For plotting and extrapolation purposes (see Chapter 12 ), it is sometimes necessary to obtain nodal stress values from element stress values that are obtained from a computer run. Specifically,...

For plotting and extrapolation purposes (see Chapter 12 ), it is sometimes necessary to obtain nodal stress values from element stress values that are obtained from a computer run. Specifically, consider the element stresses, s1, s2 , and s3 , which are constant within each element, as shown in Fig. P3.20 . It is desired to obtain nodal stresses Si , i = 1, 2, 3, 4 , which best fit the elemental values. Obtain Si from the least-squares criterion,

where s is expressed in terms of the nodal values si , using linear shape functions as

where 1 and 2 are the local numbers. Plot the distribution of stress from the nodal values