The Elastic Field of an Elliptic Cylindrical Inclusion in a Laminate With Multiple Isotropic Layers

1999 ◽  
Vol 66 (1) ◽  
pp. 165-171 ◽  
Author(s):  
H. G. Beom ◽  
Y. Y. Earmme
Keyword(s):  
Plate Theory ◽  
Elastic Field ◽  
Cylindrical Inclusion ◽  
Transverse Displacement ◽  
Laminated Plate ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Main Plane ◽  
Interior Points

An elliptic cylindrical inclusion with an eigenstrain in an infinite laminate composed of multiple isotropic layers is analyzed. The problem is formulated by using the classical laminated plate theory in which displacement fields in the laminated plate are expressed in terms of in-plane displacements on the main plane and transverse displacement. Employing a method based on influence functions, an integral type solution to the equilibrium equation is expressed in terms of the eigenstrain. Closed-Form solutions for the elastic fields are obtained by evaluating the integrals explicitly for interior points and exterior points of the ellipse. The elastic fields caused by an elliptic cylindrical inhomogeneity with an eigenstrain in the infinite laminate are determined by the equivalent eigenstrain method. Solutions for a finite laminate with an eigenstrain in a circular cylindrical inhomogeneity are also obtained in terms of material and geometric parameters for each layer composing the laminate.

The Stress Fields Caused by a Circular Cylindrical Inclusion

1992 ◽  
Vol 59 (2S) ◽  
pp. S107-S114 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Strain Energy ◽  
Elastic Solid ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Axisymmetric Stress ◽  
Displacement Fields ◽  
Elastic Fields ◽  
Stress And Displacement Fields ◽  
Interior Points

Exact solutions are presented in closed forms for the axisymmetric stress and displacement fields caused by a solid or hollow circular cylindrical inclusion (with uniform axial eigenstrain prescribed) in an infinite elastic solid. The same expressions are obtained for the elastic fields for interior and exterior points of the inclusion. Although Eshelby’s solutions for ellipsoidal inclusions are uniform in the interior points, the present solutions do not show the uniformity. When the length of inclusion becomes infinite, the present solutions agree with Eshelby ’s results. The strain energy is also shown. The method of Green’s function is used.

The Elastic Field Caused by a Circular Cylindrical Inclusion—Part I: Inside the Region x12+x22

1995 ◽  
Vol 62 (3) ◽  
pp. 579-584 ◽  
Author(s):  
Linzhi Wu ◽  
Shanyi Du
Keyword(s):  
Analytical Solutions ◽  
Elastic Field ◽  
Companion Paper ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Elastic Fields ◽  
Complete Elliptic Integrals ◽  
Nonsingular Surface ◽  
Surface Integrals

The displacement and stress fields caused by uniform eigenstrains in a circular cylindrical inclusion are analyzed inside the region x12+x22<a2,−∞<x3<∞ and are given in terms of nonsingular surface integrals. Analytical solutions can be expressed as functions of the complete elliptic integrals of the first, second and third kind. The corresponding elastic fields in the region x12+x22>a2,−∞<x3<∞ are solved by using the same technique (by Green’s functions) in the companion paper (Part II).

Hollow Circular Cylindrical Inclusion at the Surface of a Half-Space

1993 ◽  
Vol 60 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Hisao Hasegawa ◽  
Ven-Gen Lee ◽  
Toshio Mura
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Half Space ◽  
Strain Energy ◽  
Analytical Form ◽  
Cylindrical Inclusion ◽  
Displacement Fields ◽  
Elastic Fields

Exact solutions are presented in closed form for the axisymmetric stresses and displacement fields caused by a solid or hollow circular cylindrical inclusion in the present of uniform eigenstrain in a half space. The elastic fields for interior and exterior points are expressed by one analytical form. The strain energy is also obtained in closed forms.

Equilibrium Displacement and Stress Distribution in a Two-Dimensional, Axially Moving Web Under Transverse Loading

1995 ◽  
Vol 62 (3) ◽  
pp. 772-779 ◽  
Author(s):  
C. C. Lin ◽  
C. D. Mote
Keyword(s):  
Stress Distribution ◽  
Plate Theory ◽  
Transverse Load ◽  
Transverse Displacement ◽  
Transverse Loading ◽  
Closed Form Solutions ◽  
Coupled Equations ◽  
Axially Moving ◽  
Axially Moving Web ◽  
The Web

Von Karman nonlinear plate equations are modified to describe the motion of a wide, axially moving web with small flexural stiffness under transverse loading. The model can represent a paper web or plastic sheet under some conditions. Closed-form solutions to two nonlinear, coupled equations governing the transverse displacement and stress function probably do not exist. The transverse forces arising from the bending stiffness are much smaller than those arising from the applied axial tension except near the edges of the web. This opens the possibility that boundary layer and singular perturbation theories can be used to model the bending forces near the edges of the web when determining the equilibrium solution and stress distribution. The present analysis is applied to two examples: (I) a web deflecting under its own uniformly distributed weight; (II) a web deflecting under a transverse load whose distribution is described by the product of sine functions in the axial and width directions. Membrane theory and linear plate theory solutions are used to characterize the importance of the web deformation solutions.

The Elastic Field in a Half-Space With a Circular Cylindrical Inclusion

1996 ◽  
Vol 63 (4) ◽  
pp. 925-932 ◽  
Author(s):  
L. Z. Wu ◽  
S. Y. Du
Keyword(s):  
Half Space ◽  
Elastic Field ◽  
Elastic Half Space ◽  
Elliptic Integrals ◽  
Cylindrical Inclusion ◽  
Stress Fields ◽  
Function Technique ◽  
Explicit Solutions ◽  
Elastic Fields ◽  
Complete Elliptic Integrals

The problem of a circular cylindrical inclusion with uniform eigenstrain in an elastic half-space is studied by using the Green’s function technique. Explicit solutions are obtained for the displacement and stress fields. It is shown that the present elastic fields can be expressed as functions of the complete elliptic integrals of the first, second, and third kind. Finally, numerical results are shown for the displacement and stress fields.

AN INCLUSION OF ARBITRARY SHAPE IN AN INFINITE OR SEMI-INFINITE ISOTROPIC MULTILAYERED PLATE

2014 ◽  
Vol 06 (01) ◽  
pp. 1450001 ◽  
Author(s):  
XU WANG ◽  
KUN ZHOU
Keyword(s):  
Elastic Field ◽  
Laminated Plate ◽  
Equilibrium Equations ◽  
Simple Method ◽  
Remarkable Feature ◽  
Main Plane ◽  
Eshelby Inclusion ◽  
Out Of Plane ◽  
Potential Formalism ◽  
General Method

This paper proposes a simple method based on analytical continuation and conformal mapping to obtain an analytic solution for a two-dimensional arbitrarily shaped Eshelby inclusion with uniform main plane eigenstrains and eigencurvatures in an infinite or semi-infinite isotropic laminated plate. The main plane of the plate is chosen in such a way that the in-plane displacements and out-of-plane deflection on the main plane are decoupled in the equilibrium equations. Consequently, the complex potential formalism for the isotropic laminate can be readily and elegantly established. One remarkable feature of the present method is that simple elementary expressions can be obtained for the internal elastic field within the inclusion of any shape in an infinite laminated plate. Several examples are presented to illustrate the general method.

Nonlinear Oscillations of a Composite Laminated Plate with Parametrically and Externally Excitations

2013 ◽  
Vol 699 ◽  
pp. 641-644
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Laminated Plate ◽  
Rectangular Thin Plate ◽  
Third Order ◽  
Composite Laminated Plate ◽  
Strain Relationship ◽  
Relationship Of ◽  
Equations Of Motions

Nonlinear oscillations of a simply-supported symmetric cross-ply composite laminated rectangular thin plate are investigated in this paper. The rectangular thin plate is subjected to the transversal and in-plane excitations. Based on the Reddy’s third-order shear deformation plate theory and the stress-strain relationship of the composite laminated plate, a two-degree-of-freedom non-autonomous nonlinear system governing equations of motions for the composite laminated rectangular thin plate is derived by using the Galerkin’s method. Numerical simulations illustrate that there exist complex nonlinear oscillations for composite laminated rectangular thin plate.

Elastic Fields in a Polygon-Shaped Inclusion With Uniform Eigenstrains

1997 ◽  
Vol 64 (3) ◽  
pp. 495-502 ◽  
Author(s):  
H. Nozaki ◽  
M. Taya
Keyword(s):  
Composite Materials ◽  
Closed Form ◽  
Strain Field ◽  
Strain Energy ◽  
Convex Polygon ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Closed Form Solutions ◽  
Arbitrary Convex ◽  
Shaped Inclusion

In this paper the elastic fields in an arbitrary, convex polygon-shaped inclusion with uniform eigenstrains are investigated under the condition of plane strain. Closed-form solutions are obtained for the elastic fields in a polygon-shaped inclusion. The applications to the evaluation of the effective elastic properties of composite materials with polygon-shaped reinforcements are also investigated for both dilute and dense systems. Numerical examples are presented for the strain field, strain energy, and stiffness of the composites with polygon shaped fibers. The results are also compared with some existing solutions.

scholarly journals GENERAL SCALARIZATION METHOD OF DYNAMIC ELASTIC FIELDS IN TRANSVERSALLY ISOTROPIC MEDIA AND ITS NEW APPLICATIONS

2018 ◽  
Vol 18 (3) ◽  
pp. 258-264
Author(s):  
I. P. Miroshnichenko ◽  
V. P. Sizov
Keyword(s):  
Symmetry Axis ◽  
Layered Structures ◽  
Mutual Arrangement ◽  
Material Symmetry ◽  
Displacement Fields ◽  
General Technique ◽  
Elastic Fields ◽  
Scalarization Method ◽  
Isotropic Media ◽  
Transversally Isotropic

Introduction. An efficient technique of tensor field scalarization  is  successfully  used  while  investigating  tensor  elastic fields of displacements, stresses and deformations in the layered structures of different materials, including transversally isotropic composites. These fields can be expressed through the scalar potentials corresponding to the quasi-longitudinal, quasi-transverse, and transverse-only waves. Such scalarization is possible if the objects under consideration are tensors relating to  the subgroup  of general coordinate conversions, when the local affine basis has one invariant vector that coincides with the material symmetry axis of the material. At this, the known papers consider structures where this vector coincides with the normal to the boundary between layers. However, other cases of the mutual arrangement of the material symmetry axis of the  material  and  the boundaries between layers are of interest on the practical side.Materials and Methods. The work objective is further development of the scalarization method application in the boundary value problems of the dynamic  elasticity theory for the cases of an arbitrary arrangement of the material symmetry axis relative to the boundary between layers. The present research and methodological apparatus are developed through the general technique of scalarization of the dynamic elastic fields of displacements, stresses and strains in the transversally isotropic media.Research Results. New design ratios for the determination of the displacement fields, stresses and deformations in the transversally isotropic media are obtained for the cases of an arbitrary arrangement of the material symmetry axes of the layer materials with respect to the boundaries between layers. Discussion and Conclusions. The present research and methodological apparatus are successfully used in determining the stress-strain  state  in  the  layered  structures  of  transversally isotropic materials, and in analyzing the diagnosis results of the state of the plane-layered and layered cylindrical structures under operation.

The Elastic Field of an Elliptic Inclusion With a Slipping Interface

1986 ◽  
Vol 53 (1) ◽  
pp. 103-107 ◽  
Author(s):  
E. Tsuchida ◽  
T. Mura ◽  
J. Dundurs
Keyword(s):  
Closed Form ◽  
Infinite Series ◽  
Elastic Field ◽  
Elliptic Inclusion ◽  
Numerical Examples ◽  
Elastic Fields ◽  
Bonded Interface ◽  
The Matrix ◽  
Displacement Potentials ◽  
Uniform Expansion

The paper analyzes the elastic fields caused by an elliptic inclusion which undergoes a uniform expansion. The interface between the inclusion and the matrix cannot sustain shear tractions and is free to slip. Papkovich–Neuber displacement potentials are used to solve the problem. In contrast to the perfectly bonded interface, the solution cannot be expressed in closed form and involves infinite series. The results are illustrated by numerical examples.

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