CATALOGUE OF MATHEMATICA FILES

The following files are available on the web site in Mathematica format. They are all in notebook format and should be downloaded into a file with the extension .nb. If your browser is set to open the file automatically, you can download it by right-clicking on the link and selecting Save Link As. Some of these files call others of the set as subroutines, in which case the subroutine file must be saved in package format with extension .m. Conversion of .nb files to this format can be performed if required in Mathematica, following the instructions in Programming in Mathematica (item 12). However, for convenience, I give .m versions of the files likely to be needed as subroutines here.

Stress transformation

principalstresses2D.nb gives the in-plane principal stresses due to a given set of stress components in two dimensions.

principalstresses3D.nb calculates the three stress invariants (equations (1.20-1.22), the three principal stresses (1.17-1.19) and the Von Mises equivalent tensile stress (1.23) from a given set of stress components in three dimensions.

Resource files for two-dimensional problems

polynomial.nb contains the definition of a polynomial in x and y of degree 8. Polynomials of lower degree can be obtained from this by cut and paste.

Michell.nb lists the stress function for the Michell solution (equation (8.31) and Table 8.1) and the corresponding stress components. The displacement components (Table 9.1) can be obtained by a subsequent run of the program `urt'.

uxy.nb determines the displacements in Cartesian coordinates associated with a given Airy stress function. It can be called after the solution of a boundary-value problem to determine the displacements.

urt.nb determines the displacements in polar coordinates associated with a given Airy stress function. It can be called after the solution of a boundary-value problem to determine the displacements.

Solutions of boundary value problems in two dimensions

S521.nb solves the problem treated in Section 5.2.1. A two-dimensional rectangular beam is loaded by a shear force at the end.

S522.nb solves the problem treated in Section 5.2.2. A two-dimensional rectangular beam is simply supported at the two ends and is loaded by a uniformly distributed normal load on the upper surface.

S742.nb solves the problem treated in Section 7.4.2. A two-dimensional rectangular beam is accelerated from rest by equal and opposite shear forces applied at the ends.

Complex-variable calculations

Mathematica is not particularly good at handling functions of the complex variable. It can be fooled into performing these operations by treating the complex variable and its conjugate as two defined variables. This technique and some algorithms that are useful for the calculations in Chapters 19, 20 and for the three-dimensional problems of Chapter 30 are described in complex-variable.

Resource files for three-dimensional problems

Solutions A B E and T

ABExyz.nb lists the expressions for stress and displacement components for solutions A, B and E in Cartesian coordinates given in Table 22.1.

ABErtz.nb lists the expressions for stress and displacement components for solutions A, B and E in cylindrical polar coordinates given in Table 22.1.

ABErtb.nb lists the expressions for stress and displacement components for solutions A, B and E in spherical polar coordinates given in Table 22.2.

Txyz.nb lists the expressions for temperature, heat flux, stress and displacement components for solution T in Cartesian coordinates given in Table 23.1. The corresponding expressions for the isothermal solutions A, B and E are also included.

Trtz.nb lists the expressions for temperature, heat flux, stress and displacement components for solution T in cylindrical polar coordinates given in Table 23.1. The corresponding expressions for the isothermal solutions A, B and E are also included.

Trtb.nb lists the expressions for temperature, heat flux, stress and displacement components for solution T in spherical polar coordinates given in Table 23.2. The corresponding expressions for the isothermal solutions A, B and E are also included.

Spherical harmonics and related potentials

The file cyl0.nb contains the bounded axisymmetric polynomial solutions expressed in cylindrical polar coordinates.

The file cyln.nb contains bounded polynomials expressed in cylindrical polar coordinates which when multiplied by Cos[n*theta] or Sin[n*theta] generate non-axisymmetric harmonic potentials.

The file hol0.nb contains axisymmetric harmonic functions in cylindrical polar coordinates that are singular on the entire axis r=0. The bounded axisymmetric functions from `cyl0' are also included for completeness.

The file holn.nb contains functions in cylindrical polar coordinates which when multiplied by Cos[n*theta] or Sin[n*theta] generate harmonic functions that are singular on the entire axis r=0. The bounded non-axisymmetric functions from `cyln' are also included for completeness.

The file sp0.nb contains both bounded and singular axisymmetric spherical harmonics expressed in spherical polar coordinates.

The file spn.nb contains functions which when multiplied by Cos[n*theta] or Sin[n*theta] generate both bounded and singular non-axisymmetric harmonic functions in spherical polar coordinates.

The file Qseries.nb generates axisymmetric spherical harmonics from the logarithmically singular Q-series Legendre functions of equation (25.22). These functions are singular on both the positive and negative z-axes.

The file sing.nb generates axisymmetric spherical harmonics that are logarithmically singular only on the negative z-axis. The first few functions of this form are given in equation (24.9).

Solutions of boundary value problems in three dimensions

The file conetension.nb solves the axisymmetric problem of a solid cone loaded at the vertex by an axial force, treated in Section 27.2.1.

The file conebending.nb solves the non-axisymmetric problem of a solid cone loaded at the vertex by a concentrated moment, treated in Section 27.2.3.

Inclusions and elliptic integrals

These files have not been written yet. The coresponding logic can be deduced from the maple files linked below.

The files `EshelbySphere', `EshelbySpheroidal', `Eshelby' evaluate the components of the Eshelby tensor S_ijkl for a sphere, a spheroid, or a general ellipsoid respectively. The last two files call on the file Carlson as a subroutine.

The file `Carlson' evaluates the Carlson elliptic integrals of equations (28.41, 34.13, 34.14).

Files in package (.m) format

principalstresses2D.m	principalstresses3D.m	polynomial.m	Michell.m
uxy.m	urt.m	ABExyz.m	ABErtz.m
ABErtb.m	Txyz.m	Trtz.m	Trtb.m
cyl0.m	cyln.m	hol0.m	holn.m
sp0.m	spn.m	Qseries.m	sing.m