The objective of this paper is to evaluate a number of shell elements. At the same time, a new element is presented that is inspired by the quadrilateral heterosis element, Q8H, and is designated herein as the triangular heterosis element, T6H. Both elements employ the selectively reduced integration method. The elements investigated in this study include ABAQUS's three general-purpose shell elements, ANSYS's six-noded triangular element, T6, and the high-performance MITC9 element available in ADINA. The assessment is carried out by subjecting the various elements to several benchmark problems. It is found that for regular meshes, Q8H out-performs other elements and is comparable to MITC9. The performance of T6H is shown to be comparable to that of T6 in most test cases, but superior when very thin shells are considered.

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The characteristics of interdependent interpolation and mixed interpolation nonlinear beam finite elements are investigated in comparison with the equal-order interpolation element with uniform reduced integration. The stiffness matrix of the 3-noded and 4-noded equal order interpolation elements is identical to that of the 2-noded interdependent interpolation element if the internal nodal degrees-of-freedom are eliminated. The extension of the latter to include nonlinear kinematics by approximating the extensional displacement and the twist rotation with quadratic and cubic Lagrange polynomials yields unsatisfactory results. The 2-noded, 3-noded, and 4-noded mixed interpolation elements using one-, two-, and three-point quadrature rules, respectively, are shown to be equivalent to the corresponding uniform interpolation elements employing the same quadrature rules. The equivalence is established in the framework of nonlinear kinematics and anisotropic couplings. Int. J. Comput. Methods 2012.09. Downloaded from www.worldscientific.com by FUDAN UNIVERSITY on 05/16/15. For personal use only. A. Laulusa & J. N. Reddy bending-twist and bending-extension couplings. Inclusion of all these features makes the development highly complex.A relatively simple beam finite element is the displacement based uniform interpolation element. But, this element is known to suffer from locking, i.e., the beam element behaves stiffener than it actually is [Reddy (2006)]. The locking is of two kinds, shear and extensional (or membrane), and it can be very pronounced for elements with low order interpolations, e.g., linear and quadratic polynomials. It is well known that the 2-noded (linear) element that simulates a thin beam exhibits an extremely severe shear locking while it was shown in a recent study [Laulusa and Reddy (2004)] that the 3-noded (quadratic) element presents a very pronounced extensional locking when large deflections occurred without extensional deformation. In the same study, it was also shown that for the 4-noded (cubic) element, both the shear and extensional locking could be significant.The locking is often overcome by using the reduced/selective integration technique. It was shown in Laulusa and Reddy [2004] that the uniform reduced integration rule provides the best results though several linear elements must be used. Yet, for all the cases investigated, no artificial mechanisms, such as spurious energy modes were noted, unlike plate and shell elements in which these mechanisms can arise. As there is no mathematical proof that demonstrates the viability of the reduced/selective integration technique, some researchers view it more as an ad hoc technique that happen to work. In fact, the equivalence established in Malkus and Hughes [1978] between some mixed models and the reduced/selective integration displacement model gave a certain foundation to the latter approach, though linear kinematics was considered.Within the framework of linear theory, Bathe [1996] has introduced the mixed interpolation beam element ...

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