桁架频率优化解存在性及其算法研究

给出桁架在给定固频约束时，动力不优化解存在性的基本理论。指出：桁架固频约束通常是决定其动力学优化解是否存在的“关键约束”。基此，给出了一种工程算法，只用到固频对设计变量的一阶导数，就可很快确定约束是否可能满足。反之，当提出的方法判定给定固频约束不能满足时，可以求出一个解存在的极限频率的狭窄范围及相应的设计变量范围，以供设计人员重新设计时参考。三个由简到繁的算例说明了所提出方法实用、有效。

An Investigation on Solution Existence and Evaluation of the Optimization Problem of Truss Structures with Frequency Constraints

A basic theoryis presented for determining the solution existence of the frequency optimization problemfor truss structures. It is stated that the natural frequency constraint is usually thekey constraint in determining the solution existence of truss dynamic optimizationproblem. Based on this theory, a practical method in engineering is presented, in whichonly the first order derivatives of certain eigenvalues with respect to design variablesare involved to determine whether or not a specified natural frequency constraint isachievable. An obvious advantage of the method is the existent solution can be evaluatedconsequently very quickly via the method, if the specified frequency constraints are metand a solution for the structural dynamic optimization problem (SDOP) is existent.Otherwise, an extreme value of the corresponding natural frequency or a small confinerange of design variables which contains the extreme value of design variables can also beevaluated for the designer to re-design the structure. Three practical examples have shownthe feasibility and effectiveness of the method.