A co-rotational procedure of quadrilateral plane stress element for geometrical nonlinear analysis of arches

Although considerable investigation has been done for the nonlinear geometrical analysis of arches by nonlinear finite element methods, much of this early work was surprisingly sophisticated and worth re-visiting on its computation efficiency and simplification of formulation. Based on the traditional co-rotational procedure, this work presents an improved formulation for tangent stiffness matrix of quadrilateral plane stress element under large rotation with small strain. Furthermore, it successfully build-in a particular incremental iteration scheme of nonlinear FEM equations of the (n+1)-dimensional load-displacement space for the procedure. In doing so, the method maintains the band characteristic of the structural stiffness matrix and, achieves high performance of convergence and accuracy. Following the above mentioned formulation, a FORTRAN computer program, named NPSSAP, has been developed. Numerical computations for plane. beams and single span arches in this work verify that the element's formulation, the program and the nonlinear solution strategy are of strong nonlinear geometrical computation capability. Computation results presented reflect preferably a well-established nonlinear analysis procedure of plane stress problem and a better understanding of geometrical nonlinear characteristics of plane arches.