Macro-Mechanical Analysis of Laminate — Lesson 4

This lesson covers the macro-mechanical analysis of laminate, focusing on the classical lamination theory and how the constitutive equation for a layered laminate is obtained. It discusses how the force and moment resultants can be related to the mid-surface strains and curvatures by the BBD Matrix. The lesson also explains how a laminate can be analyzed based on these constitutions, how the stresses in each lamina of the laminate can be determined, and how to solve problems related to laminate subjected to load. It further discusses the concept of hydrothermal stresses in laminates and how to calculate the residual thermal stresses in each lamina.

Video Highlights

00:33 - Introduction to macro-mechanical analysis of laminate
03:37 - Steps to calculate the residual thermal stresses in each lamina
06:43 - Calculation of reduced stiffness matrix, reduced transform stiffness matrix, and A, B, D matrices for the laminate
15:20 - Calculation of the mid surface strains and curvatures
16:37 - Calculation of the strains and stresses in each lamina of the laminate
31:13 - Calculation of the residual thermal stresses under temperature change
55:37 - Total stress in each lamina under thermo-mechanical loading

Key Takeaways

- The classical lamination theory is crucial in understanding the macro-mechanical analysis of laminate.
- The BBD Matrix plays a significant role in relating the force and moment resultants to the mid-surface strains and curvatures.
- The analysis of a laminate is based on the constitutions of the laminate, and the stresses in each lamina can be determined accordingly.
- Understanding hydrothermal stresses in laminates is essential, especially when a laminate experiences a temperature change or moisture absorption.
- The calculation of residual thermal stresses in each lamina involves several steps, including determining the reduced stiffness matrix, calculating the reduced transform stiffness matrix, and calculating the mid-surface strains and curvatures.