Bisector and zero-macrospin co-rotational systems for shell elements

A principal issue in any co-rotational approach for large displacement analysis of plates and shells is associated with the specific choice of the local reference system in relation to the current deformed element configuration. Previous approaches utilised local co-rotational systems, which are invariant to nodal ordering, a characteristic that is deemed desirable on several fronts; however, the associated definitions of the local reference system suffered from a range of shortcomings, including undue complexity, dependence on the local element formulation and possibly an asymmetric tangent stiffness matrix. In this paper, new definitions of the local co-rotational system are proposed for quadrilateral and triangular shell elements, which achieve the invariance characteristic to the nodal ordering in a relatively simple manner and address the aforementioned shortcomings. The proposed definitions utilise only the nodal coordinates in the deformed configuration, where two alternative definitions, namely, bisector and zero-macrospin definitions, are presented for each of quadrilateral and triangular finite elements. In each case, the co-rotational transformations linking the local and global element entities are presented, highlighting the simplicity of the proposed approach. Several numerical examples are finally presented to demonstrate the effectiveness and relative accuracy of the alternative definitions proposed for the local co-rotational system

Innovative design of underintegrated lagrangian finite elements

Imperial Users onl

A study of transient response of initially stressed composite sandwich folded plates

In this paper a C° four node flat facetted shell element with drilling rotational degrees of freedom based on a first order shear deformation shell theory is developed to study the transient response of initially stressed composite sandwich folded plates. The new shell element contains three translations, two rotations of the normals about the shell mid-plane, and one drilling rotational degree of freedom per node. A consistent mass matrix formulation is employed to evaluate the total kinetic energy of the system. A generic validation study is carried out to evaluate the performance of the present finite element formulation. New results are presented for the transient analysis of initially stressed composite sandwich folded plate structures