Shape Optimization: Finite Element Example

by William R. Spillers, (M.ASCE), Prof.; Dept. of Civ. Engrg., Rensselaer Polytechnic Inst., Troy, N.Y.,
Sohan Singh, Grad Student; Dept of Civ. Engrg., Rensselear Polytechnic Inst., Troy, N.Y.,

Serial Information: Journal of the Structural Division, 1981, Vol. 107, Issue 10, Pg. 2015-2025

Document Type: Journal Paper


The study of shape optimization for skeletal structures is extended to a simple case of the finite element method using plane stress, constant strain triangular elements. Following earlier work, the method developed neglects the constitutive equations and is formulated using only node equilibrium and a stress-type objective function from plasticity theory. A form of constitutive equation subsequently appears through the Kuhn-Tucker conditions. As a result, the optimization algorithm used takes on the appearance of an analysis-redesign procedure. Two plane stress, beam-type examples are included.

Subject Headings: Finite element method | Constitutive relations | Stress strain relations | Case studies | Plane strain | Optimization models | Structural members | Stress analysis

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