# Use of the Gene-Expression Programming Equation and FEM for the High-Strength CFST Columns
## 2 A Brief Background of Gene Expression Programming (GEP) and Finite Element Analysis (FEA)
### FE Modelling and Analysis  
Thirty-two CFST samples from literature [51; 52; 53; 54; 55; 56; 57; 58; 59; 60] were collected and their specifications summarized in Table 11 (Appendix A). As is obvious from Table 11, different parameters such as diameter (D), length (L), thickness (t), length to diameter ratio (L/D), diameter to thickness ratio (D/t), yield stress of the steel tube (f\({}_{\rm y}\)), and the concrete compressive strength (f\({}_{\rm c}\)), the modulus of elasticity of concrete (E\({}_{\rm c}\)), the modulus of elasticity of the steel tube (E\({}_{\rm s}\)), and the Poisson's ratio (v) were considered. Developing new techniques to analyze, assess, and predict the behaviour of composite columns is usually challenging for the engineers [51; 61]. For the modelling purpose in FEA, different types of elements were used; in order to model concrete, a 3D deformable solid element and for the steel tube, the shell element, were applied. Furthermore, for the end plates, a solid element C3D8R was applied. For the plastic behaviour of concrete, concrete damage plasticity model is considered and the specifications are assumed according to the previous similar studies which led to acceptable results in analysis [43; 44; 45; 56; 46; 47]. For simulation of the boundary conditions of models, the reference point was pinned which means the displacement assumed zero but rotation was free (U1 = U2 = U3 = 0). In addition, for the bottom end plate, it was assumed that there is no movement in x and y direction (U1 = U2 = 0). However, in the z direction the column was free to move upwards or downwards to simulate the loading condition.  
In the FE modelling and in order to achieve better simulation of the interaction between the steel tube and the concrete, the gap element was applied to achieve more accurate results. This is an element in ABAQUS software which can be inserted and  
Figure 1: Diagram of finite element analysis (FEA) of the concrete-filled steel tube (CFST) columns.  
adjusted for a better simulation of interaction specifically between two different materials. The gap element allows the simulation of slip in the way that it prevents the penetration of one node into the node next to it. The shear stress can be simulated through a friction coefficient assigned to the gap element [58; 59]. Therefore, in order to simulate more accurately, the interaction between materials was introduced to the system using the option of \"allow separation after contact\" and for this purpose, three different contacts were applied; (1) contact between steel tube and concrete with free normal and tangential separation; (2) contact between endplate and concrete, which is considered as normal interaction; and (3) contact between endplate and steel tube, which was applied as the tie connection to act like solid welding. Considering all processing data, boundary conditions, interaction between concrete and steel, and the modelling procedures, the final results were obtained and verified; afterwards they were compared with the artificial intelligence (AI) results generated from Equation (1).