On Displacement Fields in Orthotropic Laminates Containing an Elliptical Hole

2000 ◽  
Vol 67 (3) ◽  
pp. 527-539 ◽  
Author(s):  
S. M. Chern ◽  
M. E. Tuttle
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rigid Body ◽  
Circular Hole ◽  
Orthotropic Plate ◽  
Elliptical Hole ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Orthotropic Composite ◽  
Moiré Techniques

The classical Savin solution for the stress induced in an orthotropic plate containing an elliptical hole places no restrictions on remote rigid-body rotations. In this paper the Savin procedure is used to obtain a solution for which remote rigid-body rotations are required to be zero. The validity of these new results is demonstrated by comparing predicted displacement fields near a circular hole in specially orthotropic composite panels with those measured using moire´ techniques as well as those predicted using the finite element method. [S0021-8936(00)01303-9]

An Overview of the Finite Element Method on the Tool-Soil Interacting Problem of Tillage

2014 ◽  
Vol 707 ◽  
pp. 397-400 ◽  
Author(s):  
Xiao Hong Liu ◽  
Yan Yu ◽  
Li Chun Qiu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computer Aided Design ◽  
High Efficiency ◽  
Low Cost ◽  
Dynamic Effect ◽  
Research Progress ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Element Method

This article introduced the up-to-date research progress on the tool-soil interacting problem of tillage; and investigated the situation of constitutive relation usage in the finite element method (FEM). A review including the dynamic effect on the performance of tillage operation with FEM has been conducted. It showed that the virtual reality method with FEM had made much progress in evaluating the tool draft, distribution position of stress and strain, displacement fields and acceleration in soil-tool interactions, soft ware package of computer aided design of tillage tools; it will be a low cost and high efficiency assistive tool in the development procedure of tillage tools, and can be applied to study and analyze the performance of resulting prototypes.

Uniaxial Loading in an Elastic Continuum With a Doubly Periodic Array of Material Discontinuities

1969 ◽  
Vol 36 (1) ◽  
pp. 134-139 ◽  
Author(s):  
G. H. Gaonkar
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Periodic Array ◽  
Numerical Comparison ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Elastic Continuum ◽  
Stress And Displacement Fields ◽  
Material Discontinuities ◽  
Doubly Periodic Array

Stress and displacement fields are presented for uniaxially loaded infinite elastic continua with a doubly periodic array of holes, elastic or rigid inclusions with or without overlapping. The results are obtained by using an appropriate form of the finite-element method. When possible, a numerical comparison has been made with known solutions. In the treatment of not previously studied configurations, the convergence is ascertained by observing the trend with finer discretizations.

scholarly journals Determining the stress concentration change with time in a viscoelastic orthotropic solid

2020 ◽  
pp. 28-34
Author(s):  
M.F. Selivanov ◽  
◽  
Y.R. Kulbachnyy ◽  
D.R. Onishchenko ◽  
◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Stiffness Matrix ◽  
Orthotropic Material ◽  
Orthotropic Plate ◽  
Round Hole ◽  
The Finite Element Method ◽  
Time Step ◽  
Element Method

The procedure for solving the plane problem of the linear theory of viscoelasticity by the finite element method is described. Based on the virtual work principle and the assumption of the constancy of the strain rate at small intervals of time, the matrix form of the equilibrium equations of the finite-element approximation of a body is written. The solution procedure is described for the constitutive relations in the Boltzmann—Volterra integral form. This integral is transformed into an incremental form on a time mesh, at each interval of which the problem is solved by the finite element method with unknown increments of displacements. The numerical procedure is constructed by ununiformly dividing the time interval, at which the study is conducted. In this case, the stiffness matrix requires recalculation at each time step. The relaxation functions of the moduli of a viscoelastic orthotropic material are described in the form of the Proni—Dirichlet series. The solution to the problem of determining the change over time of the stress concentration in a body with a round hole in a viscoelastic orthotropic plate is presented. To construct a numerical solution, the three moduli of orthotropic material were written using one exponent with the same relaxation time. For these initial data, an analytic expression for the viscoelastic components of the stiffness matrix of an orthotropic plate under plain stress conditions is constructed. Numerical examples are presented for several ratios of the hole radius to the size of the plate. These results are compared with the solution obtained for an infinite plate by inverse transformation by a numerical method of the well-known analytic elastic solution.

Dynamic Stresses and Displacements Around Cylindrical Cavities of Arbitrary Shape

1984 ◽  
Vol 51 (4) ◽  
pp. 798-803 ◽  
Author(s):  
S. K. Datta ◽  
K. C. Wong ◽  
A. H. Shah
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Multiple Scattering ◽  
Circular Hole ◽  
Arbitrary Shape ◽  
Numerical Technique ◽  
The Finite Element Method ◽  
Dynamic Stresses ◽  
Cylindrical Holes ◽  
Cylindrical Cavities

Dynamic stresses and displacements around cylindrical cavities of various shapes, namely, circular, triangular, and square cavities are presented in this paper. Also presented are results for a pair of circular cavities of equal radii and a pair of circular and square cavities. These results are of interest in estimating the effects of corners and multiple scattering on the distribution of dynamic displacements and stresses around cylindrical holes or openings. Since exact analytical solutios are not available in these cases (except for a single circular hole) a numerical technique combining the finite element method (FEM) and the method of eigenfunction expansions is used here.

Reduction of stress concentration around a hole in a uniaxially loaded plate

1983 ◽  
Vol 18 (2) ◽  
pp. 135-141 ◽  
Author(s):  
U C Jindal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Concentration ◽  
Circular Hole ◽  
High Order ◽  
Two Dimensional ◽  
The Finite Element Method ◽  
Loaded Plate ◽  
Hole Geometry ◽  
Element Method

The stress concentration around a circular hole in a plate can be reduced by up to 21 per cent by introducing auxiliary holes on either side of the original hole. But this approach of auxiliary holes creates two more regions of stress concentration in the plate. In the present study, the hole geometry has been modified to effect stress reductions as high as 22 per cent. The problem has been analysed numerically by the finite element method and experimentally by two-dimensional photoelasticity. It has been observed that by making the hole oblong in the direction of loading, a high order of reduction in stress concentration around the hole can be obtained.

Gravitational stress field around a tunnel in soft ground

1970 ◽  
Vol 7 (1) ◽  
pp. 54-61 ◽  
Author(s):  
B. Hoyaux ◽  
B. Ladanyi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Infinite Medium ◽  
Soft Ground ◽  
The Finite Element Method ◽  
Short Term ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Gravitational Stress ◽  
Material Behaviors

The finite element method has been used for determining the stress distribution and the displacements due to gravity around an unlined tunnel driven through a semi-infinite medium, characterized by three idealized material behaviors reflecting approximately a short term behavior of natural undisturbed insensitive and sensitive clays. The knowledge of stress and displacement fields around an unlined tunnel can be used for evaluating the need for supports according to the acceptability of expected deformations.

Analysis of developable shells with special reference to the finite element method and circular cylinders

1976 ◽  
Vol 281 (1300) ◽  
pp. 113-170 ◽  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Variational Principle ◽  
Rigid Body ◽  
The Finite Element Method ◽  
Body Movements ◽  
Numerical Examples ◽  
Lines Of Curvature ◽  
Element Method

The paper begins by noting that the practical and efficient numerical analysis of thin walled shells is far from a reality. Groundwork for the investigation starts with an examination of existing sufficiency conditions for convergence of the finite element method of analysis with refinement of mesh size; new and more practical conditions are then given specifically for shells. Working formulae of a suitable first approximation theory for the linear small deflexion behaviour are then given for arbitrary shells in lines of curvature and in geodesic coordinates. A variational principle is introduced which is more general than that for the well known assumed stress hybrid finite element model; its purpose is to provide a means to overcome the excessive rank deficiency which is sometimes encountered in the derive element stiffness matrix. , The formulae are next specialized to general developable shells for they are tne simplest to analyse and frequently occur in technology. Emphasis is given to the derivation of general formulae governing inextensional deformation, membrane action and rigid body movement because these constitute important factors in any adequate numerical analysis. . . , Specific application is made to circular cylindrical shells by first considering the interpolation of the kinematic continuity conditions along an arbitrary geodesic line. Details and numerical examples are provided for the first known fully compatible lines of curvature rectangular finite element which directly recovers arbitrary rigid body movements as well as inextensional deformations and membrane actions. The paper concludes with details and numerical examples of an arbitrarily shaped triangular finite element which employs the above mentioned variational principle m conjunction with linearly varying stress fields. All the rigid body movements are directly recovered as well as inextensional deformations and membrane actions. It is anticipated that this finite element and its derivatives will find widespread application.

Geometrically Non-Linear Analysis of Composite Cylindrical Shells and Shallow Sphere Shell

2011 ◽  
Vol 71-78 ◽  
pp. 3303-3307
Author(s):  
Yan He ◽  
Xiu Qin Cui
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Procedure ◽  
Surface Displacement ◽  
Middle Surface ◽  
The Finite Element Method ◽  
Displacement Fields ◽  
Main Method ◽  
Surface Patches ◽  
Element Method

At present, the plate shell structure is broadly used in the engineering field, and the finite element method is the main method to analysis of the structural design. Because many variables are used in the finite element method and the computation is complex, this paper used Bezier surface patches as the admissible displacement fields to represent the shell’s middle surface displacement and rotation components, the deformation of the composite material cylindrical shell and shallow sphere shell under the loads are studied with a Semi-analytical procedure. The results show that semi-analytical and analytical procedure are in good agreement with the results of the analysis, it can be applied in the project.

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