An Investigation On Truss Structural Dynamic Topology Optimization

Topology optimization is a most challenging domain of structural optimization. The change of a topology improves the structural characters or decreases the weight, and makes the unsolvable problem meaningful. Structural dynamic topology optimization, under some dynamic constraints, is a hotspot for structural optimization. It is important for the research of theory and application.The main contents of truss dynamical topology optimization discussed in this paper are as follows:1. A new approach to truss topology optimization, i.e topology group concept, is introduced. It may consider many kinds of constraint, including stress, Euler buckling, static displacement and frequency constraints. The node cost as well as the member cost is incorporated in the cost function. The method can solve the difficulty caused by removing the members and the nodes.2. The character of the constraints (i.e., the feasible domain of the constraints) is analysed in this paper. An important conclusion is that the feasible domain of frequency constraints is no convex, while the others are convex. Therefore, the frequency constraint is the key constraint for the existence of the solution.3. Under the condition of unchanged topology configuration of the truss, the extremum existence of the natural frequency is demonstrated. It will orientate the optimization of structural cross-sections and the topology optimum with frequency constraints toward a further search measure.4. The solution existence for dynamic topology optimization of truss is explored from the engineering point of views: when the design variables (section areas) are continuous and their bound are not imposed, if there is no frequency constraint, the optimal solution always exists for a given optimization problem and contrarily, when the frequency constraint is considered, the frequency will become the key constraint and also the solution existence will be changed by the topology alteration. Thus, the conclusion will be beneficial to decrease the blindness and the cost of optimization.5. The topology group concept is then extended to deal with the type-selection of truss optimal design and the topology optimization based on the structural reliability.