TY - JOUR

T1 - Load capacity of bodies

AU - Segev, Reuven

N1 - Funding Information:
This work was partially supported by the Paul Ivanier Center for Robotics Research and Production Management at Ben-Gurion University. I would like to thank anonymous reviewers for pointing out the relation between the notion of optimal stress and the expression I obtained for it, and the limit analysis factor and the expressions for it in the works of Christiansen [1,2] and Temam and Strang [9] .

PY - 2007/3/1

Y1 - 2007/3/1

N2 - For the stress analysis in a plastic body Ω, we prove that there exists a maximal positive number C, the load capacity ratio, such that the body will not collapse under any external traction field t bounded by CY0, where Y0 is the yield stress. The load capacity ratio depends only on the geometry of the body and is given byfrac(1, C) = under(sup, w ∈ LD (Ω)D) frac(∫∂ Ω | w | d A, ∫Ω | ε{lunate} (w) | d V) = ∥ γD ∥ .Here, LD (Ω)D is the space of incompressible vector fields w for which the corresponding linear strains ε{lunate} (w) are assumed to be integrable and γD is the trace mapping assigning the boundary value γD (w) to any w ∈ LD (Ω)D.

AB - For the stress analysis in a plastic body Ω, we prove that there exists a maximal positive number C, the load capacity ratio, such that the body will not collapse under any external traction field t bounded by CY0, where Y0 is the yield stress. The load capacity ratio depends only on the geometry of the body and is given byfrac(1, C) = under(sup, w ∈ LD (Ω)D) frac(∫∂ Ω | w | d A, ∫Ω | ε{lunate} (w) | d V) = ∥ γD ∥ .Here, LD (Ω)D is the space of incompressible vector fields w for which the corresponding linear strains ε{lunate} (w) are assumed to be integrable and γD is the trace mapping assigning the boundary value γD (w) to any w ∈ LD (Ω)D.

KW - Continuum mechanics

KW - Plasticity

KW - Stress analysis

KW - Trace

UR - http://www.scopus.com/inward/record.url?scp=34247549558&partnerID=8YFLogxK

U2 - 10.1016/j.ijnonlinmec.2006.10.012

DO - 10.1016/j.ijnonlinmec.2006.10.012

M3 - Article

AN - SCOPUS:34247549558

SN - 0020-7462

VL - 42

SP - 250

EP - 257

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

IS - 2

ER -