An Unsymmetric Stress Formulation for Reissner-Mindlin Plates: A Simple and Locking-Free Rectangular Element

Garusi, E.; Tralli, Antonio; Cazzani, Antonio

doi:10.1142/s1465876304002587

Cited by 34 publications

(22 citation statements)

References 43 publications

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“…Very difficult numerical problems can arise when considering structures with this kind of peculiar geometry. A set of numerical tools has been elaborated to take care of this kind of problems, among which an important role is played by suitably employed isogeometric FEM (the reader is referred, e.g., to [61][62][63][64][65]). Particularly delicate is the case in which one has unilateral constraints connected to the inextensibility of the beams; this can be numerically addressed using Lagrangian Multipliers Methods, as performed in ( [66,67]).…”

Section: Discussionmentioning

confidence: 99%

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

Alibert

Corte

2015

Z. Angew. Math. Phys.

119

103

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Since the works by Gabrio Piola, it has been debated the relevance of higher-gradient continuum models in mechanics. Some authors even questioned the logical consistency of higher-gradient theories, and the applicability of generalized continuum theories seems still open. The present paper considers a pantographic plate constituted by Euler beams suitably interconnected and proves that Piola's heuristic homogenization method does produce an approximating continuum in which deformation energy depends only on second gradients of displacements. The Γ -convergence argument presented herein shows indeed that Piola's conjecture can be rigorously proven in a Banach space whose norm is physically dictated by energetic considerations.Mathematics Subject Classification. 74Q05 · 28A33 · 35B27.

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Section: Discussionmentioning

confidence: 99%

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

Alibert

Corte

2015

Z. Angew. Math. Phys.

119

103

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“…From this point of view, an investigation on proper finite element (FE) simulation [21][22][23][24][25][26][27][28][29] or regularized FE [30][31][32][33][34][35][36][37] will be welcome in order to avoid, e.g., the unpleasant occurrence of instability [38][39][40][41][42][43][44][45][46][47][48][49]. Due to the high porosity, the Biot model should probably be modified, see e.g.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

Rosi

Placidi

Dell’Isola

2017

Z. Angew. Math. Phys.

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“…Some existing results in the literature are considered as the special case of this study, for example [8][9][10][11]17,18]. Finally, in order to investigate more complex shapes, numerical formulation based on finite element method (FEM) analysis is required and, in view of avoiding numerical instabilities and locking, it is possible to refer, for example, to [79][80][81][82][83]. In this context, if the cylindrical symmetry is lost, instability problems can arise due to the lightness of the system considered, as studied, for example, in [84,85,86].…”

Section: Discussionmentioning

confidence: 99%

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

Abd-alla

Alshaikh

Giorgio

et al. 2015

Mathematics and Mechanics of Solids

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In this paper, we built a mathematical model to study the influence of the initial stress on propagation of longitudinal waves in a hollow infinite circular cylinder in the presence of an axial initial magnetic field. The elastic cylinder is assumed to be made of a tetragonal system material. The problem is described by the equations of elasticity, taking into account the effect of the initial stress and the electro-magnetic equations of Maxwell. This requires the solution of the equations of motion in cylindrical coordinates with the z-axis directed along the axis of the cylinder. The displacement components will be obtained by founding the analytical solutions of the motion's equations. The frequency equations have been obtained in the form of a determinant involving Bessel functions. The roots of the frequency equation give the values of the characteristic circular frequency parameters of the first three modes for various geometries when the initial hydrostatic stress is compression or tension. These roots, which correspond to various modes, are numerically calculated and presented graphically. This study shows that waves in a solid body propagating under the influence of an initial stress can differ significantly from those propagating in the absence of the initial stress. The results of this research are used in analyzing the relationship between magnetic field, the initial stress and the frequency equation and could lead to discussions for using the magnetic field and the initial stress in ultrasound imaging.

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An Unsymmetric Stress Formulation for Reissner-Mindlin Plates: A Simple and Locking-Free Rectangular Element

Cited by 34 publications

References 43 publications

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof

“Fast” and “slow” pressure waves electrically induced by nonlinear coupling in Biot-type porous medium saturated by a nematic liquid crystal

A mathematical model for longitudinal wave propagation in a magnetoelastic hollow circular cylinder of anisotropic material under the influence of initial hydrostatic stress

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