Chapter 2 - Macromechanical Analysis Of Lamina

Chapter 2 - Macromechanical Analysis Of Lamina - Click to...

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Unformatted text preview: Click to edit Master subtitle style 5/17/11 MAK 530E Mechanics of Materials Chapter 2 Macromechanics of a Lamina 5/17/11 Introduction A lamina is a thin layer of a composite material that is generally of a thickness on the order of 0.005 in. (0.125 mm). A laminate is constructed by stacking a number of such laminae in the direction of the lamina thickness. In this figure, a typical laminate made of three 5/17/11 Introduction The macromechanical analysis of a lamina is based on average properties and considering the lamina to be homogeneous. Methods to find these average properties based on the individual mechanical properties of the fiber and the matrix, as well as the 5/17/11 Introduction 5/17/11 Introduction 5/17/11 Introduction 5/17/11 Review of Definitions In this chapter, the stressstrain relationships based on temperature change and moisture content will also be developed for a single lamina. The effects of temperature and moisture on a laminate are discussed later in Chapter 4 . 5/17/11 Review of Definitions - Stress 5/17/11 Review of Definitions - 5/17/11 Review of Definitions Stress 5/17/11 Review of Definitions 5/17/11 Elastic Moduli 5/17/11 Elastic Moduli 5/17/11 Strain Energy Energy is defined as the capacity to do work. In solid, deformable, elastic bodies under loads, the work done by external loads is stored as recoverable strain energy. The strain energy stored in the body per unit volume is then defined as 5/17/11 Example Consider a bar of cr oss-section A and length L ( Figure 2.10 ). A uniform tensile load P is applied to the two ends of the rod; find the 5/17/11 Solution The stress state at any point is given by; If the circular rod is made of an isotropic, homogeneous, and linearly 5/17/11 Solution (contd) The strain energy stored per unit volume in the rod; 5/17/11 Hookes Law for Different Types of Materials Stress-strain or constitutive relations for anisotropic materials will be treated first, and in particular the behaviour of orthotropic and transversely isotropic materials, the latter including unidirectional composites. Then, using tensor notation based on four indices and the conventional 5/17/11 Hookes Law for Different Types of Materials Four indices tensor notation Constitutive r elations The reference state is a natural state without stress or strain, that is: In linear elasticity theory, the stress tensor is given as a function of the 5/17/11 Hookes Law for Different Types of Materials The CijkI elements are the 81 components of the elastic moduli tensor or stiffness tensor C . In a homogeneous medium, the 81 elastic moduli Cijkl are independent of the point considered....
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Chapter 2 - Macromechanical Analysis Of Lamina - Click to...

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