Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures

We introduce a systematic method for identifying the worst case load among all boundary loads of fixed energy. Here the worst case load is defined to be the one that delivers the largest fraction of input energy to a prescribed subdomain of interest. The worst case load is identified with the first eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue for this problem is the maximum fraction of boundary energy that can be delivered to the subdomain. We compute worst case boundary loads and associated energy contained inside a prescribed subdomain through the numerical solution of the eigenvalue problem. We apply this computational method to bound the worst case load associated with an ensemble of random boundary loads given by a second order random process. Several examples are carried out on heterogeneous structures to illustrate the method

An inverse homogenization design method for stress control in composites

This thesis addresses the problem of optimal design of microstructure in composite materials. The work involves new developments in homogenization theory and numerical analysis. A computational design method for grading the microstructure in composite materials for the control of local stress in the vicinity of stress concentrations is developed. The method is based upon new rigorous multiscale stress criteria connecting the macroscopic or homogenized stress to local stress fluctuations at the scale of the microstructure. These methods are applied to three different types of design problems. The first treats the problem of optimal distribution of fibers with circular cross section inside a long shaft subject to torsion loading. The second treats the same problem but now the shaft cross section is filled with locally layered material. The third one treats the problem of composite design for a flange fixed at one end and loaded at the other end

Custody outcomes for protective parents in cases with child sexual abuse

The purpose of this study was to examine unreasonable factors that may lead to an unexpected maternal custody loss and result in a non protective custody outcome including labeling a mother with a mental health condition, parental Alienation Syndrome or Alienator, and presence of child sexual abuse

Optimization of composite structures subject to local stress constraints

An extension of current methodologies is introduced for optimization of graded microstructure subject to local stress criteria. The method is based on new multiscale stress criteria given by macrostress modulation functions. The modulation functions quantify the intensity of local stress fluctuations at the scale of the microstructure due to the imposed macroscopic stress. The methodology is illustrated for long cylindrical shafts reinforced with stiff cylindrical elastic fibers with generators parallel to the shaft. Examples are presented for shaft cross sections that possess reentrant corners typically seen in lap joints and junctions of struts. It is shown that the computational methodology delivers graded fiber microgeometries that provide overall structural rigidity while at the same time tempering the influence of stress concentrations near reentrant corners. © 2006

Inverse homogenization and design of microstructure for pointwise stress control

New higher-order homogenization results are employed in an inverse homogenization procedure to identify graded microstructures that provide desirable structural response while ensuring stress control near joints or junctions between structural elements. The methodology is illustrated for long cylindrical shafts reinforced with stiff cylindrical elastic fibres with generators parallel to the shaft. The local fibre geometry can change across the shaft cross-section. The methodology is implemented numerically for cross-sectional shapes that possesses reentrant corners typically seen in lap joints and junctions of struts. Graded locally layered microgeometries are identified that provide the required structural rigidity with respect to torsion loading while at the same time mitigating the influence of stress concentrations at the reentrant corners. © The Author 2005. Published by Oxford University Press; all rights reserved

Let Me Google That: The Effect of a Paperless Classroom on Student Engagement

There has been in increase in technological advances, however it remains unclear how technology in the classroom affects student engagement. The paperless classroom is a special point of interest in the classroom, because it involves a classroom where everything is done online. In this study I used student surveys and interviews to determine how engaging students felt the paperless classroom was

Multiscale-Spectral GFEM and optimal oversampling

In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in Babuška and Lipton (2011). We outline the numerical implementation of this method and present simulations that demonstrate contrast independent exponential convergence of MS-GFEM solutions. We introduce strategies to reduce the computational cost of generating the optimal oversampled local approximating spaces used here. These strategies retain accuracy while reducing the computational work necessary to generate local bases. Motivated by oversampling we develop a nearly optimal local basis based on a partition of unity on the boundary and the associated A-harmonic extensions

Professional Reading

American National Security Policies: a Selective, Working Bibliograph

Non-dipping nocturnal blood pressure and psychosis parameters in Parkinson disease

Conclusion: These results suggest that, among PD patients, a non-dipping circadian rhythm is associated with more severe symptoms of psychosis than is a dipping circadian rhythm. This association warrants further investigation