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Presented by:Milind TaleleCLASSICAL LAMINATE THEORYDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)1ContdBy stress strain relationship , we get-

Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Steps:Reduced stiffness matrix for laminaFind co-ordinates for lamina (thickness, top and bottom surface locations)Find [A] , [B] and [D] matrices from previously derives equationsSubstitute these values in derived [6X6] matrixFind mid-plane strains and curvaturesFind global strainsFind local strainsFind local stressesDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Reduced stiffness matrix

Transformation matrixReuters matrixDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)5Resultant laminate forces and moments:

Moments on flat laminateIn plane forces on flat laminateDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)56

ContdDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)6

Extensional stiffnessesBending extension coupling stiffnessesBending stiffnessesDepartment of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Contd

Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Global strains in each ply:

Local strains in each ply:

Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Global stresses in each ply :

=

Local and Global directions

Local stresses in each ply :Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)Conclusion:Using reduced stiffness matrix we calculated A, B, D matricesLocal strains can be calculated form midplane strains and curvatureStress distribution in each lamina can be calculated by analytical methodPercentage of load taken by each lamina can be calculated

Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)References:Robert M. Jones (1999), Mechanics of composite materials, 2nd edition, Taylor and Francis Inc., Philadelphia.

P.K.Mallick (1946), Fiber-reinforced composites : materials, manufacturing, and design, CRC Press , Taylor and Francis Inc., New York.

Autar K. Kaw (2006), Mechanics of composite materials, CRC Press , Taylor and Francis Inc., Boca Raton, Florida.

Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)THANK YOU!Department of Mechanical and Aerospace Engineering, IIT HyderabadEngineering Optics LabClassical Laminate Theory (CLT)