Main objective of the course is to teach students the fundamental principles of the mechanics of аnisotropic plates and shells with emphasis on orthotropic plates. This theory is further applied to design and analyze unidirectional and multidirectional fiber orthotropic laminates. Within the course the basic issues associated with the design of аnisotropic plates and shells will be studied as well. A special attention will be devoted to the practical stress and strain analysis of mechanical components made out of аnisotropic plates and shells. Issues connected to the characterization of mechanical properties of composite materials will be tackled as well.

1. Within the course students will learn various methods of the assessment of elastic constants entering into constitutive equations which describe mechanical behavior of anisotropic materials. The course will cover also the study of different failure criteria for various types of composite materials. 2. Students will learn how to perform stress – strain analysis of laminate composite materials. 3. The course will devote some attention to the influence of the environmental conditions (e.g. temperature and humidity) to the variation of mechanical properties of composite materials. This will be studied with a special focus on unidirectional and multidirectional composite laminates. 4. By completing this course students will become familiar with basic concepts of analyzing of аnisotropic plates and shells. A special attention will be devoted to the practical procedures of stress analysis of mechanical components made out of these materials, with numerical implementation of the most frequently used techniques.

1. Introduction to anisotropic materials: Basic concepts. Classification, main characteristics and the most frequent applications of anisotropic plates and shells in modern engineering. Orthotropic laminates. 2. Macro mechanical elastic behavior of unidirectional lamina composites. The Hooke’s Law for a two dimensional lamina. Determining stiffness of parallel arrays of fibers in matrix. Rules of mixture. Off-axis properties of a lamina. 3. Determining strength of unidirectional lamina. Analysis of failure criteria. Diverse failure criteria and their applications. 4. Macro mechanical elastic behavior of multidirectional оthotropic laminates. Stress and strain analysis of single lamina, and of the entire оrthotropic material. General laminate plate theory. Studding of coupling effects – coupled flexure and torsion. 5. Stress – strain and failure analysis of multidirectional оthotropic materials. Strength of lamina under tension and shear. Inter-laminar stresses. Laminate strength analysis. First ply failure.

1. Analytical examples of the assessment of macro mechanical properties of the оrthotropic materials. 2. Examples of the Hooke’s law theory applied to the two dimensional unidirectional laminates. Determining of the stiffness matrix for these materials. 3. Numerical exercises of stress strain analysis of оrthotropic laminate. Examples of determination of local and global values for stress and strain. 4. Numerical examples of determination of the ultimate strength using diverse failure criteria. Practical applications of failure theory to the ultimate strength calculations of mechanical components made out of оrthotropic materials. 5. Examples of numerical implementations of diverse modeling techniques of оrthotropic materials into the available codes. Comparison of numerical and analytical predictions of composite material component behavior.

Taken exams: Strength of materials, The base of strenght of constructions.

The whole course material is well covered by hand-outs written by the lecturers of the course. Every attendee of the course will be provided his/hers own copy of the hand-outs. Apart of this, all the below mentioned books can be borrowed from the lecturers during the course or ordered on some relevant websites.

Total assigned hours: 65

New material: 45
Elaboration and examples (recapitulation): 5

Auditory exercises: 0
Laboratory exercises: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 5
Review and grading of the project: 0
Test: 5
Test: 0
Final exam: 5

Activity during lectures: 5
Test/test: 40
Laboratory practice: 0
Calculation tasks: 5
Seminar paper: 20
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 40

"Theory of plates and shells", S. Timoshenko, S. Woinowsky-Kreiger, McGraw Hill, 1964.; "Theory of laminated plates", J.E.Ashton, J.M.Whitney, Technomic Publication, 1970.; "Stresses in plates and shells" A. C. Ugural, McGraw-Hill Science, 1998.; "Elementary theory of elastic plates" L.G.Jaeger, Pergamon, 2013.; "Anisotropic plates" S.G.Leknitski, Defence Tehnical Information Center, 1968.