A three-dimensional Fe nonlinear analysis of membranes

Wu, Baoguo; Du, Xi; Tan, Huifeng

doi:10.1016/0045-7949(95)00283-9

Cited by 12 publications

(9 citation statements)

References 4 publications

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“…It looks natural and is also consistent with the prediction in [26]. the Mooney coefficients˛1 D 180.88 kPa and˛2 D 18.088 kPa [32]. With the circular periphery simply-supported, the membrane is inflated by pressure p as shown in Figure 25(a).…”

Section: A Square Cloth On a Spheresupporting

confidence: 75%

A geometric nonlinear rotation‐free triangle and its application to drape simulation

Zhou

Sze

2011

Numerical Meth Engineering

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SUMMARYIn this paper, a rotation-free triangle is formulated. Unlike the thin and degenerated shell finite element models, rotation-free triangles employ translational displacements as the only nodal DOFs. Compared with the existing rotation-free triangles, the present triangle is simple and physical yet its accuracy remains competitive. Using a corotational approach and the small strain assumption, the tangential bending stiffness matrix of the present triangle can be approximated by a constant matrix that does not have to be updated regardless of the displacement magnitude. This unique feature suggests that the triangle is a good candidate for fabric drape simulation in which fabric sheets are often flat initially and the displacement is much larger than those in conventional shell problems. Nonlinear shell and fabric drape examples are examined to demonstrate the efficacy of the formulation.

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Section: A Square Cloth On a Spheresupporting

confidence: 75%

A geometric nonlinear rotation‐free triangle and its application to drape simulation

Zhou

Sze

2011

Numerical Meth Engineering

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“…16: the latex rubber used in this work has an estimated α=c 2 /c 1 =1.2, while α=0.1 is commonly seen in the literature [39]. For no pre-strain (slack membrane), the linear model is unbounded, and has no validity (Λ=0).…”

Section: Numerical Model Validity Rangementioning

confidence: 97%

“…2 are utilized here. The symmetry of the problem can be exploited further by modeling only a quarter of the circular membrane [2,4,39]. Experimentally, however, it is very difficult to obtain a completely uniform state of radial pretension.…”

Section: Model Verificationmentioning

confidence: 99%

“…Both thickness and the Green-Lagrange prestrain are written in terms of the completely un-deformed, slack membrane. All the points that lie in the lower-right region of the plot can be accurately modeled with the lowest fidelity linear-stress stiffening model: computed pole displacement is to within 5% of the displacement computed with a high fidelity hyperelastic model (includes both material and geometric nonlinearities [39]). Points that fall within the middle region can be accurately measured with a geometrically nonlinear model: the inextensibility assumption has failed (and thus linear models cannot be used), but the linear stress-strain relationship (Hooke's law) has not.…”

Section: Numerical Model Validity Rangementioning

confidence: 99%

“…where G is a matrix linking the nodal degrees of freedom to a displacement gradient vector [39], M is a stress matrix whose elements can be found in [13], and D T is a 3 × 3 tangent elasticity matrix. This is found by taking the derivative of the stress vector with the strain vector.…”

Section: Geometric Nonlinearitiesmentioning

confidence: 99%

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The Validity Range of Low Fidelity Structural Membrane Models

Stanford

Ifju

2008

Exp Mech

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Three classes of structural models can be considered for the characterization of thin extensible pressurized membranes. A low-fidelity, linear model assumes that all of the membrane's resistance to a transverse pressure is provided from geometric stressstiffening, and that movement along the membrane is purely out-of-plane. A medium-fidelity model can include geometric nonlinearity (finite strains, non-conservative pressure loads); while the highest level of membrane modeling assumes material nonlinearity: specifically, hyperelasticity. Common modeling applications such as performance prediction, failure prevention, and structural optimization all require repeated function evaluations. As computational cost is proportional to model fidelity, what is the validity range of the two lower fidelity models discussed above? The presence of a large pre-tension within the membrane is known to lessen the role of nonlinear elastic effects: the range of linear transverse deformation increases with pre-tension. Conversely, very low pre-tensions require the use of a nonlinear model, as the linear model becomes unbounded. This work studies the Hencky-Campbell problem for model validation purposes: hydrostatic inflation of a thin flat circular membrane, clamped along its boundary, with an arbitrary initial tension. A full-field, non-contact visual image correlation system is used to estimate the material properties of the rubber membrane, measure the state of pre-tension in the circular sheet, and document the displacement and strain fields as a function of applied pressure. The resulting data set is then compared directly with numerical simulations, in order to estimate the location of the surface of data points wherein a particular low fidelity model (either linear or geometrically nonlinear) loses its predictive capability.

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F.E.M. for Prestressed Saint Venant-Kirchhoff Hyperelastic Membranes

Gil

Computational Methods in Applied Sciences

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A three-dimensional Fe nonlinear analysis of membranes

Cited by 12 publications

References 4 publications

A geometric nonlinear rotation‐free triangle and its application to drape simulation

A geometric nonlinear rotation‐free triangle and its application to drape simulation

The Validity Range of Low Fidelity Structural Membrane Models

F.E.M. for Prestressed Saint Venant-Kirchhoff Hyperelastic Membranes

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