Node-based independent continuous mapping method for topological optimization of continuum structures

A new node-based independent continuous mapping method for topological optimization of continuum structures is presented. Modifying the previous ICM method, the element-based topological variables is replaced by node-based topological variables which illustrate the features of every element. Continuity of topological variables is ensured by interpolation of shape functions in an element. Reciprocal relationship between topological variables and design variables are introduced. According to the principle for partial derivative of compound function, the derivatives of different kinds of structural responses and weight are deduced. The procedure of formulating and solving the topological optimization model of continuum structure is illustrated by the example with displacement constraints. Two different image-filter methods are developed to eliminate numerical instabilities in topology optimization, such as checkerboard patterns and mesh-dependence problems. The validity of the proposed methods is substantiated by some two-dimensional examples.