Optimal design of bending elements

Abstract

SUMMARYDerivation of an optimality criterion for finite element structural representations using constant-moment plate-bending triangular elements is presented. Numerical examples of minimum-mass design of both simply-supported and clamped elastic plates for concentrated and distributed loading conditions under a single displacement constraint serve to illustrate the suggested procedure. Interpretation of the solutions obtained and difficulties involved are discussed in the light of recent applications of optimal control theory to structural optimization.

Optimization in Elliptic Problems with Applications to Mechanics of Deformable Bodies and Fluid Mechanics

“…These approaches have been initiated by Olhoff (1974), Lurie and Cherkaev (1976), Armand and Lodier (1978). For further results, see Rozvany (1989), Lurie (1993), Bends0e (1994).…”

A family of homogeneous analysis models for the design of scalable structures

“…Optimization examples of plate structures can be found in Armand and Lodier (1978) and in Prasad and Haftka (1979). We have chosen to test the plate example given in Fleury and Sander (1981).…”

“…In their case, the plate seems to be composed of strips of constant thickness running parallel to the diagonals of the plate, thus creating a diamond shape material distribution (Fig. The discrepancy ]between the two designs can most probably be explained by the statement in Armand and Lodier (1978) that plate optimization problems have a multitude of local minima in the design space. This design is a far cry from the minimum weight solution.…”

Structural Optimization

“…It should be emphasized that these solutions are local optima, as are the solutions for vibrating rectangular plates by OlhofI (1974) and for limited static deflection by Armand and Lodier (1978), as these authors point out [see OlhofI (1975)]. Minimum volume of solid plates of general shape for assigned load factor at plastic collapse has been considered by Cinquini (1981), who treated an example of a simply supported, square plate subjected to a centrally concentrated force.…”