Formulation for nonlinear dynamic analysis of steel frames considering the plastic zone method

摘要

A corotational Lagrangian formulation for nonlinear dynamic analysis of steel planar frames is addressed. This formulation employs the Plastic Zone Method and is capable of considering second-order effects, initial geometric imperfections and residual stresses. The element dynamic equilibrium is derived from the virtual power theorem, and local cubic shape functions are used to deduce the element tangent stiffness and mass matrices. The integration of stresses over the cross-section area is executed based on elastic-perfectly plastic stress-strain curve, which is applied for each slice of the cross-sections located at the Gauss points along the member length. In order to solve the system of dynamic nonlinear equations in time domain, the numerical analysis procedure makes use of the Newmark's implicit time integration method and the Newton-Raphson technique. The PPLA-NLEP computational program, which is based on the finite element method, is modified to perform the nonlinear time-history analyses. A good correspondence between the found numerical solutions and those reported by other researchers and obtained by OpenSees software is observed, indicating that the proposed method is efficient in predicting the nonlinear dynamic behavior of steel structures.