Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

Norris, Andrew N.

doi:10.1098/rspa.1994.0134

Cited by 105 publications

(24 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A 3D Green's function for static piezoelectricity and its derivatives have been presented by Deeg (1) for piezoelectrics of general anisotropy. Dynamic piezoelectric Green's functions have been presented by Norris (6) in the frequency domain and by Khutoryansky and Sosa (20), (21) in the time domain. For the particular case of transversely isotropic piezoelectricity, Dunn and Wienecke (22) for piezoelectrostatics, and Daros and Antes (23) for transient analysis developed simplified expressions for the Green's functions.…”

Section: Introductionmentioning

confidence: 99%

Application of Hypersingular Integral Equation Method to a Three-Dimensional Crack in Piezoelectric Materials

Tong

Noda

2004

JSME Int. J., Ser. A

View full text Add to dashboard Cite

Using the Green's functions, the general solutions of a three-dimensional crack problem in piezoelectric materials under mechanical and electrical loads is derived by boundary element method. Then this crack problem is reduced to solve a set of hypersingular integral equations coupled with boundary integral equations. The unknown functions are the discontinuities of the elastic displacements and electrical potential of the crack surface. The singularity of the unknowns at the crack front is analyzed by the main-part analysis method of two-dimensional hypersingular integral equations, and the exact analytical solution of the singular stresses and electrical displacements near the crack front in a transversely isotropic piezoelectric solid is given.

show abstract

Section: Introductionmentioning

confidence: 99%

Application of Hypersingular Integral Equation Method to a Three-Dimensional Crack in Piezoelectric Materials

Tong

Noda

2004

JSME Int. J., Ser. A

View full text Add to dashboard Cite

show abstract

“…Formally, the solution of the boundary-value problem (2.3) at a distance from the boundary V of the region V can be presented in the form [6][7][8][9][10] vi(r)=fG# (r,rl)fj (r 91 .4 where G(r, r I ) is the Green's function that satisfies the equation…”

Section: Ui(r )=U~[r-a(r )]+ Vi(r )mentioning

confidence: 99%

Solution of the stochastic boundary-value problem of elasticity theory for composites with disordered structures in the correlative approximation of the method of quasi-periodic components

Pan’kov¹

1999

Mech Compos Mater

View full text Add to dashboard Cite

1. Statement of the Problem. The problem of investigating the stress and strain fields in structural elements, taking into account that these fields are stochastic and highly inhomogeneous, is critical when studying the deformation of composites with random structures. This analysis is possible only on the basis of the solution of the stochastic boundary-value problem [1][2][3][4][5] ~=[C0m~(r)~r um(r)]--~ Uilr =e;/r 2, jr. .J (1.1) for example, relative to the field of displacements u(r)in the case of a homogeneous elastic macrostrain ~* over a certain representative region C( r ) of a composite with the boundary F and a statistically homogeneous field of elastic properties C(r ) Let us consider quasi-periodic structures [ 1 ] with inclusions whose shape and size are determinate and whose random distribution over the region V is given by some probability law for the vector a of random deviations of their centers from the nodes of the known periodic lattice. We assume that the inclusions cannot extend beyond the boundaries of the respective cells and the displacements of the inclusions in different cells are independent random events. The elastic properties of the inclusions and matrix are determinate and known: C f and C m are the corresponding tensors of elastic properties. The quantifies related to the periodic structure are designated by p, to the inclusions --by f, and to the matrix --by m.Perm' State Technical University, Russia.

show abstract

“…Along this line, many efforts in this field have been made in theory to analyze the responses of the electric and elastic fields disturbed by cracks in a piezoelectric material subjected to dynamic electromechanical loadings. The dynamic Green's functions for anisotropic piezoelectric materials have been formulated by Narris (1994). The fundamental solutions for dynamic piezoelectricity equations of piezoelectric materials have been derived by Khutoryansky and Sosa (1995), Sosa and Khutoryansky (2001).…”

Section: Introductionmentioning

confidence: 99%

Transient response of a semi-infinite piezoelectric layer with a surface permeable crack

Lee

2006

Z. angew. Math. Phys.

View full text Add to dashboard Cite

The transient response of a semi-infinite transversely isotropic piezoelectric layer containing a surface crack is analyzed for the case where anti-plane mechanical and in-plane electric impacts are suddenly exerted at the layer end. The integral transform techniques are used to reduce the associated mixed initial boundary value problem to a singular integral equation of the first kind, which can be solved numerically via the Lobatto-Chebyshev collocation technique. Dynamic field intensity factors are determined by employing a numerical inversion of the Laplace transform. The dynamic stress intensity factors are presented graphically and the effects of the material properties and geometric parameters are examined. Mathematics Subject Classification (2000). 74H35, 74M20, 74R10.

show abstract

Dynamic Green’s functions in anisotropic piezoelectric, thermoelastic and poroelastic solids

Cited by 105 publications

References 26 publications

Application of Hypersingular Integral Equation Method to a Three-Dimensional Crack in Piezoelectric Materials

Application of Hypersingular Integral Equation Method to a Three-Dimensional Crack in Piezoelectric Materials

Solution of the stochastic boundary-value problem of elasticity theory for composites with disordered structures in the correlative approximation of the method of quasi-periodic components

Transient response of a semi-infinite piezoelectric layer with a surface permeable crack

Contact Info

Product

Resources

About