Question

For theplane stress problem in XYZ Cartesian system, σxx=σxx(x,y), σyy=σyy(x,y) and σzz=0, which option is correct regarding the associated strain field?

(a) εxx=0

(b) εyx=0

(c) εzx=0

(d) εyy=0

The question was asked by my college professor while I was bunking the class.

This key question is from Plane Elasticity topic in chapter Plane Elasticity of Finite Element Method

Answer 1

Right answer is (c) εzx=0

Easy explanation: The strain field associated with the given stress field has the form ε=Sσ, where the matrix S is a symmetric matrix, and it is called elastic compliances matrix. In the XYZ Cartesian system, all the strain components except εyz and εzx are non-zero. Thus, εxx≠0, εyy≠0, εzz≠0, εxy≠0, where as εyz=0 and εzx=0.