A simple triangular curved shell element

Stolarski, Henryk K.; Belytschko, Ted; Carpenter, Nicholas; Kennedy, J.M.

doi:10.1108/eb023574

Cited by 46 publications

(24 citation statements)

References 34 publications

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“…The wrinkling of edges described previously has an interesting connection with the model proposed by Stolarski et al , , whose basic idea is to split the deformation into in‐plane and out‐of‐plane displacements, denoted with u and w , so that the membrane strain can be written in terms of Föppl‐von Karman kinematics

ε = \nabla u + {((), \nabla w)}^{2},

combined with a co‐rotational formulation to maintain the frame invariance of the model. They first write the linearized CST energy using the three‐edge elongations

η_{i} : = ∥ e_{i} ∥ / ∥ ē_{i} ∥ - 1

E (η) = \sum_{f \in F} η_{f}^{T} K_{f} η_{f},

where K f is the stiffness matrix and η f is the vector containing the three‐edge elongations relative to the face T .…”

Section: Kinematicsmentioning

confidence: 93%

A framework for creating low‐order shell elements free of membrane locking

Quaglino

2016

Numerical Meth Engineering

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SUMMARYThis paper proposes a first step towards a framework to develop shell elements applicable to any deformation regime. Here, we apply it to the large and moderate deformations of, respectively, plates and shells, showing with standard benchmarks that the resulting low-order discretization is competitive against the best elements for either membrane-dominated or bending-dominated scenarios. Additionally, we propose a new test for measuring membrane locking, which highlights the mesh-independence properties of our element. Our strategy is based on building a discrete model that mimics the smooth behavior by construction, rather than discretizing a smooth energy. The proposed framework consists of two steps: (i) defining a discrete kinematics by means of constraints and (ii) formulating an energy that vanishes on such a constraint manifold. We achieve (i) by considering each triangle as a tensegrity structure, constructed to be unstretchable but bendable isometrically (in a discrete sense). We then present a choice for (ii) based on assuming a linear strain field on each triangle, using tools from differential geometry for coupling the discrete membrane energy with our locking-free kinematic description. We argue that such a locking-free element is only a member of a new family that can be created using our framework (i) and (ii).

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ε = \nabla u + {((), \nabla w)}^{2},

combined with a co‐rotational formulation to maintain the frame invariance of the model. They first write the linearized CST energy using the three‐edge elongations

η_{i} : = ∥ e_{i} ∥ / ∥ ē_{i} ∥ - 1

E (η) = \sum_{f \in F} η_{f}^{T} K_{f} η_{f},

where K f is the stiffness matrix and η f is the vector containing the three‐edge elongations relative to the face T .…”

Section: Kinematicsmentioning

confidence: 93%

A framework for creating low‐order shell elements free of membrane locking

Quaglino

2016

Numerical Meth Engineering

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“…The numerical values of the vertical displacement at the two reference points obtained with the BST and DKT-15 elements after a time of 0.4 ms using the 16 £ 32 mesh are compared in Table III with experimental results and also with a numerical solution reported by Stolarski et al (1984)) using a curved triangular shell element and the 16 £ 32 mesh. It is interesting to note the The deformed shapes of the transverse section for z ¼ 26:28 in: and the longitudinal section for x ¼ 0 obtained with the BST element (finer mesh) after 1 ms are compared with the experimental results in Figure 19.…”

Section: Example 2 Cylindrical Panel Under Impulse Loadingmentioning

confidence: 97%

“…2 1.213 2 0.574 KT15 (12 £ 32el.) 2 1.160 2 0.553 Stolarski et al (1984) 2 1.183 2 0.530 Experimental Stolarski et al (1984) 2 1.280 2 0.700 Balmer and Witmer (1964) are also plotted Use of BST rotation-free triangle Figure 19. Cylindrical panel.…”

Section: Example 4 Stretch Forming Of a Hemispherical Cupmentioning

confidence: 99%

Non‐linear explicit dynamic analysis of shells using the BST rotation‐free triangle

Oñate

Cendoya

Miquel

2002

Engineering Computations

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The paper describes the application of the simple rotation-free basic shell triangle (BST) to the non-linear analysis of shell structures using an explicit dynamic formulation. The derivation of the BST element involving translational degrees of freedom only using a combined finite element-finite volume formulation is briefly presented. Details of the treatment of geometrical and material non linearities for the dynamic solution using an updated Lagrangian description and an hypoelastic constitutive law are given. The efficiency of the BST element for the non linear transient analysis of shells using an explicit dynamic integration scheme is shown in a number of examples of application including problems with frictional contact situations.

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“…The finite element discretization of (8) is obtained in the same manner as for (4). The standard Newton-Raphson method is used to solve the nonlinear equations.…”

Section: Penalty Variational Modelmentioning

confidence: 99%