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Optimum stacking sequence design of composite materials Part II: Variable stiffness design

Structural optimization by methods of feasible directions.

This paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The selection of the set of active constraints does not introduce any difficulty and is achieved correctly in all cases. The subdivision of the design variables in an active and passive group is intrinsically contained in the dual formulation. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results.

Structural weight optimization by dual methods of convex programming

A brief review of the structural optimization literature and a description of the present status of optimization methods are presented. The scope of the review is limited and does not profess to cover the entire literature.

Results of the optimization of two structures (by the optimality criteria approach) are presented. There are some conclusions and recommendations for future developments in structural optimization.

Structural optimization: A review and some recommendations

This paper presents a design optimization algorithm for structural weight minimization with multiple frequency constraints. An optimality criterion method based on uniform Lagrangian density for resizing and a scaling procedure to locate the constraint boundary were used in optimization. Multiple frequency constraints of equality and inequality types were addressed. The effectiveness of the algorithm was demonstrated by designing a number of truss structures with as many as 489 design variables. No attempt was made to reduce the number of design variables by such procedures as linking and/or invoking symmetry conditions. The design examples include a 10-bar truss, 200-bar truss, a modified ACOSS-II, and COFS (Control of Flexible Structures) mast truss. All the structures contain nonstructural mass besides their own mass. The algorithm is extremely stable and, in all cases, the optimum designs were obtained in less than 20 iterations regardless of the size of the structure and the number of design variables.

Structural optimization with frequency constraints

: An automated procedure is presented for minimum weight design of structures. It is an iterative procedure in which the design for the next cycle is determined by the study of the strain energy distribution in the present cycle. The displacement method of analysis is used in developing the method. Other methods of analysis which have the capability to determine the strain energy in various parts of the structure should be applicable. Designs in the presence of stress constraints and stress and displacement constraints are also considered. Where there are only stress constraints, a simple iteration based on the study of the energy distribution is adequate. In the presence of displacement constraints, the design is carried out in two stages. The first stage of iteration is similar to that in stress constraint problems and the second stage is based on a search procedure. Examples of two and three dimensional bar structures are presented to illustrate the effectiveness of the method. It proved to be extremely efficient in arriving at minimum weight structures. (Author)

Energy distribution in an optimum structural design

: An automated procedure is presented for minimum weight design of structures. It is an iterative procedure in which the design for the next cycle is determined by the study of the strain energy distribution in the present cycle. Displacement method of analysis is used in developing the method. Any other method of analysis which has the capability to determine strain energy in various parts of the structure should be applicable. Designs in the presence of stress constraints, and stress and displacement constraints are also considered. Where there are only stress constraints, a simple iteration based on the study of energy distribution is adequate. In the presence of displacement constraints, the design is carried in two stages. The first stage of iteration is similar to that in stress constraint problems and the second stage is based on a search procedure. Examples of two and three dimensional bar structures are presented to illustrate the effectiveness of the method. It proved to be extremely efficient in arriving at minimum weight structures.

V. B. Venkayya

Papers

Energy distribution in an optimum structural design

Optimization of Structures Based on the Study of Energy Distribution