Topological optimization of continuum structures with design-dependent surface loading - Part I: new computational approach for 2D problems

This paper describes a new computational approach for optimum topology design of 2D continuum structures subjected to design-dependent loading. Both the locations and directions of the loads may change as the structural topology changes. A robust algorithm based on a modified isoline technique is presented that generates the appropriate loading surface which remains on the boundary of potential structural domains during the topology evolution. Issues in connection with tracing the variable loading surface are discussed and treated in the paper. Our study indicates that the influence of the variation of element material density is confined within a small neighbourhood of the element. With this fact in mind, the cost of the calculation of the sensitivities of loads may be reduced remarkably. Minimum compliance is considered as the design problem. There are several models available for such designs. In the present paper, a simple formulation with weighted unit cost constraints based on the expression of potential energy is employed. Compared to the traditional models (i.e., the SIMP model), it provides an alternative way to implement the topology design of continuum structures. Some 2D examples are tested to show the differences between the designs obtained for fixed, design-independent loading, and for variable, design-dependent loading. The general and special features of the optimization with design-dependent loads are shown in the paper, and the validity of the algorithm is verified. An algorithm dealing with 3D design problems is described in Part II, which is developed from the 2D algorithm in the present Part I of the paper.