On Saint-Venant’s Problem with Concentrated Loads
Source abstract
Abstract
The classical Saint-Venant problem is to find a solution of the traction problem of elastostatics in a finite cylinder Ω loaded over its bases. We prove that the problem has a unique solution for equilibrated surface forces (hat{ oldsymbol { s}}in W-1,q(partialOmega)), with q∈(2−ϵ 0,+∞) for some positive ϵ 0 depending on Ω. Hence (hat{ oldsymbol { s}}) can model force acting on ∂Ω, concentrated on sets of zero Lebesgue surface measure of ∂Ω. Moreover, if (hat{ oldsymbol { s}}) is equilibrated on each basis, we give a simple proof of the Toupin estimate expressing Saint-Venant’s principle.
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Research context
OpenAlex topics: Advanced Mathematical Modeling in Engineering · Elasticity and Material Modeling · Composite Material Mechanics
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References (23)
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