Efficiency of the Strain Based Approach Compared to the Displacement Formulation for the Analysis of Structures

The formulation of finite elements based on the strain approach has continued in recent years and many elements were developed; for general plane elasticity problems, plate bending and shells elements. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the membrane elements remain stable with geometrical distortions and plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. The main objective of this paper is to present the efficiency and the performance of the strain based approach compared to well known displacement formulation; and this is through some validation tests using elasticity plane elements, bending plates and shell elements.