Question

B=\(\frac{1}{x_2-x_1}\)[-1 1]  is an ___________

(a) Strain matrix

(b) Element-strain displacement matrix

(c) Displacement matrix

(d) Elemental matrix

I got this question in my homework.

This is a very interesting question from One Dimensional Problems topic in division One Dimensional Problems of Finite Element Method

Answer 1

Right option is (b) Element-strain displacement matrix

To elaborate: ε=Bq

 Here B is element strain displacement matrix. Use of linear shape functions results in a constant B matrix. Hence, in a constant strain within the element. The stress from Hooke’s law is

σ=EBq.