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Applied Mechanics Program

Applied Mechanics Program


 

The aim of the Applied Mechanics program at University of Tehran is to offer the highest and up to date level of understanding into advanced topics in theoretical, numerical and experimental solid mechanics, and to prepare students for research on knowledge-boundary subject areas in the field. In the program, the students can develop independence, creativity, research skills, and grow the knowledge required to continue the profession, and distinguished faculty members are a valuable asset in this regard to help the students as instructors and supervisors.

 

 

Key facts

 

Program Title:

Mechanical Engineering – Applied Mechanics

Credentials:

Master of Science (M.Sc.) or Doctor of Philosophy (Ph.D.) degrees

Awarding Institute:

University of Tehran

Language:

English

Duration:

two years

Format:

full time, on campus

Starting date:

September 23, 2021

 
Course structure

 

SEMESTER 1: FALL 2021

Credits

Advanced Engineering Mathematics

3

Continuum Mechanics

3

Finite Element Method

3

SEMESTER 2: WINTER 2022

Credits

Elasticity

3

Fracture Mechanics

3

Advanced Mechanics of Composite Materials

3

Experimental Stress Analysis

3

SEMESTER 3: FALL 2022

Credits

Optimization

3

Engineering Plasticity

3

Plates and Shells

3

Advanced Space Structural Design

3

Computational Nano-mechanics

3

Crystal Plasticity

3

Computer-aided Design

3

Nano-composites

3

Seminar

2

SEMESTER 4: WINTER 2023

Credits

Dissertation

6

 
 
 
Course descriptions

 

Advanced Engineering Mathematics

This course deals with topics in advanced mathematics and aims to show the relevance of mathematics to quotidian mechanical engineering problems. The materials are designed in a way to facilitate the articulation to courses in all streams of mechanical engineering disciplines and to form a basis for more specialized branches of mathematics. The course provides participants with the skills, knowledge and techniques required to perform fundamental mathematical procedures and processes for the solution of engineering problems, particularly partial differential equations, optimization and vector analysis.

Continuum Mechanics

The course deals with deriving the field equations of classical mechanics, considering the medium (solid, fluid, ...) as continuous and without gaps. The course outline includes algebra and calculus of tensors, kinematics of deformation and motion, balance laws of continuous media, and constitutive laws for linear and nonlinear elastic solids. The focus is only on deriving the field equations and not solving them.

Finite Element Method

In this course, the governing equations of mechanics are approximated by discretization. Using the concepts of nodes, elements and stiffness matrix, and applying the loads and boundary conditions, the discretized equations are solved numerically. Different problems in the fields of solid mechanics, fluid mechanics, and heat transfer are formulated in this way. The students get to write the codes to build the finite element form of the problems on their own, and also to work with commercial finite element software.

Elasticity

The course deals with the review of deriving field equations for an isotropic linear elastic solid medium in different formulations and solving them. Different (exact or approximate) analytical and numerical techniques are introduced for solving these equations, with the focus mostly on two dimensional (plane strain and plane stress) problems formulated in Cartesian or polar coordinate systems. For some problems, the exact elasticity solutions are compared with those of elementary strength of materials and the strength and weakness of the latter method are discussed.

Fracture Mechanics

The focus of this course is on the basic aspects of linear elastic fracture mechanics. They are as follows: Griffith Theory of fracture, Energy release rate, Fracture mechanisms and Crack growth, Necessary and sufficient conditions for fracture, Extension of Griffith Theory by Irwin, Modes of loading, Westergaard and Williams solutions, the development of stress field equations in fracture mechanics, Stress and Displacement fields in the near crack tip, plastic zone at the crack-tip, Irwin and Dugdale models, R-Curve, Crack branching, Equivalence between SIF and G, Experimental and theoretical methods for evaluating Stress Intensity Factors, Fracture toughness testing, Fedderson strength diagram. Also covered: interface fracture mechanics, fatigue damage fatigue crack growth models and mechanisms, J-integral, Mixed-mode fracture, Crack arrest methodologies, and experimental techniques in fracture mechanics.

Advanced Mechanics of Composite Materials

Advanced mechanics of composite materials is focused basically on long fiber reinforced polymer composites. The goal of this course is to provide the students with the knowledge of composites required for design, analysis, and manufacturing of the structures made of these materials.

Experimental Stress Analysis

Optimization

The course intends to enhance students' understanding of "optimality" and "optimum design" in the context of mechanical engineering. It helps them model real-world engineering problems as optimization problems and introduces them to various classical and modern techniques to solve those problems. The techniques covered in the course range from analytical methods to numerical (both derivative-based and derivative-free) methods; and from traditional deterministic algorithms to stochastic evolutionary and nature-inspired algorithms.

Engineering Plasticity

This is a postgraduate course providing strong conceptual foundations for developing continuum theories of plastic deformation. In addition, several important formulations of plastic flow which are of much practical use in current industrial applications are developed. Phenomenological and mathematical formulation of the constitutive laws of plasticity; yield criteria and their experimental verification; plastic stress-strain relations and their associated flow rules; correspondence between rate-independent and rate dependent plasticity; solutions to basic boundary-value problems, including plane problems and those involving cylindrical and spherical symmetries; variational and minimum principles; limit analysis; plane-strain problems and crystal plasticity; finite-strain theory are the main subjects covered in this course.

Plates and Shells

The course deals with different theories for bending and buckling of thin, moderately thick, and thick linear elastic plates, neglecting or considering shear effect,  with special focus on rectangular and circular plates. Both exact and approximate methods of analysis are presented. The second part of the course deals with geometry of thin shells and the governing equations for their bending. Cylindrical shells and shells of revolution are specially investigated.

Advanced Space Structural Design

The aim of this course is to increase student's skills in design, analysis, manufacturing and test of space structures (especially, satellite structure in this course). All of these educations are according to space standards and the students will acquaintance with space engineering concepts too. At the end of this round, the students will be able to involve in space project as the structure subsystem expert.

Computational Nano-mechanics

This is a course to provide a practical introduction to modern molecular simulation techniques that are widely used as tools in different fields of nano-mechanics research, such as fluid flow, heat transfer, fracture analysis and vibrations in nanostructures. More specifically, classical molecular dynamics simulation methods are discussed in this course. Necessary statistical mechanics required to understand and properly interpret the molecular simulations and link the results into measured bulk properties are also to be introduced. Assignments include some computer programming as well as working with the open source codes, such as LAMMPS, NAMD, OVITO and VMD, which are widely used packages in the field of nano-computations. Employing these facilities, different approaches are also addressed to observe atomistic phenomena and measure corresponding quantities.

Crystal Plasticity

Crystal plasticity is the science of describing plastic deformation in crystalline materials based on finite slip occuring on different slip systems of the crystals. Metallic materials are widely considered the backbone of any industrial endeavour and as such understanding their behaviours is crucial in any industry. Through studying the crystalline slip of individual grains at the microscopic level, their macro behaviour may be further understood and furthermore it allows engineers to miniaturise their designs knowing how the material behaves as it is being deformed plastically.

Computer-aided Design

Design is a process of generating solutions, which should satisfy all requirements including customer needs, legislation considerations, expected performance and costs. Design process may be considered as technical level of generating solutions, but activities such as market analysis and sales should be taken into account in design process, too. Therefore, one can consider technical and market related activities as total design which requires a blend of different skills in order to produce a marketable and functioning product. In total design, the process starts with collecting information on customer needs and expectations from the market, and ends with selling products in the market. Therefore, the total design process could be categorized into the following steps:

  • Identifying customer needs
  • Conceptual Design
  • Detailed design
  • Testing and refinement
  • Production
  • Sales and after sale services

The main purpose of this course concerns application of computer in total design process, although the progress of computer application in different steps is not the same. The main topics which will be covered in this course are as follows:

  • Product Life-Cycle
  • Product Design and Development
  • Geometric Modeling
  • Product Life-Cycle Management

 

Nano-composites

Seminar

In this course, the students will be walked through different aspects of research process including thinking about research questions, designing a study, engaging with the existing literature, analyzing data, and concluding results. Moreover, the instructions for writing research proposals, abstracts, grant proposals, ethics applications, and poster presentations will be given.