principalstresses3D calculates the three stress invariants (equations (1.16-1.18), the three principal stresses (1.12-1.15) and the Von Mises equivalent tensile stress (1.19) 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 (8.59) 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.
Resource files for three-dimensional problems
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 19.1.
ABErtz lists the expressions for stress and displacement components for solutions A, B and Ein cylindrical polar coordinates given in Table 19.1.
ABErtb lists the expressions for stress and displacement components for solutions A, B and E in spherical polar coordinates given in Table 19.2.
Txyz lists the expressions for temperature, heat flux, stress and displacement components for solution T in Cartesian coordinates given in Table 20.1. 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 20.1. 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 20.2. 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 (22.32). 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 (21.22).
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 24.2.1.
The file `conebending' solves the non-axisymmetric problem of a solid cone loaded at the vertex by a concentrated moment, treated in Section 24.2.3.
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