Quadratic velocity-linear stress interpolations in limit analysis

Abstract

We compare a family of mixed interpolations on triangles with straight edges as applied to limit analysis. The aim of this paper is to prove theoretically that the approximate collapse factors obtained with these finite elements always comply with certain inequalities that exist among them. Two of these interpolations are used in limit analysis for the first time in this article. The inequalities in the proposition are also demonstrated via numerical applications. To this end, the most frequently used benchmark problems in limit analysis are revisited and discussed with respect to the results computed with these finite elements.

Shakedown analysis of porous materials via mixed meshless methods

“…The finite element mesh used to solve this example has 160 triangular elements, with 369 nodes for velocities and 105 nodes for stresses. The element used is a mixed triangular finite element which is composed by six nodes of velocities and three nodes of stresses and is described in detail in Borges et al [5] and Zouain et al [39].…”

“…The finite element mesh used for the solution of this example has 32 triangular elements, with 81 nodes for velocities and 25 nodes for stresses. The triangular element used in the comparison is a mixed finite element, composed by six nodes of velocities and three nodes of stresses [5,39]. Table 2 shows the numerical results obtained by the mixed moving least squares, mixed Shepard's, and finite element method for the particular case of a plate with b = 100 mm and a = 20 mm , which is subjected to a biaxial compressive load distribution p x =p y = 600 MPa .…”

An adaptive strategy based on conforming quadtree meshes for kinematic limit analysis

“…The upper bound limit analysis is to find a load factor that results in minimizing the plastic dissipation problem (without the work of any additional loads) for any kinematically admissible displacement field, while the lower bound limit analysis determines statically and plastically admissible stress field that maximizes the plastic load factor. Among them, finite element methods have become popular in limit analysis [7][8][9][10][11][12][13][14][15][16][17][18]. Moreover, lower-order finite elements based on triangular or quadrilateral types are largely used due to its simplicity and efficiency, and specially, the flexibility in adaptive mesh refinements.…”

“…Nevertheless, they do not perform well with unstructured meshes [17] and are sensitive to volumetric locking in the incompressibility limit. Several advanced technologies have therefore been devised in the literature [16][17][18][19].…”

Análise Limite Numérica De Problemas Axissimétricos Em Geotecnia

“…Se o objetivo da análise não é estabelecer os valores limite da carga de colapso mas sim uma solução aproximada, podem-se empregar formulações mistas, a partir das quais podem ser obtidas soluções que não garantem o cumprimento a rigor de nenhum dos dois teoremas da AL. Nos trabalhos de Casciaro e Cascini [42], Christiansen [43], Christiansen e Andersen [44] e Zouain et al [45] é empregada essa técnica que permite obter um fator de colapso que necessariamente será inferior ao limite superior e superior ao limite inferior, sendo dessa maneira mais próximo ao fator de colapso real [23]. Em Aráujo [46] se demostrou que a formulação mista apresenta como vantagens principais a maior facilidade de implementação e o fato de possuir consistência em relação aos campos de tensões e velocidades obtidos, na busca de uma solução com aproximações nos campos estático e cinemático.…”