Flexibility-based large increment method for nonlinear analysis of Timoshenko beam structures controlled by a bilinear material model

Abstract

The displacement-based finite element method is currently used for solving nonlinear structural problems. This method utilizes the step-by-step solution approach to perform the nonlinear analysis of structures. This solution approach requires linearization of the constitutive equations. Therefore, there are several shortcomings of the displacement-based method that can affect the computational efficiency of this method such as errors accumulation and propagation in the step-by-step solution approach and the consumption of the computational time due to the high computational efforts during the calculations. The large increment method (LIM) can overcome these shortcomings by separating the linear global equilibrium and compatibility equations from the local constitutive equations which are considered the source of the nonlinearity.This paper discusses the development and application of the large increment method for the nonlinear analysis of Timoshenko beam structures. Timoshenko finite beam element is developed and formulated for solving beam structures with rectangular and wide flange sections. A nonlinear strain-hardening plasticity (bilinear model) material model is used for the newly developed beam elements in LIM algorithm. The proposed elements were verified by two numerical examples covering all possible cases and the results of these examples are compared with the displacement-based finite element software ABAQUS. This work proves that the LIM can be used successfully for solving the static nonlinear analysis of structures and can produce accurate results with less computational efforts and time consumption compared with the common displacement method.