Optimal Layout Design using the Element Connectivity Parameterization Method: Application to Three Dimensional Geometrical Nonlinear Structures

The topology design optimization of “three-dimensional geometrically-nonlinear” continuum structures is still a difficult problem not only because of its problem size but also the occurrence of unstable continuum finite elements during the design optimization. To overcome this difficulty, the element connectivity parameterization (ECP) formulation with two implementation strategies is presented. Unlike in the conventional element density method, the degrees of connectivity between elements are varied to represent various material distributions in ECP. Depending on the location of connectivity-controlling link elements, ECP can be classified as either the E-ECP (External element connectivity parameterization) or I-ECP (Internal element connectivity parameterization) methods. In terms of computation time, the I-ECP method, a newly-developed version of ECP, is much more efficient because the degrees of freedom of the element-connectivity parameterizing links are eliminated in element level before the total system matrix is assembled. In terms of implementation, however, the E-ECP is easier to use because the sensitivity analysis in E-ECP does not require the explicit expression of the (tangent) stiffness matrix of continuum finite elements. Therefore, any finite element code, including commercial codes, can be readily used for the ECP implementation. The key ideas and characteristics of these methods will be presented in this paper.