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.

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.

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.

3D quench simulation using finite element method for CR superconducting magnet's strand

The CR superconducting magnet is a dipole of the FAIR project of GSI in Germany. The quench of the strand is simulated using FEM software ANSYS. From the simulation, the quench propagation can be visualized. Programming with APDL, the value of propagation velocity of normal zone is calculated. Also the voltage increasing over time of the strand is computed and pictured. Furthermore, the Minimum Propagation Zone (MPZ) is studied. At last, the relation between the current and the propagation velocity of normal zone, and the influence of initial temperature on quench propagation are studied.