טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentMadah Hazem
SubjectOptimal Design of Skeletal Structures with Geometric
Nonlinearity
DepartmentDepartment of Civil and Environmental Engineering
Supervisor Professor Oded Amir
Full Thesis textFull thesis text - English Version


Abstract

Optimized designs of skeletal structures are attractive to structural engineers and architects for utilization in the conceptual design stage, due to their efficiency in transferring loads and their aesthetic shapes. To shorten the detailed design stage, most of the structural considerations should be integrated into the optimization process, e.g. allowable stresses, buckling, and other manufacturing and construction limitations. Buckling is considered one of the most important aspects that must be accounted for, especially in long span structures and in structures with high-strength materials, in which slender members and instable configurations may be present.

In the literature, buckling has been classified into three types: Euler buckling of single members, global buckling of the whole structure and chain instability of trusses which results from the use of the ground structure approach. Therefore, including buckling considerations in the optimization problem requires several different constraints. Local buckling stability can be achieved by adding an Euler buckling constraint on every bar. Global buckling stability can be achieved by an eigenvalue-based formulation or by semi-definite programming. Chain stability requires special treatment, e.g. by identifying instable nodes and adding overlapping bars across hinges, or by identifying melting nodes. Remarkably, no studies were found in the literature that treat all buckling types simultaneously. In this study, all buckling types of 2-D skeletal structures have been imposed in a new formulation that is based on geometric nonlinear (GNL) analysis, where buckling of members and instable configurations are taken into account implicitly. For the purpose of this study, all optimization procedures and structural analyses were programmed in MATLAB.

Buckling is strongly influenced by the imperfections that are assumed. In the context of structural optimization, imperfections have been considered mainly to account for chain instability in trusses, using geometrical imperfections or nominal forces in relation to robust design. In some cases, the imperfections have been assumed constant along the optimization process. In other cases, a large number of imperfection samples have been accounted for, leading to a very costly optimization procedure. In the current contribution, the idea of “worst imperfection” proposed in the literature for continuum structures is extended and adapted for the design of trusses and frames. Imperfections are considered consistently throughout the optimization process using a two-step approach: First, shape optimization is performed to find the worst-case imperfection shape of joints’ positions. Thereafter, sizing-topology optimization is performed to find the minimum volume of a buckling-resistant structure with the given imperfection. The advantages of this approach are: 1) It can lead to robust designs in an efficient manner; and 2) It can numerically overcome bifurcation buckling in the GNL analysis. To take into account material nonlinearity in optimization of frames, the GNL analysis had been extended to consider nonlinear material relations. Results related to the combination of buckling with nonlinear constitutive behavior, have been examined and led to more viable conceptual designs that require less post-rationalization. Preliminary results for maximizing energy absorption show that the proposed approach is capable of optimizing various functionals. These arguments and further considerations are discussed and presented in detail.