Improved Formulation in Mixed-Based State-Space Approach for Large Displacement Inelastic Analysis of Frames

Abstract

In this research, an enhanced flexibility- (force-) based formulation is developed for a shear deformable beam-column element by using force interpolation functions. The development is derived from Reissner’s exact stress resultant theory and its finite strain field for a Timoshenko frame element. Here, the state-space approach is applied, and the differential-algebraic equation system, consisting of a conservation global system and local constitutive equations, is formed and solved simultaneously. To improve the element’s accuracy, a polynomial-based displacement field approximation is implemented to evaluate the element flexibility matrix. The proposed technique is verified by nonlinear examples, including material and geometric nonlinearities, to examine its precision. It is shown that shear-locking is alleviated by the element; therefore, shear effects can easily be considered. The proposed method is more reliable and accurate than general displacement-based methods and existing force-based formulations.