Locking-free stabilized conforming nodal integration for meshfree Mindlin–Reissner plate formulation

Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2010) SUMMARYA meshless Element-Free Galerkin (EFG) equilibrium formulation is proposed to compute the limit loads which can be sustained by plates and slabs. In the formulation pure moment fields are approximated using a moving least squares technique, which means that the resulting fields are smooth over the entire problem domain. There is therefore no need to enforce continuity conditions at interfaces within the problem domain, which would be a key part of a comparable finite element formulation. The collocation method is used to enforce the strong form of the equilibrium equations and a stabilized conforming nodal integration scheme is introduced to eliminate numerical instability problems. The combination of the collocation method and the smoothing technique means that equilibrium only needs to be enforced at the nodes, and stable and accurate solutions can be obtained with minimal computational effort. The von Mises and Nielsen yield criteria which are used in the analysis of plates and slabs respectively are enforced by introducing second-order cone constraints, ensuring that the resulting optimization problem can be solved using efficient interior-point solvers. Finally, the efficacy of the procedure is demonstrated by applying it to various benchmark plate and slab problems.

Section: Introductionmentioning

confidence: 96%

Limit analysis of plates and slabs using a meshless equilibrium formulation

Gilbert

Askes

2010

“…It is known as the stabilized conforming nodal integration (SCNI) scheme. The SCNI scheme has been applied successfully to various problems, for instance, elastic analysis [12][13][14], plastic limit analysis [15], error estimation [16] and a stabilized mesh-free equilibrium model for limit analysis [17]. It is shown that, when the SCNI scheme is applied, the solutions obtained are accurate and stable, and locking problems can also be prevented.…”

Section: Introductionmentioning

confidence: 99%

“…Figure 2. Geometry definition of a smoothing cell Substituting equation (13) into equation (11), and applying the divergence theorem, one …”

Section: Cell-based Smoothed Finite Element Methods (Cs-fem)mentioning

confidence: 99%

A cell‐based smoothed finite element method for kinematic limit analysis

Nguyen‐Xuan

Askes

et al. 2010

Published paperLe, Canh V., Nguyen-Xuan, H., Askes, H., Bordas , Stéphane P. A., Rabczuk, T. and Nguyen-Vinh, H. (2010) SUMMARYThis paper presents a new numerical procedure for kinematic limit analysis problems, which incorporates the cell-based smoothed finite element method (CS-FEM) with second-order cone programming. The application of a strain smoothing technique to the standard displacement finite element both rules out volumetric locking and also results in an efficient method that can provide accurate solutions with minimal computational effort. The non-smooth optimization problem is formulated as a problem of minimizing a sum of Euclidean norms, ensuring that the resulting optimization problem can be solved by an efficient second order cone programming algorithm. Plane stress and plane strain problems governed by the von Mises criterion are considered, but extensions to problems with other yield criteria having a similar conic quadratic form or 3D problems can be envisaged.

“…So there is no need to discretize the director field n and n is readily obtained from eq. (6). The variation of the motion x (and their spatial derivatives) is given by…”

Section: Discretizationmentioning

confidence: 99%

“…Garcia et al [5] developed meshfree methods for plates and beams; the higher continuity of meshfree shape functions was exploited for Mindlin-Reisner plates in combination with a p-enrichment. Wang and Chen [6] proposed a meshfree method for Mindlin-Reisner plates. Locking is treated using second order polynomials for the approximation of the translational and rotational motion in combination with a curvature smoothing stabilization.…”

Section: Introductionmentioning

confidence: 99%

A meshfree thin shell method for non‐linear dynamic fracture

Rabczuk

Areias

Belytschko

2007

446

135

SUMMARYA meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The C 1 displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straight forward.