GEOMETRICALLY NONLINEAR ANALYSIS USING A QUADRILATERAL 8-NODE CO-ROTATIONAL PLANE ELEMENT

A new geometric nonlinear element tangent stiffness matrix for the quadrilateral 8-node plane element under a large rotation with small strain is presented by changing the origin of the coordinate system and adopting a field consistency principle, which is different from other existing co-rotational approach adopting the origin of a local coordinate system and a geometric consistency principle. The stiffness matrix is asymmetric. However, it requires less computation and positively meaningful in reducing the accumulated round-off errors and increasing the convergence of iterations. A Fortran-based nonlinear finite element iteration procedure is established by the Newton-Raphson technique. Two examples including a cantilever beam with a concentrated load and a distributed load and a shallow arch under a concentrated load at arch crown are solved to verify the reliability and computational efficiency of the proposed element formulation.