| Compared with the continuous optimization design method, the results of the discrete optimum design are more in line with the actual needs of projects. However, because of the discontinuity of design variables, many effective analytical mathematical optimization algorithms and conditions are no longer applicable. Therefore, a new function for the continuous method of structural optimization design with discrete variables is proposed in this paper, which is called S-type curve integral function. The function has the property of continuous differentiability, and when the independent variable is zero or one, the corresponding function value is zero. According to the properties of the proposed function, new zero-one design variables are introduced to replace original design variables, and discrete optimum design is transformed into an equivalent zero-one programming. Then, the constraint condition that the new design variable is zero or one is replaced by the condition that the value of S-type curve integral function is zero, and the continuous processing of the discrete variable optimization problem is realized in this way. In addition, the mathematical model and the corresponding algorithm of the nonlinear programming problem equivalent to the original problem are given, which can be solved by the general mathematical programming method. Finally, a numerical example and several classical truss structure section size optimization problems are calculated by MATLAB numerical analysis software. Numerical results show that the proposed method is effective and has the advantage of being insensitive to the scale of the problem. |
