Limit analysis of plates and isoperimetric inequalities

This paper treats the problem of computing the collapse state in limit analysis for a solid with a quadratic yield condition, such as, for example, the von Mises condition. After discretization with the finite element method, using divergence-free elements for the plastic flow, the kinematic formulation reduces to the problem of minimizing a sum of Euclidean vector norms, subject to a single linear constraint. This is a nonsmooth minimization problem, since many of the norms in the sum may vanish at the optimal point. Recently an efficient solution algorithm has been developed for this particular convex optimization problem in large sparse form.The approach is applied to test problems in limit analysis in two different plane models: plane strain and plates. In the first case more than 80% of the terms in the objective function are zero in the optimal solution, causing extreme ill conditioning. In the second case all terms are nonzero. In both cases the method works very well, and problems are solved which are larger by at least an order of magnitude than previously reported. The relative accuracy for the solution of the discrete problems, measured by duality gap and feasibility, is typically of the order 10 −8 .

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Solving the transverse bending problem of thin elastic orthotropic plates with form factor interpolation method

Korobko¹,

Коробко²,

Savin³

et al. 2016

J Serb Soc Comp Mech

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The article deals with the transverse bending problem of thin elastic orthotropic plates with combined boundary conditions. The form factor interpolation method is used for deformation calculations. Analytical expressions of maximum deflection surfaces are obtained. It is proposed to use these expressions as the reference solutions. The example of the solution to the problem of transverse bending plate in the form of a parallelogram is given.

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Limit analysis of plates and isoperimetric inequalities

Cited by 3 publications

References 19 publications

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Computing Limit Loads by Minimizing a Sum of Norms

Solving the transverse bending problem of thin elastic orthotropic plates with form factor interpolation method

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