Developing Force-Based Matrix Formulation for Materially and Geometrically Nonlinear Analysis of Structure

Because the strong form of the equilibrium is satisfied, force-based approaches offer more convergence and stability compared with displacement-based approaches and therefore seem more suitable for analyses with extreme nonlinear constraints. This paper first demonstrates the development and extension of force-based matrix formulation for geometrically nonlinear analysis and developing it into materially nonlinear analysis, in line with two general approaches of solving and formulating. It is obvious that because the stiffness matrix is presented in a local coordinate system, the matrix needs to be transformed into a generalized coordinate system for a general analysis. Due to using the Homogeneous transformation method and its flexibility in problems with large displacements, the transformations used in this method will be briefly discussed. Correspondingly, transformation matrices are also discussed. Additionally, the extension of the aforementioned problem to materially nonlinear states, and also the three-dimensional analyses while considering the added effects, are finalized. It should be noted that the fiber theory is used for the analysis of plastic.

Keywords:

Force-based approach , Geometrically nonlinear analysis , materially nonlinear analysis , Shear deformations