A two-dimensional model for linear elastic thick shells

Nzengwa, Robert; Simo, B.H.Tagne

doi:10.1016/s0020-7683(98)00165-6

Cited by 17 publications

(23 citation statements)

References 20 publications

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“…The constitutive law through the strain tensor contains the change of third fundamental form as shown in the tables; the thickness ratio impacts the behavior of the shell because of the significant energy contribution due to as the ratio increases unlike the K-L classical model [3].…”

Section: Discussionmentioning

confidence: 99%

“…is a truncated thick shell or the best first-order thick shell variational equation under N-T's model; see [3]. It can be observed that this equation has similarities with familiar equations in engineering literature.…”

Section: Variational Equationsmentioning

confidence: 92%

“…Mathematical Problems in Engineering 3 is a more generalized Kirchhoff-Love displacement [3] and can also be written in Reissner-Mindlin format as follows:…”

Section: The N-t Model Of Thick Shellsmentioning

confidence: 99%

“…Surveys of various shear stresses in linear elastic thick shells can be found in the works of [3] where they are mathematically substantiated. We have obtained good convergence results for thin shells with the half side element = 12 and a pressure in the load point = 0.53 Pa for a spherical shell.…”

Section: Impact Of the Transverse Stressesmentioning

confidence: 99%

“…Moreover it is well known that transverse stresses can not be neglected as the shell becomes thicker. Without any ad hoc geometrical hypothesis, it was deduced that the strain tensor is planar; that is, ∈ 3 = 0 and, as a consequence, the limit displacement reads = + and the stresses depend on the in-plane strains and 3 are computed from appropriate differential equations; see [3].…”

Section: Introductionmentioning

confidence: 99%

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Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method

Feumo

Nzengwa

Joseph

2017

Mathematical Problems in Engineering

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This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne's model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed and 0 finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. The gradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099.

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Section: Discussionmentioning

confidence: 99%

Section: Variational Equationsmentioning

confidence: 92%

“…Mathematical Problems in Engineering 3 is a more generalized Kirchhoff-Love displacement [3] and can also be written in Reissner-Mindlin format as follows:…”

Section: The N-t Model Of Thick Shellsmentioning

confidence: 99%

Section: Impact Of the Transverse Stressesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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