Improved stiffness-based first-order approximations for structural optimization

Improved first-order approximations of displacements, stresses, and forces are presented. The main objectives in developing the method presented are 1) to preserve the ease of implementation and the efficiency of the common first-order approximations and 2) to improve significantly the quality of the results, such that the method can be used in problems with very large changes in the design variables, including geometrical changes and elimination of members. The method is based on results of a single exact analysis and can be used with a general finite element system. It is suitable for different types of design variables and structures. Results obtained by the proposed method are compared with various first-order approximations for modifications in the cross section as well as the geometry and the topology of the structure. It is shown that the proposed approximations are most effective in terms of the accuracy, the efficiency, and the ease of implementation.