Finite-Element Bending Analysis for Plates

Herrmann, Leonard R.

doi:10.1061/jmcea3.0000891

Cited by 179 publications

(38 citation statements)

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“…In this study, an assembly of four linear triangular elements sharing the same node to form a quadrilateral element is referred to as crossed patch arrangement. This arrangement of triangular elements, which was previously presented by Herrmann [33] and Nagtegaal et al [34], is further extended to overcome volumetric locking in the upper bound finite-element analysis of plane strain metal forming problems. Numerical examples of block compression and extrusion are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field in plastic deformation.…”

Section: Introductionmentioning

confidence: 94%

“…To avoid volumetric locking due to incompressibility, the functional is formulated with the finite-element procedure using the combination of triangular and special quadrilateral elements previously described by Herrmann [33] and Nagtegaal et al [34] for bending analysis of plates and limit analysis of solid structures, respectively. Each single quadrilateral element is constructed with four three-noded triangular elements, as shown in Fig.…”

Section: Finite-element Discretizationmentioning

confidence: 99%

“…In his analysis of the bending of plates, Herrmann [33] presented a special arrangement of linear triangular elements to form a four-noded quadrilateral element. This composite quadrilateral element is effective for dealing with volumetric locking.…”

Section: Introductionmentioning

confidence: 99%

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Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

Chang¹

2010

Proceedings of the Institution of Mechanical Engineers, Part C:

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In standard linear finite-element formulations, volumetric locking because of the incompressibility constraint that may occur in computational plasticity is often encountered. This study uses crossed patch arrangements of triangles to form quadrilateral elements in order to overcome the locking in the upper bound finite-element analysis of plane strain deformation problems. The velocity field is described in terms of linear triangular elements, while the incompressibility constraint is imposed by quadrilateral elements. Rigid, perfectly plastic materials, and strain hardening materials that form the von Mises model have been considered. The velocity formulation is presented and has been implemented in a finite-element code. Several examples, some benchmarks problems, are presented to illustrate the applicability of the approach for predicting the load, strain, and velocity field during the plastic deformation. Numerical results show that the crossed patch arrangements of linear triangular elements are free of volumetric locking and achieve well-defined limit loads. This study shows that the presented method can be used to simulate large plastic deformation under plane strain conditions.

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Section: Introductionmentioning

confidence: 94%

Section: Finite-element Discretizationmentioning

confidence: 99%

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Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

Chang¹

2010

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…It was clear to him that no work had been done to examine the nature of the mathematical solutions for loaded thin-walled cylindrical shells, which could then be compared with those delivered by finite element models. In developing the Morley shell theory, Morley had implicitly employed the fact that first-order thin-shell theory admits small differences in the physical quantities of the same order as those due to the inherently neglected transverse normal and shearing strains, a conjecture rigorously demonstrated by Koiter (1969). In a paper (11) Morley re-derived his governing partial differential equation for cylindrical shells on a consistent basis within the context of Koiter's first-approximation theory.…”

Section: Research Achievementsmentioning

confidence: 99%

Leslie Sydney Dennis Morley FREng FRAeS. 23 May 1924 — 16 June 2011

Morris

2016

Biogr. Mems Fell. R. Soc.

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Leslie Morley's research focused on modelling structural behaviour, with particular emphasis on plates and shells. He developed the Morley shell equation, which has been acknowledged as the simplest equation consistent with first-order shell theory. As the finite element method rose to prominence he developed elements for both plates and shells. He then worked on developing a set of new finite elements able to handle complex shell behaviour in both the linear and nonlinear regimes. He also observed that it was possible to augment the finite element solution by using singular solutions to calculate the stress intensity factor at a crack tip in a thin-walled metal structure and thereby to compute crack propagation rates. In undertaking his research Morley probed into the mathematical and physical depths of the problems he confronted, and produced some outstanding and significant results.

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“…This later development paved the way to mixed formulation can be extended and applicable to the Finite Strip Method [9]. Although this Mixed Formulation is a matter of many researches for Finite Element Method (FEM) for plate and shell analysis [10]- [13] as well as Finite Strip Method (FSM) for plate bending problems [14] [15], but the explicit forms of the Augmented Matrix, were not given for some reasons such as in [3][4]. This paper describes the construction of this augmented matrix and presents its explicit form through systematic way in order to overcome the size difficulty for spline finite strip plate bending.…”

Section: Introductionmentioning

confidence: 99%

Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

Ahmed¹,

Barony²

2019

EJERS

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Although Spline finite strip method for the analysis of plate bending based on a mixed variational formulation principle , using a variety B-Spline series as interpolation function was widely used in researches , the explicit form of the Augmented Matrix nowhere given. This leads to some difficulties concerning the verification and understanding the published results. The main objective of this paper is to introduce this matrix in abbreviated size through a detailed review of the mixed formulation for different spline finite strip models. The derived matrix will be helpful subject of research future work as it is examined by the time, reveals a very good accordance results compared with the analytical and published solutions of different plate bending problems as the reader can verified.

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Finite-Element Bending Analysis for Plates

Cited by 179 publications

References 0 publications

Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

Crossed patch arrangements of linear triangular elements for upper bound finite-element analysis of plane strain deformation problems

Leslie Sydney Dennis Morley FREng FRAeS. 23 May 1924 — 16 June 2011

Derivation of Explicit Augmented Spline Finite Strip Matrix Using Mixed Formulation For Plate Bending

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