The paper presents a simultaneous numerical analysis of the geometric and material nonlinearity of the beams. It describes a process of determining the bearing capacity of a stratified cross-section of a beam made of homogeneous and isotropic material in linear and nonlinear domains of material behaviour. Material nonlinearity is analysed by the variation of the cross-sectional stiffness of the beam on bending EI in the stiffness matrix of the system obtained according to the first-order theory. Geometric nonlinearity is introduced into the calculation using the geometric stiffness matrix of the system. Numerical examples present an application of the procedure for solving problems of nonlinear structure analysis. The calculation results obtained in accordance with the procedure described in the paper are compared with the results of the SCIA software package.

The paper presents a calculation of a system supported on piles according to the second order theory. The influence of piles as supports on the structure is replaced by elastic supports. In the numerical model, the supports are modeled as elastic springs. To compare the calculation results, a system based on rigid and deformable supports was analyzed. The analysis of the system was performed according to the first order theory and the second order theory, which introduces geometric nonlinearity into the calculation. The process of soil modeling around a pile with replacement springs is presented. The applicability of the described procedure is shown in a numerical example. The comparison of the calculation results was done on numerical models of systems with rigid and elastic supports.

The paper presents a procedure for numerical modelling of the rod cross-section bearing capacity. Equilibrium between cross sectional forces and cross-sectional stresses is determined by iterative procedures. According to the described procedure, the load-bearing capacity of the cross-section is determined according to the isotropic linear and nonlinear behavior of the material, for homogeneous and inhomogeneous cross-sections. The nonlinear behavior of the material reduces the stiffness of the cross section of the rod EA and EI, with a significant increase in the deformation values ε and κ. The applicability of the calculation and analysis of obtained results is presented using numerical examples.

The paper shows the calculation of the system by second order theory on elastic supports. At the calculate it adopted a linear relationship of stress-displacement soil. The method of calculating the beams based on rigid and deformed supports was presented by introducing geometric nonlinearity into the calculate. Expressions were performed for the rigidity of the supports in the vertical direction and on the rotation of the foundation, due to the elastic deformation of the soil. Numerical examples show the application of the procedure described. Through diagrams and charts of static and deformation, a comparison of calculate results was made.

This paper presents a numerical analysis of a reinforced concrete beam in which the concrete and reinforcement are above the yield strength of the material. Further, the procedure for determining the relationship between the cross-sectional forces and the deformations of the layered cross-section of a rod is described. For a short rod with reduced stiffness of the EI and EA cross-sections, a stiffness matrix with variable members is formed. The applicability of the proposed analysis method for the material nonlinearity in a beam calculation is demonstrated through a numerical example. The aim of the present paper is to show the flow of plastification and the load deformation of the system nodes. Finally, the results of the manual deformation calculation system are compared with the results from SCIA software.