ABSTRACT
In this chapter, fi nite element development of two-dimensional solid elements is described. The development is limited to plane stress-strain elements. The plane stress is defi ned as the state of stress in which the normal and shear stresses are perpendicular to the plane, and is assumed zero. Or, the loads on the body are in the x-y plane only. On the other hand, when the strain is normal to the x-y plane, the strain is called plane strain. Physically, the plane stress-strain elements are characterized by
0, 0, 0z yz xzσ = τ = τ = (3.1)
Figure 3.1 shows a two-dimensional stress acting on an element with length dx and width dy. The element is treated as two-dimensional with a unit depth. The normal stresses σx and σy are acting in the x-and y-directions, respectively. Shear stress τxy is acting in the y-direction normal to x-plane, and shear stress τyx is acting in the x-direction normal to y-plane. From the moment equilibrium, τxy must be equal to τyx.
