Stability Analysis And Optimization Of Truss And Frame Structures

Truss and frame structures are commonly used and very important skeletal structures widely constructed in structural engineering as well as in industrial and civil buildings. Among various modes of failure related to skeletal structures, the global instability and local buckling are major concerns. With the technical progress of design and construction, skeletal structures are becoming larger in span and more flexible, which bring up more strict requirement for the structural stability. Consequently, accurate and practical theoretical analyses as well as numerical approaches become research needs.There have existed two types of stability analyses for skeletal structures. One is the nonlinear eigenvalue theory and the other is the theory of geometrically nonlinear critical point. The eigenvalue theory was proposed earlier than the theory of critical pint and has been extensively applied for critical load of global buckling of structures. However, recently it was found out that application of this theory may-lead to overwhelmingly big stress, sometimes even bigger than the yield stress of the material or the stress of Euler buckling. This indicates that due to members yielding and/or Euler buckling, the structure may lose its loading-carrying ability long before the theoretically predicted global buckling happens To overcome this shortcoming, new stability analysis theories e.g. the linear Eulerian theory and nonlinear Eulerian theory have been proposed. It is important to adopt practical theory to solve stability problems for truss and frame structures.In this dissertation, the author compares various theories of stability analysis, and makes comments on their applications in truss and frame structures through examples. The main issues include:1. The analysis for stability of truss structures through the linear Eulerian theory. The computation of critical load and the optimal design with buckling constraints are carried out.2. The analysis for stability of truss structures through the nonlinear Eulerian theory. The computation of critical load and the optimal design with buckling constraints are carried out.3. The analysis for stability of frame structures through the nonlinear Eulerian theory. The computation of critical load and the optimal design with buckling constraints are carried out.4. The analysis for stability of frame structures through the nonlinear Eulerian theory. The computation of critical load and the optimal design with buckling constraints are carried out.This dissertation is funded by the Natural Secience Foundation of China under contract numbers 10332010,10002005.