Consider two stiffness matrices of the square element in example 7.9: [ (left.mathbf{k}_{1} ight]) for (1 times 1) integration and (left[mathbf{k}_{2} ight]) for (2 times

Consider two stiffness matrices of the square element in example 7.9: [ \(\left.\mathbf{k}_{1}\right]\) for \(1 \times 1\) integration and \(\left[\mathbf{k}_{2}\right]\) for \(2 \times 2\) integration. When nodal displacements are given as \(\{\mathbf{q}\}^{\mathrm{T}}=\) \(\{0.1,0,-0.1,0,0.1,0,-0.1,0\}\), check the reaction forces and determine if the stiffness matrix has extra zeroenergy modes.

Data From Example 9:

Calculate the element stiffness matrix of the square element shown in figure 7.15 using

(a) \(1 \times 1\) Gauss quadrature and

(b) \(2 \times 2\) Gauss quadrature.

2m y 2m 4 1 Figure 7.15 Numerical integration of a square element 3 2 X