Consider the finite element modeling setup below in which a cantilevered beam is

Question

Consider the finite element modeling setup below in which a cantilevered beam is modeled based on a plane stress assumption. Two triangular finite elements are used. The beam is fixed to zero displacement in the x and y directions at the right end, and force Fis applied in the negative y direction at the left end. Point 1 and Point 2 are two points within Element 2 that each have the samex-coordinate, but different y-coordinates. Based on the information in the course notes and the course textbook by Logan, stresses and deflections can be calculated at points within an element after nodal deflections are calculated. For this case, according to beam theory, the normal stress in the x-direction varies through the cross-section, so it varies with y coordinate location. Choose the best answer below regarding finite element modeling results for this case. In the answers below, "CST" refers to constant strain triangle, and "LST" refers to linear strain triangle. Element 1 Point 1 1" Element 2 Point 2 10"

Explanation / Answer

CST element signifies constant strain triangular element. The strain inside these types of elements remains constant inside the element and these elements can not capture any strain gradient within an element. As the strain remains constant inisde the element, the stress also remains constant in an element.

But Linear strain triangular elements can cpature strain/stress gradients within an element.

So the first option is true i.e., for CST, normal stress should be same but for LST normal stress would be different for point 1 and point 2

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