Student name and ID Please provide the pros and cons of sol

Student name and & ID: Please provide the pros and cons of solving a plane-stressed structure(1) using CST elements compared with that using quadrilateral 4-node elements; and that of (2) using quadratic (second order) elements compared to linear elements for the same problem.

Solution

the linear triangular elements are less susceptible to shear locking than bi-linear quad elements in bending problems. Use linear quad elements and increase the number of quads through the beam thickness ( at least 3 or 4 elements) to avoid shear locking.

CST refers to in-plane stresses but in bending problems the out of plane deflection and rotation plays important role. In bending formulation various approaches are used to tackle the problem of shear locking etc. A typical popular triangular shell element is DKT (Discrete Kirchhoff Theory) element, which works with second order expression for rotation using a special procedure to eliminate mid-side nodes. It has improved behaviour as far as shear locking is concerned. This may do in plane analysis with linear displacement function (CST) or quadratic in-plane displacement function (LST) (an AT/DKT-Allman Triangle/DKT element). In all the cases only three corner nodes are used and mid side nodes are eliminated in the formulation. Of course, in simple bending problems the advantages of these elements may not be visible. The point is that the 3 nodes triangle may deceptively look simple but it may have all the features of higher order element. If you are having your own code you may look at these references for details or the theoretical details provided by the software developer could be seen. QUAD4 element often has linear in-plane displacement function and unless special features are built in the bending formulation it may not behave as well as the triangular element.