WORK-RATIO-EXTREMUM METHOD FOR TOPOLOGY OPTIMIZATION OF TRUSSES SUBJECTED TO LOADS INCLUDING SELF-WEIGHT

The work-weight-distribution criterion is derived from the first-order extremum conditions of minimal truss weight under the work constraint with self-weight loads. It indicates that structural weight can be optimally distributed according to the difference of external force work and self-weight work. The work-ratio-extremum method of the truss topology optimization is derived from the Kuhn-Tucker conditions with inequality constraints and the regular influences of a ratio step on the first order derivations of the work function. The method includes three steps, i.e., formulate the optimal ratio step and the multiplier, and solve the work-criterion equations. Using the regular influences of a scale of all design variables on the fixed-point iterative solution and its Jacobi matrix, it is proved that the algorithm is globally convergent. Based on the incompatility of the work constraint and the stress constraints, the stress ratio method can be used to optimize the structure next to the topology optimization. Numerical examples of a three-bar truss and a ten-bar truss for multiple loadings show that the methods are effective.