DEVELOPMENT OF OPTIMIZATION PROCEDURE FOR TRUSS STRUCTURES WITH DYNAMIC CONSTRAINTS

Abstract

The research of this thesis focuses on the design optimization of truss structures with dynamic constraints. First, the solution existence of structural dynamic optimization problems is discussed. In this part, a basic theory is presented for determining the solution existence of frequency optimization problems of truss structures. This theory states that the natural frequencies remain unchanged when a truss is modified uniformly and that 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, its existence can be proven very quickly using the present 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. Second, an optimal design method to minimize the weight of a linear elastic structural system subjected to random excitations is presented. It is focused on the response mean square (RMS) at certain degrees of freedom. Constraints on natural frequencies and bounds of design variables are also considered in the optimization. Both correlated and un-correlated generalized random excitations are considered in the present formulation. The sensitivities of the expected number of crossings as well as the displacement RMS with respect to the design variables are also derived. The present method is applicable to stationary Guassian random excitation. Computed examples show the feasibility and efficiency of the proposed method. Third, an optimization procedure is presented for minimum weight optimization with discrete design variables for truss structures subjected to constraints on stresses, natural frequencies and frequency responses. The optimization process consists of two steps. The first step is to find a feasible basic point by defining a global normalized constraint function using the difference quotient method. The second step is to determine the discrete values of the design variables by converting the structural dynamic optimization process into a zero-one programming. A binary number combinatorial algorithm is employed to perform the zero-one programming. To speed up the convergence, a mode summation technique is used in the structural dynamic reanalysis. Examples of discrete optimum truss design are presented to demonstrate the feasibility of the presented optimization procedure. Finally, a general-purpose design procedure is presented for the optimal design of truss structures with variable geometry (joint locations) and discrete member size selected from specified tables of member sectional areas. The optimization is subjected to constraints on member stress, Euler buckling, joint displacements, natural frequencies and frequency responses. It is demonstrated in this chapter that the shape optimization not only reduces the weight of the structure but also improves the solution existence of the optimal problem. The design problem is cast as a multilevel numerical optimization problem. For each proposed configuration, the member sizes are updated in a size sub-optimization process. This size sub-problem is solved using a difference quotient method based on the concept of the global normalized constraint function. The shape optimization is performed using a feasible direction method. The discrete sizing variable values are determined via an improved approximate rounding off method which needs few structural analyses. The capabilities of the method are illustrated by examples.