By Richard A. DeMillo
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There are only two independent material constants for isotropic material. Usually, the two most commonly used material constants are the Young’s modulus and the Poisson’s ratio. This book deals mostly with isotropic materials. Nevertheless, most of the formulations are also applicable to anisotropic materials. Boundary conditions are another important consideration in mechanics. There are displacement and force boundary conditions for solids and structures. For heat transfer problems there are temperature and convection boundary conditions.
1 Stress and Strain Three-dimensional problems can be drastically simplified if they can be treated as a twodimensional (2D) solid. For representation as a 2D solid, we basically try to remove one coordinate (usually the z-axis), and hence assume that all the dependent variables are independent of the z-axis, and all the external loads are independent of the z coordinate, and applied only in the x–y plane. Therefore, we are left with a system with only two coordinates, the x and the y coordinates.
1. Four common types of structural components. Their geometrical features are made use of to derive dimension reduced system equations. Therefore, there are six stress components in total at a point in solids. These stresses are often called a stress tensor. 2. Solid subjected to forces applied within the solid (body force) and on the surface of the solid (surface force). 3. Six independent stress components at a point in a solid viewed on the surfaces of an infinitely small cubic block. 4) ∂w ∂u ∂v ∂u ∂w ∂v εxy = + ; εxz = + ; εyz = + ∂y ∂x ∂z ∂x ∂z ∂y “chap02” — 2002/12/14 — page 15 — #4 16 CHAPTER 2 MECHANICS FOR SOLIDS AND STRUCTURES where u, v and w are the displacement components in the x, y and z directions, respectively.