Application of vectorial rotational variables in large displacement analysis of structures

Abstract

The chapter explains that the introduction of vectorial rotational variables in the large displacement analysis brings several advantages: these vectorial rotational variables are commutative and additive, so a consistent result can be easily achieved during updating the rotation description in the incremental/iterative solution procedure; all local variables can be obtained from global variables by applying a vector transformation matrix; symmetric-consistent tangent stiffness matrices can be achieved in the local and global systems, provided the equations of equilibrium are work-conjugate with the adopted displacement and rotation parameters; large incremental step can be adopted in the incremental loading process; and the rotational variables can describe the element large displacement response accurately. Verification examples provided in the chapter demonstrate that the proposed unified co-rotational approach provide accurate predictions of the large displacement response of two-dimensional/three-dimensional framed structures as well as curved shell problems, providing computational efficiency through the use of a symmetric tangent stiffness matrix and step-insensitivity.