On transversely isotropic, orthotropic and relative isotropic functions of symmetric tensors, skew-symmetric tensors and vectors. Part I: Two dimensional orthotropic and relative isotropic functions and three dimensional relative isotropic functions

1993 ◽  
Vol 31 (10) ◽  
pp. 1399-1409 ◽  
Author(s):  
Q.-S. Zheng
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Two Dimensional ◽  
Symmetric Tensors ◽  
Isotropic Functions

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

scholarly journals Three-dimensional Green's functions for two-dimensional quasi-crystal bimaterials

2011 ◽  
Vol 467 (2133) ◽  
pp. 2622-2642 ◽  
Author(s):  
Yang Gao ◽  
Andreas Ricoeur
Keyword(s):  
Amorphous Materials ◽  
Green's Functions ◽  
Green’S Functions ◽  
Solid Phase ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Special Cases ◽  
Quasi Crystals

Owing to their specific structure, which can neither be classified as crystalline nor amorphous, quasi-crystals (QCs) exhibit properties that are interesting to both material science and mathematical physics or continuum mechanics. Within the framework of a mathematical theory of elasticity, one major focus is on features evolving from the coupling of phonon and phason fields, which is not observed in classical crystalline or amorphous materials. This paper deals with the problems of combinations of point phonon forces and point phason forces, which are applied to the interior of infinite solids and bimaterial solids of two-dimensional hexagonal QCs. By using the general solution of QCs, a series of displacement functions is adopted to obtain the analytical results when the two half-spaces are supposed to be ideally bonded or to be in smooth contact. In the final expressions, we provide three-dimensional Green’s functions for infinite bimaterial QC solids in the closed form, which are very convenient to be used in the study of dislocations, cracks and inhomogeneities of the new solid phase. Furthermore, the paper is concluded by a discussion of some special cases, in which Green’s functions for infinite transversely isotropic solids and Green’s functions for a half-space with free or fixed boundary are given.

Theories for Elastic Plates Via Orthogonal Polynomials

1981 ◽  
Vol 48 (4) ◽  
pp. 900-904 ◽  
Author(s):  
S. Krenk
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Displacement Function ◽  
Shear Stresses ◽  
Transverse Displacement ◽  
Normal Strain ◽  
Two Dimensional ◽  
Elastic Plates

A complementary energy functional is used to derive an infinite system of two-dimensional differential equations and appropriate boundary conditions for stresses and displacements in homogeneous anisotropic elastic plates. Stress boundary conditions are imposed on the faces a priori, and this introduces a weight function in the variations of the transverse normal and shear stresses. As a result the coupling between the two-dimensional differential equations is described in terms of a single difference operator. Special attention is given to a truncated system of equations for bending of transversely isotropic plates. This theory has three boundary conditions, like Reissner’s, but includes the effect of transverse normal strain, essentially through a reinterpretation of the transverse displacement function. Full agreement with general integrals to the homogeneous three-dimensional equations is established to within polynomial approximation.

Role of Material Properties in the Finite Element Solution for Three-Dimensional Composites—A Sensitivity Study

1995 ◽  
Vol 209 (2) ◽  
pp. 157-160
Author(s):  
H-B Hellweg ◽  
M A Crisfield
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Material Properties ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Sensitivity Study ◽  
Two Dimensional ◽  
Element Analysis ◽  
The Impact

Three-dimensional material test data for orthotropic laminae are difficult to obtain. Consequently, various simplifications are made for the material properties of individual layers in a finite element analysis, ranging from the assumption of transversely isotropic layers to applying two-dimensional material data in a three-dimensional analysis. In order to investigate the impact and validity of such simplifications, the sensitivity of the stresses and deformations in a finite element analysis on the material properties was investigated.

Sign in / Sign up

Export Citation Format

Share Document