ABSTRACT
Flexibility-based method is used to formulate the distributed plasticity model of a 3D frame element (12 DOF) under the above assumptions. An element is represented by several cross sections (i.e. stations) that are located at the numerical integration scheme points. The spread of inelastic zones within an element is captured considering the variable section flexural EIy and EIz and axial EA rigidity along the member length, depending on the bending moments and axial force level, cross-sectional shape and nonlinear constitutive relationships. Based on Green’s integration formula according to which the domain integrals appearing in the evaluation of internal resultant efforts and tangent stiffness matrix coefficients of the section can be evaluated in terms of boundary integral. This approach is extremely rapid because stress integrals need only be evaluated at a small number of points on the section boundary and rapid convergence is assured by the inclusion of exactly determined tangent stiffnesses and, of great importance, it is assure convergence for any load case. The geometrical nonlinear effects for each element are taken into account in the present analysis, in a beam column approach, by the use of the inelastic stability stiffness functions and updating at each load increment the length, axial force and the flexural rigidity about of each principal axes of the element. In order to trace the equilibrium path, for proportionally and non-proportionally applied loads, the proposed model has been implemented in a simple incremental matrix structural-analysis program. Using an updated Lagrangian formulation (UL) the nonlinear
geometrical effects are considered updating the element forces and geometry configurations at each load increment (Chiorean 2009).
