
Accession Number : ADA194165
Title : Optimal Design of Fibered Structures.
Descriptive Note : Rept. no. 1 (Final) 1 Jan 8331 Dec 87,
Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE
Personal Author(s) : Strang, Gilbert
PDF Url : ADA194165
Report Date : Feb 1988
Pagination or Media Count : 8
Abstract : The problem of shape optimization is the minimize the area that must be filled by expensive material in order to satisfy design constraints. Those constraints require the structure to withstand a given external load (or family of loads) without exceeding a permissible deformation, or a permissible compliance, or the yield limit of a plastic material. The design problem is mathematically subtle, because the underlying optimization problem is not convex. Structural equilibrium is governed by a partial differential equation of the form div(c(x)grad u) = f, but in contrast to the analysis problem (which solves for u), the design problem is to choose c. The control variable is the coefficients, and frequently a conventional solution does not exist. The minimum weight design is approached by coefficients c which jump more and more frequently between alternative states. The design develops a complicated microstructure, and the challenge is to see within that structures a simple and computable pattern. The limit is a composite material, in which the original materials have welldefined densities and orientations. The composite is achieved by homogenization of the original materials. Mathematically this is expressed by a relaxation, or convexification, of the original minimization problem. The project has seen a successful integration of these fundamental theories (previously developed along separate lines), and the explicit computation of optimal designs in a series of significant engineering problems.
Descriptors : *COMPOSITE MATERIALS, *FIBERS, COEFFICIENTS, DEFORMATION, DENSITY, ENGINEERING, EQUILIBRIUM(GENERAL), EXTERNAL, HOMOGENEITY, LIMITATIONS, MATERIALS, MICROSTRUCTURE, OPTIMIZATION, PARTIAL DIFFERENTIAL EQUATIONS, PLASTICS, SHAPE, SOLUTIONS(GENERAL), STRUCTURAL PROPERTIES, WEIGHT, YIELD
Subject Categories : Laminates and Composite Materials
Distribution Statement : APPROVED FOR PUBLIC RELEASE