טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBogomolny Michael
SubjectOptimal Design of Structures Subjected to Dynamic Loading
Using a Reanalysis Approach
DepartmentDepartment of Civil and Environmental Engineering
Supervisors Professor Emeritus Uri Kirsch
Professor Emeritus Izhak Sheinman


Abstract

The general structural optimization problem is mathematically nonlinear, therefore numerical iterative methods are often used in the solution process. In general the constraints value, the objective function value and their gradients (partial derivatives with respect to the design variables) must be calculated at each iteration cycle. Since the constraints are implicit functions of the design variables, the analysis equations must be solved repeatedly in order to calculate the values of the constraints.

In typical structural optimization problems solutions of the analysis and sensitivity analysis equations will require most of the computational effort. Repeated solutions of these equations many times might be very expensive, particularly in large-scale structures having nonlinear dynamic response. The general approach presented in this study is intended to alleviate this difficulty. It is suitable for both direct (zero-order) and gradient (first-order) optimization methods, various classes of analysis models, and different types of design variables. The analysis models considered include linear and nonlinear models of dynamic analysis.

In the presented approach approximate reanalysis methods are developed and used for repeated analysis and sensitivity analysis. The dynamic analysis for both linear and non-linear response is solved using the Mode Superposition method, which requires calculation of vibration modes. Repeated solution of eigenproblems, which is needed for evaluation of the vibration modes, is based on the Combined Approximation method. Several procedures are developed to improve the efficiency and the accuracy of the approximations. Using these procedures, the basis vectors are calculated for a limited number of design points and then used to evaluate the response for any modified design. The concepts of shifts and Gram-Schmidt orthogonalizations are applied to improve the accuracy of the results. Eigenproblem reanalysis has been used effectively in dynamic reanalysis and sensitivity analysis of linear and non-linear models.

Finite-difference sensitivity reanalysis is considered for intermediate designs assumed during the solution process. A new procedure has been developed for effective calculation of analytical derivatives. Linear and Non-linear dynamic sensitivity analysis procedures have been developed. These procedures provide efficient and sufficiently accurate results.

Exact analysis of the structure is carried out only for the assumed initial design and for the final design reached by the optimization procedure. It is shown that the reductions in the computational effort achieved by the proposed approach for large-scale structures may reach several orders of magnitude. Typical numerical examples show that the results achieved by the approach presented are similar to those obtained by exact reanalysis and sensitivity analysis.