M.Sc Thesis

M.Sc StudentAmir Oded
SubjectNonlinear Analysis and Reanalysis of Structures Using
Combined Approximations
DepartmentDepartment of Civil and Environmental Engineering
Supervisors PROFESSOR EMERITUS Izhak Sheinman
Full Thesis textFull thesis text - English Version


Multiple repeated analyses (reanalyses) are required in various problems of structural analysis, design and optimization. Typical such problems include structural optimization, nonlinear analysis, damage analysis and probabilistic analysis. In structural optimization, a major part of the computational effort involved in the solution process is invested in structural analysis. The Combined Approximations (CA) approach provides accurate and efficient results that can significantly reduce the computational effort. In previous studies, the CA approach has been proven to be an effective tool in various reanalysis problems, including linear reanalysis, vibration reanalysis, dynamic reanalysis and design sensitivity analysis. The object of this study is to further develop the approach for nonlinear analysis and reanalysis of structures.

First, formulation of the CA approach for nonlinear problems is presented. Then, several solution strategies and procedures are developed for various nonlinear problems. The approach is implemented in the solution of various numerical examples, representing different types and degrees of nonlinear response, i.e. material nonlinearity, geometric nonlinearity, buckling, snap-through etc. The presented solution strategies differ in accuracy and efficiency of the approximations. Problems having highly nonlinear response are solved by strategies that are more accurate and less efficient. The results obtained by the various approximate procedures are compared with those obtained by standard solution procedures. In cases where the approximate solutions are not sufficiently accurate, the source of the problem is pointed out and various means intended to overcome such difficulties are proposed. Finally, an evaluation of the computational effort involved in the approximate solution of realistic large-scale problems is presented. The computational effort is compared with that of standard solution procedures in order to evaluate the relative effectiveness of the proposed procedures.

It is shown that in general, the procedures presented provide accurate results. For reanalysis problems, the savings in the computational effort can be significant. For analysis problems, the expected savings depend on the degree of nonlinearity: for moderate nonlinear response, substantial savings can be achieved; for highly nonlinear response the savings are not significant.