Solution existence of the optimization problem of truss structures with frequency constraints

A basic theory is presented for determining the solution existence of frequency optimization problems for truss structures. This theory says that the natural frequencies remain unchanged when a truss is modified uniformly and that the natural frequency constraint is usually the key constraint in determining the solution existence of a truss dynamic optimization problem. Based on this theory, a practical method is presented, in which only the first order derivatives of certain eigenvalues with respect to design variables are used to determine whether or not a specific natural frequency constraint is achievable. If there is a solution for a given frequency constraint, a solution existence result can be obtained very quickly using the method. Otherwise, the extreme value of the corresponding natural frequency or a small confined range of design variables which contains the extreme value can be obtained. Numerical examples are presented to illustrate the feasibility and efficiency of the proposed method. (C) 2000 Elsevier Science Ltd. All rights reserved.