Nonlinear analysis and optimal design of structures via force method and genetic algorithm

In this paper analysis, design and optimization of structures are performed considering material and geometric nonlinearity. For this purpose, the force method, energy concepts and genetic algorithm are employed. The first part of this paper contains the formulation of the problem based on the force method and energy principles using linear analysis. In this method, the material nonlinearity is also included. The formulations are examined by simple illustrative examples. Reduction of the complementary energy is efficiently incorporated in this approach. The second part of the article combines the process of the analysis and design to achieve specified stress ratios for the members of the structure. This problem is especially important in the seismic deign of structures. Geometric nonlinearity is then formulated, in the third part by employing two approaches. Considering the energy term next to the weight of the structure, optimal dimensions of the structures are selected. In each part, the efficiency of the methods is illustrated by means simple examples.