Discrete Structural Optimization Research Articles

ON METHODS FOR DISCRETE STRUCTURAL OPTIMIZATION

Abstract Three algorithms for discrete structural optimization are considered. The original discrete structural optimization problem is replaced by a sequence of approximate discrete subproblems. For small size problems a Branch and Bound method is used to find a global minimum for each subproblem. The use of a generalized Lagrangean function and nonconvex duality is compared to the use of the Branch and Bound method. The generalized Langrangean function is minimized over the discrete set using a neighbourhood search technique. The dual function is maximized using a subgradient method. A method for rounding off the continuous solution is also used. The performance of the algorithms is investigated on several numerical examples. Global discrete minima are found for two convex test problems by using Branch and Bound on the original discrete structural optimization problem.

Discrete Structural Optimization

A new method for solving discrete structural optimization problems is presented. An interior penalty function is used to convert the original constrained problem into an unconstrained parametric problem. Then the search for the optimal solution to the parametric problem is based on a discrete direction gradient. Solving an appropriate sequence of these unconstrained parametric problems is equivalent to solving the original constrained optimization problem. This method is illustrated first on a small reinforced concrete problem, and then to the design of steel building frames which are made up of standard sections. Results for a one-story four-bay unsymmetrical frame and an eight-story three-bay symmetrical frame are described.

On the optimization of discrete structures with aeroelastic constraints

It is observed that modern optimal design of structures represents a confluence of two streams of theoretical development: Matric finite element approximation on the digital computer—a technology of which Professor Argyris is one of the founders; and practical application of the variational calculus. The present paper addresses optimization problems wherein complicated constraints involving dynamic aeroelastic behavior are prominent. Search procedures based on optimality criteria are believed to offer special advantages relative to such problems. With the principal constraint formulated in terms of the “ V- g method” of flutter analysis, three search schemes are applied to the minimum-weight redesign of a particular wing. The first scheme is based on the method of feasible directions and is representative of mathematical programming methods. The other two are derived from necessary conditions for a local optimum and can be classed as optimality-criteria schemes. Although the results are by no means definitive, they do suggest that a heuristic redesign algorithm based on an optimality criterion may be the best candidate for incorporation in a more general design procedure capable of treating multiple constraints with large numbers of design variables. The paper's final section undertakes to show how optimality criteria might be constructed when the aeroelastic constraint is written in the time domain. Three special forms of the aerodynamic generalized forces are considered: quasi-steady, quasi-steady with dissipation omitted, and fully unsteady. The resulting criteria for the first and last cases are based on an unproven hypothesis, but it is suggested that their simplicity merits a trial application.

Discrete Structural Optimization

The application of discrete programming to structural optimization permits the use of tabulated section properties and eliminates the need for approximate relations, such as between weight and section modulus, which may obscure the optimal solution. Linear discrete programming techniques are applied to elastic design problems by linearizing the constraint functions. The AISC Code formulae for allowable compression stresses in truss members are included exactly in the formulation. The program can also select the best material from various grades of structural steel. For computational economy, tables of structural sections are truncated, so that the solution may be restricted to a local optimum. For this reason, a fast approximate procedure may be as effective as an exact, but slower, implicit enumeration algorithm. Since the local optima depend upon the initial design, a search for the global optimum can be made by generating random starting points. Decision rules based on Bayesian statistics are developed to determine the optimal number of alternate designs to be investigated in the design process.

Parallel Distributed Optimization Of DiscreteStructures

Parallel Distributed Optimization Of DiscreteStructures