TY - GEN

T1 - Load capacity of perfectly plastic bodies and structures

AU - Segev, Reuven

AU - Falach, Lior

PY - 2011/12/1

Y1 - 2011/12/1

N2 - For a statically indeterminate structure we examine the class of internal forces that are in equilibrium with a given external loading/. We define the optimal stress φ opt as the smallest possible magnitude of any equilibrating internal force distribution. The stress sensitivity k = max f{φ f opt/||f||}, a purely geometric property of structure, is a measure of the sensitivity of the structure to variable external loading. Using the result for optimal stresses, an expression for the stress sensitivity factor is obtained in terms of the structure's kinematic interpolation mapping. For a given structure made of a perfectly plastic material with a yield stress σ y, we consider the load capacity ratio of the structure: the largest positive number C, depending only on the geometry of the structure, which satisfies the following property. For any loading distribution / on the structure whose maximum is /max, the structure will not undergo plastic collapse as long as f max ≤ σ yC, independently of the distribution of the load. The paper presents the mathematical aspects, related mechanical notions, algorithms and examples corresponding to load capacity ratios of structures. These notions, the corresponding theoretical results, and a simple implementation to finite element models are presented using linear and conic programming.

AB - For a statically indeterminate structure we examine the class of internal forces that are in equilibrium with a given external loading/. We define the optimal stress φ opt as the smallest possible magnitude of any equilibrating internal force distribution. The stress sensitivity k = max f{φ f opt/||f||}, a purely geometric property of structure, is a measure of the sensitivity of the structure to variable external loading. Using the result for optimal stresses, an expression for the stress sensitivity factor is obtained in terms of the structure's kinematic interpolation mapping. For a given structure made of a perfectly plastic material with a yield stress σ y, we consider the load capacity ratio of the structure: the largest positive number C, depending only on the geometry of the structure, which satisfies the following property. For any loading distribution / on the structure whose maximum is /max, the structure will not undergo plastic collapse as long as f max ≤ σ yC, independently of the distribution of the load. The paper presents the mathematical aspects, related mechanical notions, algorithms and examples corresponding to load capacity ratios of structures. These notions, the corresponding theoretical results, and a simple implementation to finite element models are presented using linear and conic programming.

UR - http://www.scopus.com/inward/record.url?scp=84866891820&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84866891820

SN - 9781617380839

T3 - 50th Israel Annual Conference on Aerospace Sciences 2010

SP - 970

EP - 982

BT - 50th Israel Annual Conference on Aerospace Sciences 2010

T2 - 50th Israel Annual Conference on Aerospace Sciences 2010

Y2 - 17 February 2010 through 18 February 2010

ER -