Allmanʹs triangle, rotational DOF and partition of unity

A simplification of the 1984 Allman triangle (one of historically most important elements with rotational dofs) is presented. It is found that this old element takes a typical form of the partition of unity approximation. The Allman’s rotation presented in the partition of unity form offers merits and convenience in formulation and practical applications. The stiffness matrix of the 1984 Allman triangle, which is originally computed from the linear strain triangular element (the 6 nodes quadratic triangle), can be obtained instead in a cheaper way from that of the constant strain triangular element. The constraint of the rotational terms during essential boundary treatment, which remains equivocal and ambiguous, is understood to be mandatory. The partition of unity notion enables a straightforward extension of the Allman’s rotational dof to meshfree approximations. In numerical examples, we discuss suppression of spurious zero-energy modes and patch tests. Standard benchmarks are carried out to assess performance of the newly formulated triangle and a meshfree approximation with the rotational dofs. Copyright q 2006 John Wiley & Sons, Ltd.