On using different finite elements with an automatic adaptive refinement procedure for the solution of 2-D stress analysis problems

A series of numerical tests is carried out employing some commonly used Þnite elements for the solution of 2-D elastostatic stress analysis problems with an automatic adaptive reÞnement procedure. Di¤erent kinds of elements including Lagrangian quadrilateral and triangular elements, serendipity quadrilaterals, incompatible elements and hybrid elements have been tested. It is found that for a general problem involving compressible material and when a moderate accuracy of the Þnal solution is sought, the nine-node Lagrangian (L9) element will be the most e¤ective element, while when an extremely accurate solution is needed, higher order Lagrangian quadrilaterals or triangles will be a suitable choice. However, if only linear elements are available, the well known 5bI linear hybrid element is the best choice