Efficient parametric uncertainty analysis within the hybrid Finite Element/Statistical Energy Analysis method

This paper is concerned with the development of efficient algorithms for propagating parametric uncertainty within the context of the hybrid Finite Element/Statistical Energy Analysis (FE/SEA) approach to the analysis of complex vibro-acoustic systems. This approach models the system as a combination of SEA subsystems and FE components; it is assumed that the FE components have fully deterministic properties, while the SEA subsystems have a high degree of randomness. The method has been recently generalised by allowing the FE components to possess parametric uncertainty, leading to two ensembles of uncertainty: a non-parametric one (SEA subsystems) and a parametric one (FE components). The SEA subsystems ensemble is dealt with analytically, while the effect of the additional FE components ensemble can be dealt with by Monte Carlo Simulations. However, this approach can be computationally intensive when applied to complex engineering systems having many uncertain parameters. Two different strategies are proposed: (i) the combination of the hybrid FE/SEA method with the First Order Reliability Method which allows the probability of the non-parametric ensemble average of a response variable exceeding a barrier to be calculated and (ii) the combination of the hybrid FE/SEA method with Laplace's method which allows the evaluation of the probability of a response variable exceeding a limit value. The proposed approaches are illustrated using two built-up plate systems with uncertain properties and the results are validated against direct integration, Monte Carlo simulations of the FE and of the hybrid FE/SEA models. © 2013 Elsevier Ltd.

A fixed-grid b-spline finite element technique for fluid-structure interaction

We present a fixed-grid finite element technique for fluid-structure interaction problems involving incompressible viscous flows and thin structures. The flow equations are discretised with isoparametric b-spline basis functions defined on a logically Cartesian grid. In addition, the previously proposed subdivision-stabilisation technique is used to ensure inf-sup stability. The beam equations are discretised with b-splines and the shell equations with subdivision basis functions, both leading to a rotation-free formulation. The interface conditions between the fluid and the structure are enforced with the Nitsche technique. The resulting coupled system of equations is solved with a Dirichlet-Robin partitioning scheme, and the fluid equations are solved with a pressure-correction method. Auxiliary techniques employed for improving numerical robustness include the level-set based implicit representation of the structure interface on the fluid grid, a cut-cell integration algorithm based on marching tetrahedra and the conservative data transfer between the fluid and structure discretisations. A number of verification and validation examples, primarily motivated by animal locomotion in air or water, demonstrate the robustness and efficiency of our approach. © 2013 John Wiley & Sons, Ltd.

An important pitfall of pseudo-static finite element analysis

Finite Element (FE) pseudo-static analysis can provide a good compromise between simplified methods of dynamic analysis and time domain analysis. The pseudo-static FE approach can accurately model the in situ, stresses prior to seismic loading (when it follows a static analysis simulating the construction sequence) is relatively simple and not as computationally expensive as the time domain approach. However this method should be used with caution as the results can be sensitive to the choice of the mesh dimensions. In this paper two simple examples of pseudo-static finite element analysis are examined parametrically, a homogeneous slope and a cantilever retaining wall, exploring the sensitivity of the pseudo-static analysis results on the adopted mesh size. The mesh dependence was found to be more pronounced for problems with high critical seismic coefficients values (e.g. gentle slopes or small walls), as in these cases a generalised layer failure mechanism is developed simultaneously with the slope or wall mechanism. In general the mesh width was found not to affect notably the predicted value of critical seismic coefficient but to have a major impact on the predicted movements. © 2012 Elsevier Ltd.

Finite element beam propagation method for analysis of plasmonic waveguide

The basic idea of the finite element beam propagation method (FE-BPM) is described. It is applied to calculate the fundamental mode of a channel plasmonic polariton (CPP) waveguide to confirm its validity. Both the field distribution and the effective index of the, fundamental mode are given by the method. The convergence speed shows the advantage and stability of this method. Then a plasmonic waveguide with a dielectric strip deposited on a metal substrate is investigated, and the group velocity is negative for the fundamental mode of this kind of waveguide. The numerical result shows that the power flow direction is reverse to that of phase velocity.

Finite element analysis of stress and strain distributions in InAs/GaAs quantum dots

In this paper, we perform systematic calculations of the stress and strain distributions in InAs/GaAs truncated pyramidal quantum dots (QDs) with different wetting layer (WL) thickness, using the finite element method (FEM). The stresses and strains are concentrated at the boundaries of the WL and QDs, are reduced gradually from the boundaries to the interior, and tend to a uniform state for the positions away from the boundaries. The maximal strain energy density occurs at the vicinity of the interface between the WL and the substrate. The stresses, strains and released strain energy are reduced gradually with increasing WL thickness. The above results show that a critical WL thickness may exist, and the stress and strain distributions can make the growth of QDs a growth of strained three-dimensional island when the WL thickness is above the critical value, and FEM can be applied to investigate such nanosystems, QDs, and the relevant results are supported by the experiments.

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.

A finite-element algorithm for modeling variably saturated flows

A general numerical algorithm in the context of finite element scheme is developed to solve Richards’ equation, in which a mass-conservative, modified head based scheme (MHB) is proposed to approximate the governing equation, and mass-lumping techniques are used to keep the numerical simulation stable. The MHB scheme is compared with the modified Picard iteration scheme (MPI) in a ponding infiltration example. Although the MHB scheme is a little inferior to the MPI scheme in respect of mass balance, it is superior in convergence character and simplicity. Fully implicit, explicit and geometric average conductivity methods are performed and compared, the first one is superior in simulation accuracy and can use large time-step size, but the others are superior in iteration efficiency. The algorithm works well over a wide variety of problems, such as infiltration fronts, steady-state and transient water tables, and transient seepage faces, as demonstrated by its performance against published experimental data. The algorithm is presented in sufficient detail to facilitate its implementation.

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.

Finite element simulation of the physical gelation of rennet casein(酶凝干酪素物理凝胶化过程的有限元模拟)

以酶凝干酪素的凝胶化过程为对象,利用有限元方法数值分析了在凝胶化过程中温度场的空间分布和时间演变规律.在此基础上,基于一阶的凝胶化动力学方程,数值模拟了凝胶体系的复剪切模量场,进而分析了材料配方、体系尺寸与冷却方案对复剪切模量场的影响规律.模拟结果表明,由于热阻的差异,体系表面的冷却速率大于内部,表面首先发生凝胶化;而由于预凝胶化阶段的平均冷却速率决定了无穷复剪切模量的值,最终体系内部的复剪切模量超过表面的.

Applications of finite element computer modelling and thermal infrared remote sensing to the study of geothermal anomalies

Buried heat sources can be investigated by examining thermal infrared images and comparing these with the results of theoretical models which predict the thermal anomaly a given heat source may generate. Key factors influencing surface temperature include the geometry and temperature of the heat source, the surface meteorological environment, and the thermal conductivity and anisotropy of the rock. In general, a geothermal heat flux of greater than 2% of solar insolation is required to produce a detectable thermal anomaly in a thermal infrared image. A heat source of, for example, 2-300K greater than the average surface temperature must be a t depth shallower than 50m for the detection of the anomaly in a thermal infrared image, for typical terrestrial conditions. Atmospheric factors are of critical importance. While the mean atmospheric temperature has little significance, the convection is a dominant factor, and can act to swamp the thermal signature entirely. Given a steady state heat source that produces a detectable thermal anomaly, it is possible to loosely constrain the physical properties of the heat source and surrounding rock, using the surface thermal anomaly as a basis. The success of this technique is highly dependent on the degree to which the physical properties of the host rock are known. Important parameters include the surface thermal properties and thermal conductivity of the rock. Modelling of transient thermal situations was carried out, to assess the effect of time dependant thermal fluxes. One-dimensional finite element models can be readily and accurately applied to the investigation of diurnal heat flow, as with thermal inertia models. Diurnal thermal models of environments on Earth, the Moon and Mars were carried out using finite elements and found to be consistent with published measurements. The heat flow from an injection of hot lava into a near surface lava tube was considered. While this approach was useful for study, and long term monitoring in inhospitable areas, it was found to have little hazard warning utility, as the time taken for the thermal energy to propagate to the surface in dry rock (several months) in very long. The resolution of the thermal infrared imaging system is an important factor. Presently available satellite based systems such as Landsat (resolution of 120m) are inadequate for detailed study of geothermal anomalies. Airborne systems, such as TIMS (variable resolution of 3-6m) are much more useful for discriminating small buried heat sources. Planned improvements in the resolution of satellite based systems will broaden the potential for application of the techniques developed in this thesis. It is important to note, however, that adequate spatial resolution is a necessary but not sufficient condition for successful application of these techniques.

Comparison of finite element and finite volume methods application in geometrically nonlinear stress analysis

A novel three-dimensional finite volume (FV) procedure is described in detail for the analysis of geometrically nonlinear problems. The FV procedure is compared with the conventional finite element (FE) Galerkin approach. FV can be considered to be a particular case of the weighted residual method with a unit weighting function, where in the FE Galerkin method we use the shape function as weighting function. A Fortran code has been developed based on the finite volume cell vertex formulation. The formulation is tested on a number of geometrically nonlinear problems. In comparison with FE, the results reveal that FV can reach the FE results in a higher mesh density.