Question

Stiffness integration for quadratic element for 2*2 matrix is ____

(a) Nt=(1-ξ)(1-η)

(b) kij=\(\sum_{IP=1}^{4}\)WIP∅IP

(c) Nt=(1-η)

(d) Nt=\(\frac{1}{4}\)(1-ξ)(1-η)

The question was posed to me in examination.

My question comes from Numerical Integration in portion Two Dimensional Isoparametric Elements and Numerical Integration of Finite Element Method

Answer 1

The correct option is (b) kij=\(\sum_{IP=1}^{4}\)WIP∅IP

For explanation I would say: Stiffness is the rigidity of an object, the extent to which it resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. A stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely small.