scholarly journals FINITE ELEMENTS OF THE PLANE PROBLEM OF THE THEORY OF ELASTICITY WITH DRILLING DEGREES OF FREEDOM

Author(s):  
Виктор Карпиловский

Twelve new finite elements with drilling degrees of freedom have been developed: triangular and quadrangular elements based on a modified hypothesis about the value of approximating functions on the sides of the element, which made it possible to avoid dimensional instability when all rotation angles are zero; incompatible and compatible triangular and quadrangular elements which can have additional nodes on the sides. Approximating functions satisfy the following condition: the value of the rotational degree of freedom of a node is nonzero and equal to one only for one of them. Numerical examples illustrate estimated minimum orders of convergence for displacements and stresses. All created elements retain the existing symmetry of the design models.

Author(s):  
Alexander Gorodetsky ◽  
Maryna Romashkina ◽  
Bogdan Pysarevskiy

The article describes new types of finite elements that allow you to take into account all six degrees of freedom of the shell. In order to compose the finite elements, the Allman functional with a rotational degree of freedom is used. The use of finite elements is associated with a number of restrictions that are considered in the article.


2016 ◽  
Vol 846 ◽  
pp. 518-523 ◽  
Author(s):  
Hu Chen ◽  
Yi Xia Zhang ◽  
Meng Yan Zang ◽  
Paul Jonathan Hazell

In this paper, an effective approach to couple finite elements (FEs) with discrete elements (DEs) is presented. The proposed approach conforms to displacement compatibility condition at the interface between FEs and DEs, and this constraint is enforced by the Lagrange multiplier method. The coupling system is solved by the Gauss-Seidel iteration strategy and the incompatibility of degrees of freedom between FEs and DEs can be effectively addressed. Two numerical examples are employed for validation and the effectiveness of the proposed approach is also demonstrated via comparison with other numerical methods.


2019 ◽  
Vol 37 (1) ◽  
pp. 203-236 ◽  
Author(s):  
Djamel Boutagouga

Purpose This paper aims to describe the formulation of a displacement-based triangular membrane finite element with true drilling rotational degree of freedom (DOF). Design/methodology/approach The presented formulation incorporates the true drilling rotation provided by continuum mechanics into the displacement field by way of using the polynomial interpolation. Unlike the linked interpolation, that uses a geometric transformation between displacement and vertex rotations, in this work, the interpolation of the displacement field in terms of nodal drilling rotations is obtained following an unusual approach that does not imply any presumed geometric transformation. Findings New relationship linking the mid-side normal displacement to corner node drilling rotations is derived. The resulting new element with true drilling rotation is compatible and does not include any problem-dependent parameter that may influence the results. The spurious zero-energy mode is stabilized in a careful way that preserves the true drilling rotational degrees of freedom (DOFs). Originality/value Several works dealing with membrane elements with vertex rotational DOFs have been published with improved convergence rate, however, owing to the need for incorporating rotations in the finite element meshes involving solids, shells and beam elements, having finite elements with true drilling rotational DOFs is more appreciated.


Author(s):  
Jacob J. Rice ◽  
Joseph M. Schimmels

This paper presents the design and simulation results of a passive prosthetic ankle prosthesis that has mechanical behavior similar to a natural ankle. The presented design achieves active behavior with powered push-off to propel the body forward. The design contains a conventional compression spring network that allows coupling between two degrees of freedom. There is a translational degree of freedom along the leg and a rotational degree of freedom about the ankle joint. During a standard gait cycle, potential energy from the person’s weight is stored in the spring network from deflection along the leg. The energy is released by the spring network as rotation of the foot. With this design, capping the allowable leg deflection at 15 millimeters produces 45% of the rotational work that a natural ankle will produce. This is based on simulation using published average kinetic and kinematic data from gait analyses.


Author(s):  
Sifeddine Abderrahmani ◽  
Toufik Maalem ◽  
Abdallah Zatar ◽  
Djamal Hamadi

The purpose of this paper is to present the formulation of a new sector finite element based on the strain approach for the numerical analysis of circular thin plate bending. The element is named SBSPK and has four nodes and three degrees of freedom per node (3 d.o.f./node). From several numerical examples, it is shown that convergence can be achieved with the use of only a small number of finite elements. The results obtained are compared with analytical and available numerical solutions.


Author(s):  
Y Zhao ◽  
D Su ◽  
W Wei ◽  
X Dong

Thorough and systematic investigations are performed into the meshing principium of generating a cylindrical gear by an Archimedes hob based on the two-degree-of-freedom theory of gearing geometry. The numerical examples show the verification and validation of the formulated principium and the developed model. Conclusions suitable for industrial application are reached by means of numerical simulations.


1999 ◽  
Vol 6 (4) ◽  
pp. 159-167
Author(s):  
D.V. Balandin ◽  
N.N. Bolotnik ◽  
W.D. Pilkey

The limiting performance of shock isolation of a system with one and a half degrees of freedom is studied. The possibility of using a single-degree-of-freedom model for this analysis is investigated. The error of such an approximation is estimated. Numerical examples are presented.


Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3740
Author(s):  
Olafur Oddbjornsson ◽  
Panos Kloukinas ◽  
Tansu Gokce ◽  
Kate Bourne ◽  
Tony Horseman ◽  
...  

This paper presents the design, development and evaluation of a unique non-contact instrumentation system that can accurately measure the interface displacement between two rigid components in six degrees of freedom. The system was developed to allow measurement of the relative displacements between interfaces within a stacked column of brick-like components, with an accuracy of 0.05 mm and 0.1 degrees. The columns comprised up to 14 components, with each component being a scale model of a graphite brick within an Advanced Gas-cooled Reactor core. A set of 585 of these columns makes up the Multi Layer Array, which was designed to investigate the response of the reactor core to seismic inputs, with excitation levels up to 1 g from 0 to 100 Hz. The nature of the application required a compact and robust design capable of accurately recording fully coupled motion in all six degrees of freedom during dynamic testing. The novel design implemented 12 Hall effect sensors with a calibration procedure based on system identification techniques. The measurement uncertainty was ±0.050 mm for displacement and ±0.052 degrees for rotation, and the system can tolerate loss of data from two sensors with the uncertainly increasing to only 0.061 mm in translation and 0.088 degrees in rotation. The system has been deployed in a research programme that has enabled EDF to present seismic safety cases to the Office for Nuclear Regulation, resulting in life extension approvals for several reactors. The measurement system developed could be readily applied to other situations where the imposed level of stress at the interface causes negligible material strain, and accurate non-contact six-degree-of-freedom interface measurement is required.


2014 ◽  
Vol 16 (1) ◽  
pp. 288-296 ◽  
Author(s):  
Yoshikazu Ito ◽  
Kazuyuki Takai ◽  
Akira Miyazaki ◽  
Vajiravelu Sivamurugan ◽  
Manabu Kiguchi ◽  
...  

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