Automatic mesh refinement in limit analysis

Christiansen, Edmund; Pedersen, Ole

doi:10.1002/1097-0207(20010228)50:6<1331::aid-nme46>3.0.co;2-s

Cited by 44 publications

(42 citation statements)

References 17 publications

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“…However, when FEM is applied some of the well-known characteristics of mesh-based methods can lead to problems: the solutions are often highly sensitive to the geometry of the original mesh, particularly in the region of stress or displacement/velocity singularities; furthermore, volumetric locking may occur in plane strain and 3D problems [11]. Although adaptive schemes with the h-version [12][13][14][15][16] or p-version FEM [17,18] have been used to try to overcome such disadvantages, and show immense promise, the schemes quickly become complex and a large number of elements are generally required to obtain accurate solutions. On the other hand, the objective function in the associated optimization problem is convex, but not everywhere differentiable.…”

Section: Introductionmentioning

confidence: 99%

Limit analysis of plates using the EFG method and second‐order cone programming

Gilbert

Askes

2009

Numerical Meth Engineering

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Published paperLe, Canh V., Gilbert, Matthew and Askes, Harm (2009) SUMMARYThe meshless Element-Free Galerkin (EFG) method is extended to allow computation of the limit load of plates. A kinematic formulation which involves approximating the displacement/velocity field using the moving least squares technique is developed. Only one displacement variable is required for each EFG node, ensuring that the total number of variables in the resulting optimization problem is kept to a minimum, with far fewer variables being required compared with finite element formulations. A stabilized conforming nodal integration scheme is extended to plastic plate bending problems. The evaluation of integrals at nodal points using curvature smoothing stabilization both keeps the size of the optimization problem small and also results in stable and accurate solutions. Difficulties imposing essential boundary conditions are overcome by enforcing directly displacements at the nodes. The formulation can be expressed as the problem of minimizing a sum of Euclidean norms subject to a set of equality constraints. This non-smooth minimization problem can be transformed into a form suitable for solution using Second-Order Cone Programming (SOCP). The procedure is applied to several benchmark problems and is found in practice to generate good upper bound solutions for benchmark problems.

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Section: Introductionmentioning

confidence: 99%

Limit analysis of plates using the EFG method and second‐order cone programming

Gilbert

Askes

2009

Numerical Meth Engineering

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“…A bo = B bo ; (11) where A bo is the coe cient matrix and B bo is the vector of speci ed values of stresses along the boundary.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…This adaptive procedure has been proposed for the nite-element limit analysis [10][11][12][13][14][15] as well as the mesh-free limit analysis [16] approaches. The main policy in these methods is de ning a posteriori error estimator and establishing an adaptive re nement strategy based on the reduction of this error.…”

Section: Introductionmentioning

confidence: 99%

Adaptive mesh-free lower bound limit analysis using non-linear programming

Binesh

Rasekh

2017

Scientia Iranica

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Abstract. An adaptive mesh-free approach is developed to compute the lower bounds of limit loads in plane strain soil mechanics problems. There is no pre-de ned connectivity between nodes in the mesh-free techniques, and this property facilitates the implementation of h-adaptivity. Nodes may be added, moved, or discarded without complex changes in the data structures involved. In this regard, the Shepard mesh-free method is used in conjunction with the nodal stress rate smoothing technique and the lower bound limit analysis theory to establish a non-linear optimization problem. This problem is solved by the second-order cone programming technique, and the result is a stress eld that satis es the lower bound requirements in a non-rigorous manner. The lack of rigorousness arises from relaxation during nodal stress rate smoothing process. An error estimator is introduced by the application of Taylor series expansion, and by controlling the local error via a user-de ned tolerance, the adaptive re nement strategy is established. To demonstrate the e ectiveness of the proposed method, the procedure is applied to the examples of purely cohesive and cohesive-frictional soils.

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“…This problem was introduced to illustrate locking phenomena by Nagtegaal et al [54] and became a popular benchmark test for plastic analysis procedures, particularly for rigid-plastic limit analysis [2,3,5,55,56]. The test problem consists of a rectangular specimen with two external thin symmetric cuts under in-plane tensile stresses τ 0 , as shown in Figure 9.…”

Section: Double Notched Tensile Specimenmentioning

confidence: 99%

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

Nguyen‐Xuan

Askes

et al. 2010

Numerical Meth Engineering

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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.

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Automatic mesh refinement in limit analysis

Cited by 44 publications

References 17 publications

Limit analysis of plates using the EFG method and second‐order cone programming

Limit analysis of plates using the EFG method and second‐order cone programming

Adaptive mesh-free lower bound limit analysis using non-linear programming

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

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