ICM METHOD WITH A MAPPING BASED ON NODE-UNCOUPLED TOPOLOGY VARIABLES

An ICM (independent continuous mapping) method with the mapping of node-uncoupled topology variables is proposed in this paper, which is applied to model and solve the structural topology optimization problems. Firstly, the ground structure is meshed into nodes and elements. Independent and continuous topology variables are defined on the nodes, and an uncoupled mapping is established based on elemental bilinear interpolation, replacing the element-based independent and continuous topology variables. The existence or absence of elements is continuously approximated, enabling the filtering and identification of node topology variables and the interpolation of physical quantities within elements. An optimization model based on node topology design variables is derived, and a second-order dual programming algorithm based on separable variables is employed for solving. Additionally, an improved rounding technique for the optimal topology is proposed. Secondly, the modeling and solving process is demonstrated by applying the topology optimization to minimize structural weight (or volume) under displacement constraints. Finally, numerical examples of displacement-constrained topology optimization under single-load and multi-load scenarios are presented, and the computational results validate the effectiveness of the proposed method. The research in this paper has the following advantages: It overcomes the defects of previous research based on elemental topology variables, i.e., the optimal structural boundary is zigzagged, and obtains optimal structures with smooth and clear topological boundaries. The definitions of node topology variable and element topology function fields are given. The 5 criteria, which must be followed to construct the topology variable field, are extracted. Errors in the research on the ICM method based on node topology variables are addressed. The node design variables are no longer coupled, allowing for the convenient calculation of the second derivatives of structural quantities. This facilitates efficient optimization using dual optimization algorithms based on separable variables. The research not only enriches the connotation of the ICM method and promotes its development but also provides valuable references for the variable-density method based on node variables.