Notation

Index Notation

Components of tensors and matrices are given explicitly. A vector, which is a first order tensor, is denoted in indicial notation by $x_i$. The range of the index is the dimension of the vector.

To avoid confusion with nodal values, coordinates will be written as $x$ , $y$ or $z$ rather than using subscripts. Similarly, for a vector such as the velocity $v_i$ , numerical subscripts are avoided so as to avoid confusion with node numbers. So, $x_1=x,x_2=y,x_3=z$ and $v_1=v_x,v_2=v_y$ and $v_3=v_2$ .

Indices repeated twice in a list are summed. Indices which refer to components of tensors are always written in lower case. Nodal indices are always indicated by upper case Latin letters. For instance, $v_{iI}$ is the i-component of the velocity vector at node I. Upper case indices repeated twice are summed over their range.

A second order tensor is indicated by two subscripts. For example, $E_{ij}$ is a second order tensor whose components are $E_{xx},E_{xy}$ , ...

Matrix Notation

All vectors such as the velocity vector $\nu$ will be denoted by lower case letters. Rectangular matrices will be denoted by upper case letters.