflection values predicted by different methods have a considerable difference each other for a small length-to-thickness ratio. The present predictions are the largest because the present method is a full 3-dimensional finite element analysis without superfluous constraints. Illustrative numerical examples are presented to observe the distributions of stresses through the thickness of the laminates. (C) 2010 Elsevier Ltd. All rights reserved.