Special Topics in MFG:Advanced Mechanics of Composite Structures (MFG 58002)

2020 Spring
Faculty of Engineering and Natural Sciences
Adnan Kefal adnankefal@sabanciuniv.edu,
Click here to view.
Doctoral, Master
Formal lecture,Interactive lecture,Group tutorial
Click here to view.


This course will cover advanced mechanics of composite structures through macroscale modelling of composite materials using high-order laminate theories, and through experimental characterization, and data acquisition and analysis. In order to carry out conceptual design, initial sizing and preliminary modelling of composite structural components, design engineers need a thorough understanding of the experimental mechanics as well as strength, stability, and dynamic mechanical response of thin and thick plates/shells made of composite materials. In this context, students will be given an overview of standards and tests methods for experimental identification of material properties of laminates and sandwich structures. In addition, the constitutive equations and strain-stress transformation equations will be reviewed in the context of modelling composite structures. Beam, plate, and shell kinematics will be introduced based on different lamination theories including layer-wise, zigzag, high-order shear deformation theories. Principles of virtual work and minimum potential energy will be presented for bending, buckling, vibration problems of plate and shell structures. Analytical/numerical solutions of these problems will be included. Computational modelling will include post- processing methods to obtain accurate interlaminar and transverse-shear stresses and quantify damage mechanisms such as delamination, impact, and fracture resistance of composite materials.


Composite materials and sandwich structures are being used in an ever-increasing range of applications and industries; therefore, manufacturing/mechanical/aerospace/mechatronics engineers/researchers need acquiring practical skills about theoretical and experimental mechanics of such material systems to be able perform reliable and lightweight design of structural components. The current course aims at providing such skills through advanced theories of continuum mechanics within the context of applications to composite structures.

Learning Outcomes:
At the conclusion of this course, students should be able to:
(i) Design and set up experiments for identifying effective mechanical properties of composite structures.
(ii) Perform strain measurements using different measurement techniques and process experimental data.
(iii) Perform coordinate transformation of stress, strain, and stiffness properties of isotropic, orthotropic, and anisotropic materials.
(iv) Perform analytical and numerical structural analysis of unidirectional ply, composite layer, laminates, and sandwich structures using layerwise, zigzag, and higher-order shear deformation theories.
(v) Predict interlaminar displacements/stresses/strains of laminated composites and sandwich structures (beams, plates, shells) under tensile, bending, torsion, and buckling loads.
(vi) Assess strength, damage, and failure mechanisms of laminates based on various failure criterions.

Lecture 1: Review of Solid Mechanics
Fundamental principles and governing equations, kinematics, kinetics, compatibility, constitutive relations, laws of thermodynamics.

Lecture 2: Micromechanics of Lamina
Introduction to composite materials, polymer matrix composites, fiberglass/ carbon epoxy composites, volume fractions, fiber-matrix properties, rule of mixtures, representative volume element, Halpin-Tsai equations.

Lecture 3: Macro Mechanics, Strength and Failure of Lamina
Deformations of unidirectional laminate, lamina material transformations, engineering constants for generally orthotropic lamina, lamina invariants, hygrothermal effects, failure mechanisms: maximumstrain/ stress, Tsai-Hill, Tsai-Wu criterions etc.

Lecture 4: Experimental Tests Methods for Lamina Mechanics
Coupon-level tests: Constituent-level tests, tests on fibers and resin, lamina-level tests, laminate-level tests, ASTM standards, Structural element-level tests, Component-level tests: Subscale component-level tests, full-scale component-level tests.

Lecture 5: Macro Mechanics of Laminate
Laminate notation, classification, laminate types, classical lamination theory, stress resultants, plate constitutive relations, thermomechanical analysis.

Lectures 6-7: Structural Analysis of Laminated Beams and Design
Governing equations of Euler-Bernoulli beam for laminated composite structures, analytical solutions to laminated beam bending, buckling, vibrations, interlaminar stresses from equilibrium equations, Design of composite structures: Basic features of structural design, laminate design, lamina stacking sequence selection, carpet plots, solution of design examples.

Lectures 8-9: Structural Analysis of Laminated Plates
Kirchhoff-Love equilibrium equations for laminated plate bending, plate buckling and vibration, boundary conditions, solution methods including Navier, Levy, and Ritz methods, analytical solutions to specially orthotropic plates.

Lectures 10-11: Finite Element Analysis of Laminated Plates
General finite element procedures, Reissner-Mindlin plate element, kinematic relations, shape functions and displacement approximation, principal of virtual work and energy, ANSYS Mechanical APDL coding for solutions of laminated beam/plate/shell example problems.

Lecture 12: Refined Zigzag Theory (RZT)
Introduction to layerwise formulation, RZT governing equations for beams and plates, finite element implementation of the formulation using MATLAB/JAVA/Fortran.

Lectures 13-14: Nondestructive Testing and Structural Health Monitoring
Different experimental measurement techniques for composite materials, digital image correlation, strain gauge/FBG sensor measurement, thermography, acoustic emission, shape sensing and real-time structural health monitoring.


1. Develop and deepen the current and advanced knowledge in the field with original thought and/or research and come up with innovative definitions based on Master's degree qualifications

2. Conceive the interdisciplinary interaction which the field is related with ; come up with original solutions by using knowledge requiring proficiency on analysis, synthesis and assessment of new and complex ideas.

3. Evaluate and use new information within the field in a systematic approach.

4. Develop an innovative knowledge, method, design and/or practice or adapt an already known knowledge, method, design and/or practice to another field; research, conceive, design, adapt and implement an original subject.

5. Critical analysis, synthesis and evaluation of new and complex ideas.

6. Gain advanced level skills in the use of research methods in the field of study.

7. Contribute the progression in the field by producing an innovative idea, skill, design and/or practice or by adapting an already known idea, skill, design, and/or practice to a different field independently.

8. Broaden the borders of the knowledge in the field by producing or interpreting an original work or publishing at least one scientific paper in the field in national and/or international refereed journals.

9. Demonstrate leadership in contexts requiring innovative and interdisciplinary problem solving.

10. Develop new ideas and methods in the field by using high level mental processes such as creative and critical thinking, problem solving and decision making.

11. Investigate and improve social connections and their conducting norms and manage the actions to change them when necessary.

12. Defend original views when exchanging ideas in the field with professionals and communicate effectively by showing competence in the field.

13. Ability to communicate and discuss orally, in written and visually with peers by using a foreign language at least at a level of European Language Portfolio C1 General Level.

14. Contribute to the transition of the community to an information society and its sustainability process by introducing scientific, technological, social or cultural improvements.

15. Demonstrate functional interaction by using strategic decision making processes in solving problems encountered in the field.

16. Contribute to the solution finding process regarding social, scientific, cultural and ethical problems in the field and support the development of these values.

1. Develop the ability to use critical, analytical, and reflective thinking and reasoning

2. Reflect on social and ethical responsibilities in his/her professional life.

3. Gain experience and confidence in the dissemination of project/research outputs

4. Work responsibly and creatively as an individual or as a member or leader of a team and in multidisciplinary environments.

5. Communicate effectively by oral, written, graphical and technological means and have competency in English.

6. Independently reach and acquire information, and develop appreciation of the need for continuously learning and updating.

1. Design and model engineering systems and processes and solve engineering problems with an innovative approach.

2. Establish experimental setups, conduct experiments and/or simulations.

3. Analytically acquire and interpret data.

1. Employ mathematical methods to solve physical problems and understand relevant numerical techniques.

2. Conduct basic experiments or simulations.

3. Analytically acquire and interpret data.

4. Establish thorough understanding of the fundamental principles of physics.

1. Develop abstract mathematical thinking and mathematical intuition.

2. Demonstrate a broad understanding of several areas of advanced mathematics and of their interrelations.

3. Have knowledge of the fundamental and advanced concepts, principles and techniques from a range of topics.

4. The ability to tackle complex problems, reveal structures and clarify problems, discover suitable analytical and/or numerical methods and interpret solutions.

5. Analyze problems of the area of specialization, plan strategies for their solution, and apply notions and methods of abstract and/or applied mathematics to solve them.

1. Apply knowledge of mathematics, science, and engineering in computer science and engineering related problems.

2. Display knowledge of contemporary issues in computer science and engineering and apply to a particular problem.

3. Demonstrate the use of results from interpreted data to improve the quality of research or a product in computer science and engineering.

1. Apply software, modeling, instrumentation, and experimental techniques and their combinations in the design and integration of electrical, electronic, control and mechanical systems.

2. Interact with researchers from different disciplines to exchange ideas and identify areas of research collaboration to advance the frontiers of present knowledge and technology; determine relevant solution approaches and apply them by preparing a research strategy.

3. Take part in ambitious and highly challenging research to generate value for both the industry and society.

1. Use advanced Math (including probability and/or statistics), advanced sciences, advanced computer and programming, and advanced Electronics engineering knowledge to design and analyze complex electronics circuits, instruments, software and electronic systems with hardware/software.

2. Analyze and design advanced communication networks and systems, advanced signal processing algorithms or software using advanced knowledge on diff. equations, linear algebra, complex variables and discrete math.

1. Apply knowledge of key concepts in biology, with an emphasis on molecular genetics, biochemistry and molecular and cell biology.

2. Display an awareness of the contemporary biological issues in relation with other scientific areas.

3. Demonstrate hands-on experience in a wide range of biological experimental techniques.

1. Establish a strong theoretical background in several of a broad range of subjects related to the discipline, such as manufacturing processes, service systems design and operation, production planning and control, modeling and optimization, stochastics, statistics.

2. Develop novel modeling and / or analytical solution strategies for problems in integrated production and service systems involving human capital, materials, information, equipment, and energy, also using an interdisciplinary approach whenever appropriate.

3. Implement solution strategies on a computer platform for decision-support purposes by employing effective computational and experimental tools.

4. Acquire skills to independently explore and tackle problems related to the discipline that were not encountered previously. Develop appropriate modeling, solution, implementation strategies, and assess the quality of the outcome.

1. Assess and identify developments, strategies, opportunities and problems in energy security and energy technologies.

2. Define and solve technical, economic and administrative problems in energy businesses.

3. Establish knowledge and understanding of energy security, energy technologies, energy markets and strategic planning in energy enterprises.

4. Demonstrate an awareness of environmental concerns and their importance in developing engineering solutions and new technologies.

5. Acquire a series of social and technical proficiencies for project management and leadership skills.

1. Apply a broad knowledge of structure & microstructure of all classes of materials, and the ability to use this knowledge to determine the material properties.

2. Apply a broad understanding of the relationships between material properties, performance and processing.

3. Apply a broad understanding of thermodynamics, kinetics, transport phenomena, phase transformations and materials aspects of advanced technology.

4. Demonstrate hands-on experience using a wide range of materials characterization techniques.

5. Demonstrate the use of results from interpreted data to improve the quality of research, a product, or a product in materials science and engineering.


  Percentage (%)
Final 40
Midterm 40
Group Project 20



1. Buragohain, M.K., 2017. Composite structures: design, mechanics, analysis, manufacturing, and testing. CRC press.
2. Altenbach H., Altenbach J., Kissing, W., 2018. Mechanics of composite structural elements. Springer-Verlag.
3. Oñate, E., 2013. Structural analysis with the finite element method. Linear statics: volume 2: beams, plates and shells. Springer Science & Business Media.
4. Barbero, E.J., 2007. Finite element analysis of composite materials. CRC press.
5. Reddy, J.N., 2003. Mechanics of laminated composite plates and shells: theory and analysis. CRC press.