http://dspace.univ-djelfa.dz:8080/xmlui/handle/123456789/5 2026-09-30T13:57:50Z http://dspace.univ-djelfa.dz:8080/xmlui/handle/112/8582 Handout of Elasticity GUESMI, Mohamed Context and Motivation The mechanical behavior of solid bodies under external loading constitutes one of the most fundamental and practically significant areas of engineering science. From the analysis of civil infrastructure to the design of aerospace structures, the ability to predict how materials deform, develop internal stresses, and ultimately reach their limits of safe operation is central to the work of structural and mechanical engineers. Elasticity theory provides the rigorous mathematical and physical framework that underpins all such analyses, offering tools to describe reversible deformation, stress distributions, and the recovery of shape upon removal of loads. The present course handout is designed for first-year Master's students in Civil Engineering, specializing in Structures, at Ziane Achour University of Djelfa. It responds to the need for a unified, self-contained, and pedagogically accessible treatment of elasticity theory at an advanced undergraduate and early graduate level. The course spans two theoretical pillars: the mathematical formalism necessary to express field equations in compact and invariant form, and the physical insight required to interpret solutions in terms of real engineering phenomena. Scope and Objectives The primary objective of this course is to equip students with both the analytical and conceptual tools needed to study the mechanical behavior of elastic bodies and structural elements. Students are expected to gain a deep understanding of the interrelated concepts of stress, strain, and constitutive laws, and to develop the capacity to formulate and solve elasticity problems in two and three dimensions. The course also prepares students for the study of advanced structural analysis techniques, in particular the finite element method, which is now indispensable in professional engineering practice. Beyond the acquisition of analytical skills, this course aims to cultivate a rational and critical approach to structural modeling. By working through the derivation of governing equations from first principles, students learn to distinguish between exact solutions and engineering approximations, to recognize the limitations of classical theories, and to apply simplifying assumptions judiciously in practical contexts. This capacity for theoretical rigor combined with engineering judgment is the hallmark of a well-trained structural engineer. Structure of the Course The course is organized into eight chapters, each addressing a distinct but interconnected aspect of elasticity theory. The first chapter introduces the foundational concepts of continuum mechanics, including the classification of elastic materials, Hooke's Law in its elementary form, and the mathematical tools of index notation and tensor algebra. These tools are essential for the compact and invariant expression of field equations throughout the course. Chapters Two and Three are devoted to the theory of stress and strain states, respectively. In Chapter Two, the Cauchy stress tensor is introduced, including its physical interpretation, principal stresses, stress invariants, the differential equations of equilibrium, and Mohr's circle for graphical representation. Chapter Three treats the kinematics of deformation, covering the Green–Lagrange and linearized strain tensors, the small perturbation hypothesis, strain–displacement relations in multiple coordinate systems, principal strains, compatibility equations, and experimental measurement techniques. Chapter Four presents the constitutive laws governing the elastic response of materials, including the generalized Hooke's law in one, two, and three dimensions, the role of Lamé and engineering elastic constants, orthotropy and anisotropy, thermoelastic effects, and the strain energy concept. Chapter Five consolidates these developments into the general equations of linear elasticity, specifically the Navier–Cauchy displacement equations and the Beltrami–Michell stress compatibility equations, together with Saint-Venant's principle. The remaining three chapters shift the focus toward structural applications. Chapter Six develops the theory of plane elasticity, including plane stress and plane strain formulations and the Airy stress function approach for solving two-dimensional problems analytically. Chapter Seven addresses beam bending through both the Euler–Bernoulli and Timoshenko beam theories, comparing their assumptions, governing equations, and ranges of applicability. Chapter Eight introduces the study of thin plates using the Kirchhoff–Love model, covering plate kinematics, constitutive behavior, equilibrium equations, the governing biharmonic equation, and strain energy formulations. Prerequisites and Learning Outcomes This course assumes a solid background in mathematics, particularly in linear algebra, differential equations, and vector calculus, as well as a working knowledge of Strength of Materials at the undergraduate level. Upon successful completion of the course, students will be able to apply index notation and tensor calculus to formulate elasticity problems; analyze stress and strain states including principal values, invariants, and graphical representations; use constitutive laws to relate stress and strain for isotropic, orthotropic, and anisotropic materials; derive and apply the Navier–Cauchy and Beltrami–Michell equations; solve plane elasticity problems using Airy stress functions; analyze beam bending using Euler–Bernoulli and Timoshenko theories; and study the bending behavior of thin elastic plates. Together, these competencies form a comprehensive foundation for graduate-level work in structural mechanics, numerical methods, and advanced material design, positioning students to contribute meaningfully to research and professional practice in civil and structural engineering. 2026-09-06T00:00:00Z http://dspace.univ-djelfa.dz:8080/xmlui/handle/112/8581 Numerical Methods course and solved exercies GUESMI, Mohamed Numerical methods constitute one of the fundamental pillars of modern scientific and engineering computation. In many practical situations, engineering and physical problems cannot be solved using exact analytical methods because of the complexity of the governing equations, irregular geometries, nonlinear behavior, or large amounts of data involved. As a result, numerical techniques provide approximate but highly accurate solutions that enable engineers and scientists to analyze, simulate, and optimize real-world systems efficiently. These methods transform mathematical problems into computational procedures that can be implemented using calculators or computer algorithms, making them indispensable in modern engineering practice. In civil engineering, numerical methods play a critical role in solving problems related to structural analysis, hydraulics, transportation systems, soil mechanics, environmental engineering, and construction management. Engineers frequently encounter systems of equations, interpolation problems, differential equations, optimization tasks, and integration processes that cannot be solved manually or by closed-form mathematical formulas. Numerical methods provide practical techniques to obtain approximate solutions with acceptable accuracy while reducing computational time and effort. Consequently, the study of numerical methods has become essential for engineering students and professionals who aim to solve increasingly complex engineering problems. The development of computers has significantly increased the importance of numerical analysis in engineering and scientific research. Modern engineering software such as MATLAB, ANSYS, SAP2000, ETABS, and finite element analysis tools rely heavily on numerical algorithms to perform simulations and calculations. Numerical methods allow engineers to model the behavior of structures under different loading conditions, estimate fluid flow behavior, predict material performance, and evaluate system stability. Without numerical computation, many modern engineering achievements such as high-rise buildings, bridges, dams, transportation networks, and earthquake-resistant structures would be extremely difficult to design and analyze. One of the most important applications of numerical methods is solving nonlinear equations. Many engineering systems are governed by nonlinear mathematical models where exact analytical solutions do not exist. Techniques such as the Bisection Method, Fixed-Point Iteration Method, and Newton–Raphson Method provide systematic procedures to approximate the roots of nonlinear equations. Each method has its own characteristics in terms of convergence speed, stability, and computational efficiency. Understanding these methods enables engineers to select the most appropriate technique according to the nature of the problem and the desired accuracy. Another major field addressed by numerical methods is the solution of systems of linear equations. In civil engineering applications, systems of equations arise naturally in structural analysis, finite element methods, network analysis, and fluid mechanics. Direct methods such as Gaussian Elimination, Gauss–Jordan Elimination, and LU decomposition are commonly used to obtain exact numerical solutions, while iterative techniques such as Jacobi and Gauss–Seidel methods are suitable for large systems where computational efficiency is important. Matrix analysis also provides the mathematical framework necessary for organizing and solving these systems effectively. Numerical integration and interpolation are also essential topics in numerical analysis. Numerical integration techniques, including the Rectangle Rule, Trapezoidal Rule, Simpson’s Rules, and Gaussian Quadrature, allow engineers to approximate definite integrals when analytical integration is impossible or difficult. These methods are particularly important in applications involving area calculations, load distributions, probability analysis, and differential equations. Interpolation methods such as Lagrange and Newton interpolation provide efficient ways to estimate unknown values between known data points, which is especially useful in experimental analysis, data fitting, and engineering measurements. The numerical solution of differential equations represents another important application of numerical methods. Many physical and engineering phenomena such as heat transfer, fluid flow, structural vibration, and population growth are modeled using ordinary or partial differential equations. Methods such as Euler’s Method and the Runge–Kutta Method enable approximate solutions to these equations when exact solutions are difficult to obtain. These techniques form the basis of many advanced simulation tools used in engineering analysis and scientific research. In addition, numerical methods are widely used in approximation theory, eigenvalue problems, optimization, and computational modeling. Eigenvalues and eigenvectors are fundamental in vibration analysis, structural stability, seismic engineering, and finite element analysis. Approximation techniques such as Taylor series and least squares methods help engineers simplify complex functions and fit mathematical models to experimental data. These tools improve prediction accuracy and support decision-making in engineering design and analysis. The primary objective of studying numerical methods is not only to understand the mathematical procedures behind the algorithms but also to develop the ability to analyze errors, convergence conditions, stability, and computational efficiency. Since numerical methods produce approximate solutions, it is important to evaluate the precision and reliability of the obtained results. Concepts such as truncation error, round-off error, convergence rate, and stopping criteria are therefore essential components of numerical analysis. This course aims to provide students with a solid foundation in the principles and applications of numerical methods in engineering. Through theoretical explanations, solved examples, and practical exercises, students will learn how to formulate engineering problems mathematically and solve them using appropriate numerical techniques. The knowledge acquired from this course will help students develop analytical thinking, computational skills, and problem-solving abilities necessary for advanced engineering studies and professional practice. Overall, numerical methods bridge the gap between mathematical theory and engineering applications. They provide engineers with powerful tools to solve complex problems efficiently and accurately in situations where analytical solutions are not feasible. As engineering systems continue to become more sophisticated, the importance of numerical methods in scientific computation and technological development will continue to grow. 2026-09-06T00:00:00Z http://dspace.univ-djelfa.dz:8080/xmlui/handle/112/8578 Steel Structures 2 NEHAR, Kheira Camellia This handout, entitled “Steel Structures 2”, introduces the fundamental principles required for the analysis and design of steel structural members. It focuses on the mechanical behavior of steel elements, the identification of common steel products and sections, and the verification of members subjected to different loading and stability conditions. It is primarily intended for third-year engineering students specializing in Construction and Sustainable Development (CSD). The main objectives are to: • Consolidate students’ knowledge of the principles of steel construction; • Introduce the mechanical and geometric characteristics of structural steel members; • Develop the ability of students to analyse and design steel members subjected to tension, compression, buckling, combined effects, and lateral-torsional buckling; • Prepare students to apply the basic design rules used in metal construction. Successful completion of this module requires prior knowledge in: • Structural mechanics; • Strength of materials; • Structural analysis; • Building construction; • Basic principles of steel structures; • Structural design concepts. This handout is structured into nine chapters. The first chapter presents general concepts related to steel construction, including its main fields of application, advantages, disadvantages, and the importance of considering durability, stability, fire protection, and maintenance from the earliest design stages. The second chapter introduces steel as a structural material. It deals with its composition, classification, mechanical properties, tensile behavior, standardized grades, and the usual physical and elastic coefficients required in elementary design calculations. The third chapter is devoted to steel products and sections. It presents the main families of steel profiles used in metal construction and explains how their geometric characteristics influence resistance, stiffness, stability, and detailing. The fourth chapter deals with elastic buckling phenomena. It highlights the importance of stability in steel structures and introduces the main forms of instability that may affect compressed or bent members. The fifth and sixth chapters focus respectively on the design of members under pure tension and pure compression. They present the fundamental concepts, resistance checks, and practical procedures required to verify common steel members. The seventh and eighth chapters address, respectively, the design of members subjected to simple bending and combined bending. In the case of combined bending, axial compression and bending moments interact, which helps students understand the importance of combined verification in real structural situations. The last chapter is dedicated to lateral-torsional buckling of steel members. It explains the behavior of beams under bending when lateral restraint is insufficient and presents the essential concepts required for safe design. This handout is not intended to be definitive; it may be revised and improved according to constructive feedback from readers, both in terms of content and presentation. Any suggestions or comments are therefore welcome, and I hope that this work will be a useful pedagogical resource for students in civil engineering. 2026-09-06T00:00:00Z http://dspace.univ-djelfa.dz:8080/xmlui/handle/112/8317 Handout of courses Internal Combustion Engine BENDRISS, Abdelkader This course is intended for third-year undergraduate students (LMD system) specializing in Mechanical Construction. It is designed to provide students with the knowledge and methodological tools required to carry out thermodynamic analysis and synthesis studies of internal combustion engines. The course content has been developed in accordance with the official curriculum of the sixth semester of the third-year undergraduate program in Mechanical Construction. Internal combustion engines are among the most important technological achievements in modern mechanical engineering. They are widely used in transportation, industrial applications, power generation, agriculture, and marine systems due to their ability to efficiently and reliably convert the chemical energy of fuels into usable mechanical energy. The study of internal combustion engines integrates several engineering disciplines, including thermodynamics, fluid mechanics, heat transfer, combustion science, machine dynamics, and materials engineering. This handout is designed for 3rd Year undergraduate mechanical engineering students, particularly those studying engine technology and power conversion systems. It provides a comprehensive introduction to the fundamental principles, operating characteristics, thermodynamic cycles, and mechanical behavior of internal combustion engines. The course aims to develop the theoretical understanding and practical knowledge necessary for the analysis, design, operation, and maintenance of modern engines. The first chapter begins with an overview of internal combustion engines and their classification according to ignition method, fuel type, number of strokes, cooling system, and application. Particular attention is paid to the operating principles of spark-ignition (SI) and compression-ignition (CI) engines, which represent the two main categories used in the automotive and industrial sectors. Chapter 2 includes a detailed analysis of thermodynamic cycles, including the Beau-de-Rochas (Otto) cycle, the Diesel cycle, and the Sabatier cycle. These ideal cycles are analyzed to understand the energy transformation within the cylinder and to evaluate engine performance using parameters such as thermal efficiency, compression ratio, pressure, temperature, and heat transfer. The study also presents real engine cycles and compares them with theoretical models to highlight the practical limitations resulting from energy losses during combustion, friction, heat dissipation, and incomplete gas exchange processes. Chapter 3 details the actual operating cycle of diesel engines through the four basic stages: intake, compression, combustion and expansion, and exhaust. The chapter presents diagrams and key engine characteristics to help students understand engine behavior under various operating conditions. It emphasizes the relationship between theoretical analysis and practical engine performance. Chapter 4: Dynamics of Reciprocating Engines. This chapter examines the kinematic and dynamic analysis of the sliding crankshaft mechanism, connecting rod motion, balancing of rotating and reciprocating masses, and valve timing systems to understand vibration phenomena, mechanical stresses, and power transmission within the engine. These concepts are fundamental to improving engine durability, smooth operation, and efficiency. Chapter 5 addresses engine performance parameters, such as indicated power, braking capacity, torque, specific fuel consumption, volumetric efficiency, and thermal efficiency. Engine characteristics are analyzed under full and partial load operating conditions according to international standards. The impact of fuel properties, combustion quality, and ignition systems on engine operation is also presented. The objective of this handout is therefore to provide students with a solid scientific and technical foundation in internal combustion engines, and to prepare them for advanced studies and professional applications in automotive engineering, energy systems, manufacturing industries, and research fields related to thermal machinery and sustainable energy technologies. 2026-06-07T00:00:00Z