基频约束结构优化设计的线性矩阵不等式方法

Linear Matrix Inequalities Approach to Structural Optimization Design With Fundamental Frequency Constraints

介绍了半定规划及线性矩阵不等式 (LMI)的基本概念 ,给出具有基频约束的桁架结构优化问题的半定规划形式。半定规划法 (或称线性矩阵不等式方法 )可以有效地求解该问题的全局最优解 。

The basic concept of semidefinite programs and linear matrix inequalities(LMIs)is introduced.The weight optimization of the truss structure with fundamental frequency constraints is converted into a semidefinite programs form,i.e.the minimization of a linear objective subject to LMI constraints.The global optimum can be obtained by using semidefinite programs for this optimization problem,and it is important to note that the design sensitivity coefficients of eigenvalues with respect to the design variables are not needed in the optimization process.The numerical example of a simple truss structure is provided.