Mixed-dimensional coupling method for box section member based on the optimal stress distribution pattern

Mixed-dimensional coupling is significant for the accurate performance analysis of a concurrent multi-scale model, while the stress distribution pattern is a key problem that influences the mixed-dimensional coupling method. With respect to existing coupling methods, the real stress pattern of the complicated section is replaced by the approximate formula, the uniform distribution pattern of shear stress is used along the sectional thickness direction, and the shear stress of the sectional corner is neglected. The aforementioned simplified assumptions of stress distribution pattern are the key reasons that cause a distortion of the local stress and reduce the reliability of the multi-scale model. In the study, the optimal stress distribution pattern is determined using the proposed method, in order to provide the optimal stress distribution for mixed-dimensional coupling, and improve the accuracy of the multi-scale model. First, a stress distribution calculation model based on the higher-dimensional element type and section size of member is established. Next, the stress distribution pattern is determined and optimized using the surface fitting technology and iterative calculation, in which the coefficient of determination R2 is selected as the optimization index. Third, under the specified local coordinate system, the multipoint constraint equations for mixed-dimensional coupling are determined based on the optimal stress distribution patterns and element shape functions. Finally, the optimal stress distribution patterns of box section, which consider the linear distribution along the thickness direction and stress contribution in the sectional corner, are determined. Furthermore, concurrent multi-scale models of a cantilever beam and warren truss structure with the box section are established, and are used to validate the effectiveness and applicability of the proposed method based on a comparison of the structural global responses, local responses, and dynamic characteristics.