scholarly journals Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

2021 ◽  
Author(s):  
A. V. Krysko ◽  
J. Awrejcewicz ◽  
K. S. Bodyagina ◽  
V. A. Krysko
Keyword(s):  
Numerical Experiments ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
The Finite Element Method ◽  
Mechanical Loads ◽  
Variable Parameters ◽  
Transverse Loads ◽  
Static Mechanical ◽  
Structure Lead ◽  
Deformation Diagrams

AbstractMathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.

scholarly journals Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials

2021 ◽  
Author(s):  
A. V. Krysko ◽  
J. Awrejcewicz ◽  
K. S. Bodyagina ◽  
M. V. Zhigalov ◽  
V. A. Krysko
Keyword(s):  
Deformation Theory ◽  
Theory Of Elasticity ◽  
The Finite Element Method ◽  
Variable Parameters ◽  
Transverse Loads ◽  
Edge Conditions ◽  
3D Deformation ◽  
Von Mises ◽  
Lateral Load Distribution ◽  
Von Mises Plasticity

AbstractIn this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed.

scholarly journals Finite Element Modeling of Surgical Scalpel with Piezoelectric Actuator

2019 ◽  
pp. 15-23
Author(s):  
A. S. Skaliukh ◽  
P. A. Oganesyan ◽  
A. A. Solovieva ◽  
T. E. Gerasimenko
Keyword(s):  
Finite Element ◽  
Finite Element Modeling ◽  
Medical Devices ◽  
Numerical Experiments ◽  
Soft Tissues ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Element Modeling ◽  
Oscillatory Systems ◽  
Viscosity Coefficients

The main goal of the present work is mathematical and finite element modeling of component dynamic oscillatory systems, including piezoceramic elements, elastic elements and external influences from soft tissues that describe the operation of ultrasonic medical devices, as applied to instruments and medical devices for finding the most effective forms and modes of operation. Elastic and piezoceramic solids are modeled within the linear theory of elasticity and electroelasticity, and soft tissues are acoustically medium with certain viscosity coefficients. As a research tool used CAE package ACELAN, which builds three-dimensional and axisymmetric models of the device. In numerical experiments, a modal and harmonic analysis is performed, on the basis of which the most effective operating frequencies are identified.

scholarly journals The Schwartz Alternating Algorithm for Solving 3D Exterior Helmholtz Problems

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Qing Chen ◽  
Baoqing Liu ◽  
Qikui Du
Keyword(s):  
Numerical Experiments ◽  
Domain Decomposition Method ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Natural Boundary ◽  
Helmholtz Problem ◽  
Artificial Boundaries ◽  
Overlapping Domain Decomposition ◽  
Natural Boundary Element Method ◽  
Element Method

Based on the natural boundary reduction, an overlapping domain decomposition method is discussed for solving exterior Helmholtz problem over a three-dimensional (3D) domain. By introducing two different artificial boundaries, the original unbounded domain is divided into a bounded subdomain and a typical unbounded region, and a Schwartz alternating method is presented. The finite element method and natural boundary element method are alternately applied to solve the problems in the bounded subdomain and the typical unbounded subdomain. Moreover, the convergence of the Schwartz alternating algorithm is studied. Finally, some numerical experiments are presented to show the performance of this method.

Study on the Finite Element Method for Three-Dimensional Static Property of Polyurethane Vibration Isolators

2011 ◽  
Vol 295-297 ◽  
pp. 1586-1589 ◽  
Author(s):  
Li Hong Shu ◽  
Lin He ◽  
Bai Feng Liu
Keyword(s):  
Finite Element ◽  
Constitutive Relations ◽  
Three Dimensional ◽  
Reference Value ◽  
Experimental Result ◽  
The Finite Element Method ◽  
Analysis Software ◽  
Element Analysis ◽  
Vibration Isolators ◽  
Static Mechanical

Based on the experimental study of its constitutive relations, uses the ABAQUS finite element analysis software to simulation analyzes the three-dimensional static property of one type of polyurethane vibration isolators. The numerical analysis and experimental result demonstrate that the material constitutive model built by this method can describe the three-dimensional static mechanical property of the polyurethane isolator accurately. This method provides certain reference value for establishment of the constitutive relations of other types of polyurethane isolator.

scholarly journals To the calculation of the toroidal shell with a local deepening on the external and on the inner surface

2021 ◽  
Vol 274 ◽  
pp. 03032
Author(s):  
Nukh Yakupov ◽  
Khakim Kiyamov ◽  
Inzilija Mukhamedova
Keyword(s):  
Numerical Experiments ◽  
Strain State ◽  
Three Dimensional ◽  
Toroidal Shell ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Stress Strain State ◽  
Inner Surface ◽  
Thin Walled ◽  
Toroidal Shells

Thin-walled toroidal shells are widely used in the construction During operation, various defects appear on the surface of the shells, in particular, local depressions on the outer and inner surfaces, causing stress concentration in the structure. A three-dimensional spline option of the finite element method was developed to determine the stress-strain state of a toroidal shell with a local deepening on the outer and inner surface. The numerical experiments were carried out. The regularities of the changes in a stress-strain state of the shell with the change in the geometric parameters of the deepening were noted.

Comparison of Conventional and Pontic Fixed Partial Dentures Over Implants Using the Finite Element Method: Three-Dimensional Analysis of Cortical and Medullary Bone Stress

2020 ◽  
Vol 46 (3) ◽  
pp. 175-181
Author(s):  
Marcelo Bighetti Toniollo ◽  
Mikaelly dos Santos Sá ◽  
Fernanda Pereira Silva ◽  
Giselle Rodrigues Reis ◽  
Ana Paula Macedo ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Medullary Bone ◽  
Principal Stresses ◽  
Bone Stress ◽  
Bone Damage ◽  
Rehabilitation System ◽  
Minimum Requirements

Rehabilitation with implant prostheses in posterior areas requires the maximum number of possible implants due to the greater masticatory load of the region. However, the necessary minimum requirements are not always present in full. This project analyzed the minimum principal stresses (TMiP, representative of the compressive stress) to the friable structures, specifically the vestibular face of the cortical bone and the vestibular and internal/lingual face of the medullary bone. The experimental groups were as follows: the regular splinted group (GR), with a conventional infrastructure on 3 regular-length Morse taper implants (4 × 11 mm); and the regular pontic group (GP), with a pontic infrastructure on 2 regular-length Morse taper implants (4 × 11 mm). The results showed that the TMiP of the cortical and medullary bones were greater for the GP in regions surrounding the implants (especially in the cervical and apical areas of the same region) but they did not reach bone damage levels, at least under the loads applied in this study. It was concluded that greater stress observed in the GP demonstrates greater fragility with this modality of rehabilitation; this should draw the professional's attention to possible biomechanical implications. Whenever possible, professionals should give preference to use of a greater number of implants in the rehabilitation system, with a focus on preserving the supporting tissue with the generation of less intense stresses.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

scholarly journals The effect of the outlet angle β2 on the thermomechanical behavior of a centrifugal compressor blade

2020 ◽  
Vol 29 (1) ◽  
pp. 1-8
Author(s):  
Ahmed Allali ◽  
Sadia Belbachir ◽  
Ahmed Alami ◽  
Belhadj Boucham ◽  
Abdelkader Lousdad
Keyword(s):  
Mechanical Behavior ◽  
Centrifugal Compressor ◽  
Three Dimensional ◽  
Complex Form ◽  
Compressor Blade ◽  
Stress Fields ◽  
The Finite Element Method ◽  
Mechanical Fatigue ◽  
Outlet Angle ◽  
The Impact

AbstractThe objective of this work lies in the three-dimensional study of the thermo mechanical behavior of a blade of a centrifugal compressor. Numerical modeling is performed on the computational code "ABAQUS" based on the finite element method. The aim is to study the impact of the change of types of blades, which are defined as a function of wheel output angle β2, on the stress fields and displacements coupled with the variation of the temperature.This coupling defines in a realistic way the thermo mechanical behavior of the blade where one can note the important concentrations of stresses and displacements in the different zones of its complex form as well as the effects at the edges. It will then be possible to prevent damage and cracks in the blades of the centrifugal compressor leading to its failure which can be caused by the thermal or mechanical fatigue of the material with which the wheel is manufactured.

Mathematical Theory of Transversally Isotropic Shells of Arbitrary Thickness at Static Load

2019 ◽  
Vol 968 ◽  
pp. 496-510
Author(s):  
Anatoly Grigorievich Zelensky
Keyword(s):  
Mathematical Theory ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Theory Of Elasticity ◽  
Elastic Plates ◽  
Dimensional Problem ◽  
Boundary Problems ◽  
Complex Boundary ◽  
Plates And Shells ◽  
Basic Equations

Classical and non-classical refined theories of plates and shells, based on various hypotheses [1-7], for a wide class of boundary problems, can not describe with sufficient accuracy the SSS of plates and shells. These are boundary problems in which the plates and shells undergo local and burst loads, have openings, sharp changes in mechanical and geometric parameters (MGP). The problem also applies to such elements of constructions that have a considerable thickness or large gradient of SSS variations. The above theories in such cases yield results that can differ significantly from those obtained in a three-dimensional formulation. According to the logic in such theories, the accuracy of solving boundary problems is limited by accepted hypotheses and it is impossible to improve the accuracy in principle. SSS components are usually depicted in the form of a small number of members. The systems of differential equations (DE) obtained here have basically a low order. On the other hand, the solution of boundary value problems for non-thin elastic plates and shells in a three-dimensional formulation [8] is associated with great mathematical difficulties. Only in limited cases, the three-dimensional problem of the theory of elasticity for plates and shells provides an opportunity to find an analytical solution. The complexity of the solution in the exact three-dimensional formulation is greatly enhanced if complex boundary conditions or physically nonlinear problems are considered. Theories in which hypotheses are not used, and SSS components are depicted in the form of infinite series in transverse coordinates, will be called mathematical. The approximation of the SSS component can be adopted in the form of various lines [9-16], and the construction of a three-dimensional problem to two-dimensional can be accomplished by various methods: projective [9, 14, 16], variational [12, 13, 15, 17]. The effectiveness and accuracy of one or another variant of mathematical theory (MT) depends on the complex methodology for obtaining the basic equations.

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