Modeling of Modified Vehicle Crashworthiness using a Double Compound Pendulum

Vehicle crash modeling has been a challenge for researchers for several decades. Occupant injury prevention and prediction is a critical area within vehicle safety design. The modeling of material failure in structural members during a full frontal crash has been presented in this paper. This study presents a Lumped Parameter Model (LPM) with an elastic double compound pendulum replicating the impact kinematics. The model defined using Lagrangian formulation; presents a novel methodology to represent material fracture caused due to heat affected zones or welding in Ultra High Strength Steels (UHSS) in a non-linear crash event. The material fracture leads to rotation of the vehicle; presente…

Crash Response of a Repaired Vehicle - Influence of Welding UHSS Members

Non-standard Problems in an Ordinary Differential Equations Course

International audience; We report first results from a teaching intervention in an ordinary differential equations (ODEs) course for engineering students. Our aim is to challenge traditional approaches to teaching of Existence and Uniqueness Theorems (EUTs) through the design of problems that students cannot solve by applying well-rehearsed techniques or familiar methods. We analyse how the use of nonstandard problems contributes to the development of students' conceptual understanding of EUTs and ODEs.

Mathematical models for assessment of vehicle crashworthiness: a review

This article reviews approaches to mathematical modeling of a vehicle crash. The growing focus on vehicle and occupant safety in car crashes has triggered the need to study vehicle crashworthiness in the initial stages of vehicle development. The major motivation for this work is to support vehicle crashworthiness design during the product development process.The article is divided into two parts; the first one overviews existing mathematical models used to solve engineering problems. The second part describes modeling strategies applied for replicating non-linear vehicle crash event and occupant kinematics in an occupant protection loadcase. We also highlight alternative modeling strategie…

Effect of welding and heat treatment on the properties of UHSS used in automotive industry

This paper deals with the undesired effects of the heat treatments on the mechanical properties of (UHSS) Ultra High Strength Steel used nowadays in automotive industry to improve crashworthiness performance of vehicles. The UHSS specimens were extracted from certain parts of the car body and subjected to different heat treatments. Four types of specimens were tested: untreated, welded with metal inert gas welding, heat treated at 800 °C, and heat treated at 1250 °C. All heat-treated specimens showed dramatically reduced values of strength. The results suggest that it is important to follow the official repair manuals avoiding unnecessary welding and improper heat treatments of UHSS. The ex…

Methods and Materials for Professional Development of Lecturers

A Novel Technique for Modeling Vehicle Crash using Lumped Parameter Models

This paper presents a novel technique for modeling a full frontal vehicle crash. The crash event is divided into two phases; the first until maximum crush and the second part when the vehicle starts pitching forward. This novel technique will help develop a three degrees of freedom (DOF) lumped parameter model (LPM) for crash and support in the vehicle development process. The paper also highlights the design process for reducing vehicle pitching in occupant protection load cases. The model has been validated against a finite element (FE) simulation of a full frontal crash of a Chevrolet Silverado developed by the National Highway Traffic Safety Administration (NHTSA), and the LPM shows goo…

Vehicle crashworthiness performance in frontal impact: Mathematical model using elastic pendulum

Vehicle occupant injuries due to collisions cause many fatalities every year. Safe vehicle design plays a critical role in averting serious injuries to occupants and vulnerable road users in the event of a crash. In this paper we study a full frontal vehicle crash against a rigid barrier introducing a Lumped Parameter Model (LPM) inspired by the elastic pendulum motion. The model uses polar coordinates to simplify the problem and the governing equations have been defined using Lagrangian formulation. The Simulink model has been validated against Finite Element (FE) data demonstrating good correlation with pitching angle and maximum crush of the vehicle. These parameters are crucial for desi…

Dynamics of a Single Species in a Fluctuating Environment under Periodic Yield Harvesting

We discuss the effect of a periodic yield harvesting on a single species population whose dynamics in a fluctuating environment is described by the logistic differential equation with periodic coefficients. This problem was studied by Brauer and Sánchez (2003) who attempted the proof of the existence of two positive periodic solutions; the flaw in their argument is corrected. We obtain estimates for positive attracting and repelling periodic solutions and describe behavior of other solutions. Extinction and blow-up times are evaluated for solutions with small and large initial data; dependence of the number of periodic solutions on the parameterσassociated with the intensity of harvesting i…

Mathematical Modelling Problems in a Mathematics Course for Engineers: A Commognitive Perspective

Mathematical knowledge is very important for engineers; both quantitative and qualitative analysis of physical systems and manufacturing processes require solid scientific principles and appropriate mathematical tools. Teaching of mathematical modelling at the university contributes to the development of mathematical competencies, motivates the interest to mathematics and plays a significant didactical role in promoting advanced mathematical thinking. These views are supported by the analysis of students’ work on a mathematical modelling assignment in a university mathematics course for future engineers with the help of the commognitive framework. Students’ narratives in written solutions a…

THE USE OF NONSTANDARD PROBLEMS IN AN ODE COURSE FOR ENGINEERING STUDENTS

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A new tool for the assessment of the development of students' mathematical competencies

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