## CATALOGUE OF MAPLE FILES

The following files are available on the web site in Maple format. If your browser is set to open the file automatically, you can download it by right-clicking on the link and selecting Save Link Target As. Alternatively, you can simply cut and paste the commands into a text file.

### Stress transformation

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

principalstresses3D 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 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.

uxy 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.

Michell 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'.

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

S522 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 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

Maple 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.

### Solutions A B E and T

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

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

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

Txyz 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 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 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' contains the bounded axisymmetric polynomial solutions expressed in cylindrical polar coordinates.

The file `cyln' 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' 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' 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' contains both bounded and singular axisymmetric spherical harmonics expressed in spherical polar coordinates.

The file `spn' 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 `Q-series' generates axisymmetric spherical harmonics from the logarithmically singular Q-series Legendre functions of equation (24.32). These functions are singular on both the positive and negative z-axes.

The file `sing' 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).

The file `spsing' generates the same potentials as `sing' except that they are cast in spherical polar coordinates.

### Solutions of boundary value problems in three dimensions

The file `conetension' 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' 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

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

The file `LegendreEshelby' uses the Legendre elliptic functions to calculate the Eshelby tensor.

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

### Hertzian contact

The file `Hertz' gives the solution for the example in Section 34.2. It can easily be adapted to other Hertzian contact problems by changing the input values.

Back to J.R.Barber, Elasticity