Fundamentals of composite laminate structures

• Motor Vehicles, Semester 2, position 4

Main objective of the course is to teach students the fundamental principles of the mechanics of laminated composite plates and beams. This theory is applied to analyze unidirectional and multidirectional fiber reinforced composite plates and beams. Within the course the basics associated with the design of composite plates and beams will be studied as well. A special attention will be devoted to the practical stress and strain analysis of structural components made out of laminated composite materials which are subject to tension (compression), bending and torsion.

1. Within the course students will learn various methods for determining elasticity constants for one layer of composite material (lamina), as well as, ways of assessment of stiffness matrix for multi-layered composite material (laminate). Students will also learn to define carrying capacity of composite plates and beams in case when mechanical properties of each layer of composite material are known. Students will learn how to apply different failure criteria. 2. Students will learn how to perform stress – strain analysis of laminated composite plates and beams. 3. Within the course students will learn to analyse the influence of the environmental conditions (e.g. temperature and humidity) on mechanical properties of laminated composite materials. 4. By completing this course students will become familiar with fundamentals of mechanics of composite plates and beams. A special attention will be devoted to the practical implementation of composite plates and beam as structural elements.

1. Introduction to composite materials- Basic concepts. Classification, main characteristics and the most frequent applications of composite materials in mechanical engineering with emphasis on laminated composite plates and beams. Concept of lamina and laminate. 2. Theory of elasticity of anisotropic body. Stress and strain tensor. Generalized Hooke’s Law. Plane stress state. Fundamentals of anisotropic thin plate theory. 3. Elastic behavior of unidirectional composite lamina. Generalized Hooke’s Law for a unidirectional composite lamina. Elastic properties of a lamina in local coordinates (case when local coordinates are aligned with principal material axes). Off-axis properties of a lamina (case when local coordinates are not aligned with principal material axes). The influence of the environmental conditions (e.g. temperature and humidity). Analysis and application of failure criteria. 4. Elastic behavior of multi-directional composite laminates. Classical lamination theory. Forces and moments in the cross section of laminated composite plate. Stress and strain analysis in cross section of laminated composite plate. Constitutive relations for laminate. Effective elastic constants of symmetric laminate. The environmental conditions (e.g. temperature and humidity) and their influence on laminate. The application of failure criteria on multi-directional composite laminates. Delamination. Interlaminar stresses. Free edge effects. 5. Fundamentals of laminated composite beam theory. Composite beam with rectangular cross section – case when loading plane is perpendicular to its middle plane. Composite beam with rectangular cross section – case when loading plane matches to its middle plane. Thin-walled composite beams of various cross sections.

1. Analytical examples of variation of stress and strain components when coordinate system is rotated by arbitrary angle. 2. Examples of the Generalized Hooke’s law applied to the unidirectional lamina. Determination of the stiffness and compliance matrix for the unidirectional lamina. Examples of determination of local and global stress and strain values for unidirectional lamina exposed to applied load. 3. Stress-strain analysis of laminated composite plates. Examples of determination of local and global stress and strain values of laminated composite plate for defined loads. The influence of temperature – analytical examples. 4. The use of different failure criteria - examples. “Ply by ply” failure approach. 5. Stress-strain analysis of laminated composite beams. Examples of determination of local and global stress and strain values of laminated composite beam for defined loads. The use of different failure criteria – examples on composite beams. 6. Numerical methods used in structural analysis of laminated composite plates and beams. Comparison of results obtained by analytical and numerical methods.

None

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 books listed in literature can be borrowed from the lecturers during the course or ordered on some relevant websites.

Total assigned hours: 75

New material: 25
Elaboration and examples (recapitulation): 5

Auditory exercises: 15
Laboratory exercises: 0
Calculation tasks: 10
Seminar paper: 5
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 4
Review and grading of lab reports: 0
Review and grading of seminar papers: 1
Review and grading of the project: 0
Test: 4
Test: 1
Final exam: 5

Activity during lectures: 5
Test/test: 40
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 20
Project: 0
Final exam: 35
Requirement for taking the exam (required number of points): 40

"Mechanics of composite materials", Autar K. Kaw, CRC Press, 2005.; "Engineering Mechanics of Composite Materials", Isaac M. Daniel, Ori lshai, Oxford University Press (2006); "Principles of composite material mechanics", Ronald F. Gibson, Taylor & Francis, CRC Press (2012); "Mechanics of Composite Materials", Robert M. Jones, Taylor & Francis (1999); "Mechanics of Composite Materials with MATLAB" George Z. Voyiadjis and Peter I. Kattan, Springer, 2005.