9 - FEM for 3D solids

Abstract

This chapter focuses on the development of finite element (FE) equations for three-dimensional (3D) solids. A three-dimensional (3D) solid element can be considered to be the most general of all solid FEs because all the field variables are dependent of x, y, and z. A 3D solid can also have any arbitrary shape, material properties and boundary conditions in space. There are altogether six possible stress components as such, three normal and three shear, that need to be taken into consideration. Typically, a 3D solid element can be a tetrahedron or hexahedron in shape with either flat or curved surfaces. Each node of the element will have three translational degrees of freedom. The element can thus deform in all three directions in space. The formulation of 3D solids elements is straightforward, because it is basically an extension of 2D solids elements. All the techniques used in 2D solids can be utilized, except that all the variables are now functions of x, y, and z.