Theory and implementation of sub-model method in finite element analysis

Through finite element analysis (FEA) software to study mechanical performance of a bridge structure is currently a commonly used method. The keys to obtain accurate results are to select the appropriate element type and establish a refine mesh model. With the construction of a large number of kilometer-level long-span bridges in practical projects, the time cost of establishing and analyzing a fine mesh solid finite element model (FEM) of a long-span bridge with complex structure can not be ignored. In order to find the balance between accuracy and efficiency, sub-modeling technique can be used to analyze the bridge structure. It is often thought that the sub-modeling technique is only applicable to shell and solid elements, but in fact it is also applicable to plane frame models. Based on two-dimensional (2-D) beam element model, the theory of sub-model was theoretically deduced. Meanwhile the sub-modeling technique was applied and verified by an example of plane frame model. Furthermore, based on the three-dimensional (3-D) solid FEM of a skew bridge, the influence of mesh size on the calculation accuracy was illustrated. Based on sub-modeling technique of nodal displacements, the results of the global model and the sub-model for the skew bridge were compared and studied in terms of stress field and plastic damage of concrete. It is found that the sub-model technique based on nodal displacements is suitable for solid FEM.