Irina Viktorova

Modeling of fatigue fracture under stationary stochastic loading conditions

Abstract A new effective mathematical model of fatigue fracture under stationary stochastic loading is proposed. The main idea is based on the concept of fatigue damage accumulation. Compared to the linear theory, the new model accounts for the important physical phenomenon—the influence of history of stochastic loading on the life expectancy of the structure under consideration. The problem of a distribution for the random life expectancy value is replaced by determination of the characteristic life term. The proposed model is formulated for the case when the amplitudes of stochastic loadings are distributed according to the Rayleigh distribution law and the fatigue curve can be approximated by a power function.

An Empirically Derived Arc Flash Discharge Energy Model and Comparison to Established Safety Codes

Arc flash is a constant hazard when discussing industrial safety, however, little is known about the arc flash. Current safety standards require the use of the NFPA 70E equation to establish safety limits for arc flash hazards. However, when compared to an empirically derived model, these safety limits are much too low to account for all working conditions. A comparison of these two methods will lead to the conclusion that arc flash safety distances must be increased. 1. Introduction. In industrial electrical safety, arc flash hazards can be some of the most disastrous and deadly accidents in the work place. An arc flash can reach temperatures of over 35000 degC and cause an explosion with a blast force of 2000 psi and an audible report of over 140 decibels. At a current of just 0.5 Amps, an electrical shock, such as the shock generated from an arc flash, will stop the heart of an adult. [1]. Current arc flash safety codes require that the worker be at a distance that, if an arc flash were to occur, would only result in 2nd degree burns. The current accepted standard for arc flash energy calculations is given by the NFPA 70E equation, which was derived experimentally. However, an empirical approach to determining arc energy will be derived in this paper and the results compared and examined.

Using Biomedical Applications in Touch and Ink Mobile Apps to Engage and Retain Stem Students in Calculus

With support from three Hewlett-Packard Awards and a 4-year NSF-CCLI Grant, the Department of Mathematical Sciences at Clemson partnered with Computer Science to develop and implement pen technology in Engineering Calculus I. Our goals from 2006 to 2011 included personalizing instruction in large activelearning classrooms, reducing the DFW rate through in-class active learning and the analysis of errors in inked submissions. Our current focus, via a 2011NSF-TUES grant, is to motivate interest in calculus by immersing students in bioengineering and biomedical applications, and then converting ideas from these experiences, again with the help of Computer Science, into interactive touch and ink “mobile apps” for both Apple iPad and Android tablets. Beginning in Fall 2011 and continuing into 2013, students with STEM majors can enroll in four (1 credit hour) creative inquiry modules on epidemiology, orthopedics, heat propagation in the human body, or radiology. These modules are taken in parallel with the freshman and sophomore calculus curriculum. Students create presentations on the content in these modules, which include a pedagogical component. We ask them how best to convey the information within a touch and ink environment, so as to engage and clearly convey the connection with calculus. We will present brief descriptions of each module’s content, student responses and performance, and how we are developing ink and touch mobile apps with the help of students both in mathematics and computer science.

Analysis of Resonance Frequencies for the Problem of Induced Vibrations Along the Human Arm

The problems of vibro-safety are connected with the consideration of the human reaction to various mechanical inputs. Traditionally this problem is solved as a mechanical system with concentrated (not distributed) parameters. The goal of this study is to set up a mechanical system following the actual conditions of the human arm response to mechanical vibrations and to develop an approach to model the effect of resonance frequencies.

Modeling Heat Explosion for a Viscoelastic Material

In the scope of material science, it is well understood that the mechanical behavior of a material is temperature dependent. The converse is also true and for specific loading cases contributes to a unique thermal failure mechanism known as heat explosion. We will model the heat conduction across a cylinder to help predict heat explosion created by cyclic loading by electrical pulses. This is done by using a computational analysis to solve for an internal heat parameter that determines thermal failure at a critical value. This critical value is calculated under conditions either accounting for or negating the effect of heat dissipated by the material. We will then use the Maxwell–Cattaneo equation to determine the heat propagation through the material subjected to cyclic loading. Given the temperature gradients and heat propagation determined by the Maxwell–Cattaneo equation, we can use the critical thermal failure value to determine if and how the heat explosion phenomenon will occur.

Quantitative Methods in Biomedical Applications: Creative Inquiry and Digital-Learning Environments to Engage and Mentor STEM Students in Mathematics (NSF Funded Research)

With an increasing demand for biomedical and bioengineering professionals in the coming decades, educators are tasked with readying a greater number of STEM students who are able to apply mathematical concepts to critical health care decisions. In this work, we have developed a series of for-credit, applied learning modules that are being given in parallel to the freshman and sophomore calculus curriculum. These modules use creative inquiry and applied learning experiences to connect mathematical concepts with bioengineering and medical applications. We hypothesize that exposure and participation in the applied learning experiences outside of standard mathematics classes will improve the students’ performance and perceived appreciation for their math curriculum.The four module series is offered over a 2-year period to groups of up to 25 students and emphasizes mathematics and statistics relevant to four biomedical research areas (1) orthopedics, (2) infectious diseases, (3) heat propagation in the human body, and (4) mammography and radiology.This scalable project utilizes a diverse set of faculty from the math and bioengineering departments. The project value to STEM goals is found in (1) convincing students through applied learning experiences that mathematics is an important component of any research plan and indispensable to their career success and (2) ensuring that these students do not falter in calculus and abandon their STEM goals. This paper presents our developed methods and initial findings from module one with the hopes of inspiring other institutions to adopt similar applied learning experiences for their STEM students.

The nonlinear hereditary-type stress–strain relations for metals with temperature effects

The objective of this paper is to present the approach to the development of hereditary-type theory with due account of temperature influencing the time dependent mechanical behavior of metals and alloys. The primary step included the designing of the model with the hereditary-type governing equation structured to account for the thermal effect. It is shown that the whole temperature influence can be modeled by introducing the special power function with one additional parameter, which is put under the integral. Isothermal and quasi-isothermal processes with abrupt change of temperature are considered. The proposed hereditary-type model with temperature effect is verified experimentally.

The application of mathematical methods to some problems of technological microbiology

Mathematical modeling of the biological processes is of great importance nowadays. This is especially valuable for microbiology, which deals with a substantial amount of experimental work, some being extremely accurate and unique. Mathematical modeling allows one either to solve the stated problem, or to indicate ways to find the correct solution. Thus modeling can be seen as a time saving addition to any scientific efforts in microbiology. There appears to exist some problems with the unclear mechanisms of the phenomena (as for example, in the aeration problem, considered next). Mathematical simulation and process modeling allow one to achieve a rather accurate description of the process in general [1], and to understand and analyze the effects of various factors. This paper considers the application of the mathematical methods [2] to the problem of the closed microbiological system and to the problem of aeration for the microbiological reactor.