Multi-transform based spectral element to include first order shear deformation in plates

For obtaining dynamic response of structure to high frequency shock excitation spectral elements have several advantages over conventional methods. At higher frequencies transverse shear and rotary inertia have a predominant role. These are represented by the First order Shear Deformation Theory (FSDT). But not much work is reported on spectral elements with FSDT. This work presents a new spectral element based on the FSDT/Mindlin Plate Theory which is essential for wave propagation analysis of sandwich plates. Multi-transformation method is used to solve the coupled partial differential equations, i.e., Laplace transforms for temporal approximation and wavelet transforms for spatial approximation. The formulation takes into account the axial-flexure and shear coupling. The ability of the element to represent different modes of wave motion is demonstrated. Impact on the derived wave motion characteristics in the absence of the developed spectral element is discussed. The transient response using the formulated element is validated by the results obtained using Finite Element Method (FEM) which needs significant computational effort. Experimental results are provided which confirms the need to having the developed spectral element for the high frequency response of structures. (C) 2015 Elsevier Ltd. All rights reserved.

Spray: A Multi-Modal Localization System for Stationary Sensor Network Deployment

We present a localization system that targets rapid deployment of stationary wireless sensor networks (WSN). The system uses a particle filter to fuse measurements from multiple localization modalities, such as RF ranging, neighbor information or maps, to obtain position estimations with higher accuracy than that of the individual modalities. The system isolates different modalities into separate components which can be included or excluded independently to tailor the system to a specific scenario. We show that position estimations can be improved with our system by combining multiple modalities. We evaluate the performance of the system in both an indoor and outdoor environment using combinations of five different modalities. Using two anchor nodes as reference points and combining all five modalities, we obtain RMS (Root Mean Square) estimation errors of approximately 2.5m in both cases, while using the components individually results in errors within the range of 3.5 and 9 m.

A Reliable Residual Based A Posteriori Error Estimator for a Quadratic Finite Element Method for the Elliptic Obstacle Problem

A residual based a posteriori error estimator is derived for a quadratic finite element method (FEM) for the elliptic obstacle problem. The error estimator involves various residuals consisting of the data of the problem, discrete solution and a Lagrange multiplier related to the obstacle constraint. The choice of the discrete Lagrange multiplier yields an error estimator that is comparable with the error estimator in the case of linear FEM. Further, an a priori error estimate is derived to show that the discrete Lagrange multiplier converges at the same rate as that of the discrete solution of the obstacle problem. The numerical experiments of adaptive FEM show optimal order convergence. This demonstrates that the quadratic FEM for obstacle problem exhibits optimal performance.