American Society of Civil Engineers

Plane Stress Limit Analysis by Finite Elements

by Ted Belytschko, A.M.ASCE, (Asst. Prof. of Struct. Mech., Univ. of Illinois at Chicago, Chicago, IL) and Philip G. Hodge, Jr., (Prof. of Mech., Illinois Inst. of Technol., Chigaco, IL)

Journal of the Engineering Mechanics Division
, Vol. 96, No. 6, November/December 1970, pp. 931-944

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Document type: Journal Paper
Discussion: by Raffaele Casciaro and et al.    (See full record)
Abstract: A numerical method is presented for the determination of lower bounds on the yield-point load of plane stress problems. In this method, a finite element technique is used to construct a parametric family of piecewise quadratic, equilibrium stress fields. The best lower bound is then found by maximizing the load, subject to the yield constraints, by means of the sequential unconstrained minimization technique. Because all conditions of the Lower Bound theorem are met exactly, the resulting solutions are true bounds. Results are given for square slabs with various cutouts and compared to upper bounds and complete elastic plastic finite element solutions.

ASCE Subject Headings:
Computer applications
Computer programming
Engineering mechanics
Finite element method
Plastic analysis