Background: The paper presents a numerical procedure for kinematic limit analysis of Mindlin plate governed by von Mises criterion. Methods: The cell-based smoothed three-node Mindlin plate element (CS-MIN3) is combined with a second-order cone optimization programming (SOCP) to determine the upper bound limit load of the Mindlin plates. In the CS-MIN3, each triangular element will be divided into three sub-triangles, and in each sub-triangle, the gradient matrices of MIN3 is used to compute the strain rates. Then the gradient smoothing technique on whole the triangular element is used to smooth the strain rates on these three sub-triangles. The limit analysis problem of Mindlin plates is formulated by minimizing the dissipation power subjected to a set of constraints of boundary conditions and unitary external work. For Mindlin plates, the dissipation power is computed on both the middle plane and thickness of the plate. This minimization problem then can be transformed into a form suitable for the optimum solution using the SOCP. Results and Conclusions: The numerical results of some benchmark problems show that the proposal procedure can provide the reliable upper bound collapse multipliers for both thick and thin plates.
This study proposes a pseudo-lower bound method for direct limit analysis of two-dimensional structures and safety evaluation based on isogeometric analysis integrated through Bézier extraction. The key idea in this approach is that the stress field is separated into two parts: fictitious elastic and residual, and then the equilibrium conditions are recast by the weak form. Being different from the displacement approach which employs the kinematic formulation, the approximations based on the stress field satisfy automatically volumetric locking phenomena. Dealing with optimization problems, a second-order cone programming, providing significant advantages of the conic representation for yield criteria, is employed. The examination of various numerical benchmark problems shows an efficient and reliable method for the proposed approach.
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