Notice of RetractionOn solving the min-max problem of the stress of the structural elements in the structural topology optimization
In this paper, we deal with the min-max problem of the stress of the structural elements in the structural topology optimization. A generalized KS function is presented which transforms the local stress to global strain energy of structure through Von Mises Criterion. The ICM method is employed for solving the topology optimization problem. Some classic numerical examples are presented which provide quality solutions and the minimum stress design to obtain the final design.
Recent advances in optimal structural design
Sponsored by the Technical Committee on Structural Design of the Technical Administrative Committee on Analysis and Computation of the Technical Activities Division of the Structural Engineering Institute of ASCE. This report documents the dramatic new developments in the field of structural optimization over the last two decades. Changes in both computational techniques and applications can be seen by developments in computational methods and solution algorithms, the role of optimization during the various stages of structural design, and the stochastic nature of design in relation to structural optimization. Topics include: methods for discrete variable structural optimization; decomposition methods in structural optimization; state of the art on the use of genetic algorithms in design of steel structures; conceptual design optimization of engineering structures; topology and geometry optimization of trusses and frames; evolutionary structural optimization; design and optimization of semi-rigid framed structures; optimized performance-based design for buildings; multi-objective optimum design of seismic-resistant structures; and reliability- and cost-oriented optimal bridge maintenance planning. The book concludes with an extensive bibliography of journal papers on structural optimization published between 1987 and 1999.
ON TOPOLOGY OPTIMIZATION OF TRUSSES
The selection of a minimum weight truss, out of a large set of candidate trusses, is treated. An initial configuration is generated by connecting all the n nodal points with n(n − 1)\2 truss members. A feasible displacement field, satisfying displacement and stress constraints, is obtained from a static analysis of this truss, followed by a uniform scaling of all truss dimensions. The finite element formulation for the initial configuration is then reformulated to yield a linear programming problem. The solution to this leads to a new configuration which is further optimized by solving a small nonlinear programming problem. With the method proposed, trusses subject to one loading condition and subject to stress and displacement constraints can be selected and optimized using a modest computational effort. Three examples are given to demonstrate the usefulness of the proposed method.