Effects of Geometry Change on Essential Features of Inelastic Behavior

by Giulio Maier, (M.ASCE), Prof.; Dept. of Struct. Engrg., Politecnico di Milano, Milan, Italy; Visiting Prof., Dept. of Civ. Engrg., Univ. of Illinois, Urbana, IL,
Daniel C. Drucker, (F.ASCE), Dean; Coll. of Engrg., Univ. of Illinois, Urbana, IL,

Serial Information: Journal of the Engineering Mechanics Division, 1973, Vol. 99, Issue 4, Pg. 819-834

Document Type: Journal Paper


Essential features include normality or lack of normality of the inelastic strain or displacement rates to a meaningful surface, convexity or concavity of this surface, stability, and uniqueness of the incremental response. The correlation between system features and those of its constituent elements is studied in the presence of significant geometric effects on equilibrium. The system is regarded as an assembly of a discrete number of constituents via finite element discretization; consequently, algebraic description is adopted. The carrying over of normality from the element to the system is proved by means of virtual work equations, and alternatively, by deriving a suitable matrix description of the system incremental laws. This description combined with some recent results in mathematical programming, leads to sufficient conditions for stability and for existence and uniqueness of the incremental response. These conditions are formulated for both individual elements and systems and can be used for actual calculations. Convexity does not in general carry over from element to system in the presence of significant geometry changes

Subject Headings: Geometrics | Inelasticity | Strain rates | Displacement (mechanics) | Correlation | Equilibrium | Finite element method | Matrix (mathematics)

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