All of the below functions can be found in the boundary_element
module of the package.
This module contains functions related to boundary element solvers for contact
mechanics calculations. Please see the /demo directory for minimum
examples of how to combine the below functions to perform contact mechanics
calculations.
beinflumat(x_axis, y_axis, e_eff)[source]¶Generate a complete influence coefficient matrix as required for boundary element contact mechanics calculations.
| Parameters: |
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|---|---|
| Returns: | infl_mat – The complete four-dimensional influence coefficient matrix of size
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| Return type: | ndarray |
beinflumatred(infl_mat)[source]¶Calculate a reduced influence coefficient matrix from a complete influence coefficient matrix.
| Parameters: | infl_mat (ndarray) – The complete influence coefficient matrix. |
|---|---|
| Returns: | reduced_infl_mat – The reduced influence coefficient matrix. The matrix is square and of
order n = np.shape(infl_mat)[0] \(\times\)
np.shape(infl_mat)[1]. |
| Return type: | ndarray |
besolve(profile_1, profile_2, outer_force, red_infl_mat, delta_x, delta_y, norm_disp=0.1, max_offset=0.005)[source]¶Solve a system of linear equations to find the pressure and displacement distribution in a boundary element contact problem:
\([\text{pressure}] = [\text{reduced influence matrix}]^{-1} \cdot [\text{displacement}]\)
The start value for the relative normal displacement is defined by the
norm_disp parameter. The default value corresponds to 0.1 units of
length. If the start value of the normal displacement is close to the
equilibrium displacement, the calculation time may be reduced significantly.
The solver stops once inner and outer forces are in equilibrium. The maximum
allowed discrepancy between inner and outer forces is defined by the
max_offset parameter. The default value corresponds to 0.5 %.
| Parameters: |
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| Returns: |
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All of the below functions can be found in the hertz
module of the package.
This module contains functions related to Hertz contact theory. As of now, the equations are limited to elliptical and circular contacts. Equations for line contacts (cylinder-on-flat or cylinder-on-cylinder) are currently not implemented.
ahertz(r_eff, r_eff_x, r_eff_y, e_eff, force)[source]¶Calculate the contact area in an elliptic (including circular) Hertzian contact.
| Parameters: |
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|---|---|
| Returns: |
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approx_hertz_rad(axis, profile, iterations=10)[source]¶Approximate the Hertz contact radius of a profile, i.e., find the radius of a circle that minimizes the average discrepancy between the actual profile and a circle profile. The secant method is used to find the circle approximation.
This method has been tested for continuous (or at least semi-continuous) profiles only. It works best for cases where the circle radius is larger than the absolute minimum and maximum of the profile axis.
The function will not produce sensible results for profiles where the maximum profile height is large compared to the axis length.
| Parameters: |
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| Returns: |
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dhertz(e_eff, r_x_1, r_y_1, r_x_2, r_y_2, force)[source]¶Calculate the elastic normal displacement in an elliptic (including circular) Hertzian contact.
| Parameters: |
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|---|---|
| Returns: | norm_disp – The elastic normal displacement of the contact problem. |
| Return type: | scalar |
eeff(e_1, nu_1, e_2, nu_2)[source]¶Calculate the effective (Young’s) modulus of two contact bodies according to Hertzian contact theory.
| Parameters: |
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|---|---|
| Returns: | e_eff – The effective modulus. |
| Return type: | scalar |
fhertz(r_eff, r_eff_x, r_eff_y, e_eff, p_critical)[source]¶Calculate the load carrying capacity of an elliptic (including circular) Hertzian contact.
| Parameters: |
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|---|---|
| Returns: | f_crit – The load carrying capacity of the Hertzian contact. |
| Return type: | scalar |
phertz(r_eff, r_eff_x, r_eff_y, e_eff, force, ret='mean')[source]¶Calculate the contact pressure in an elliptic (including circular) Hertzian
contact. By default, the mean pressure is returned. Use ret='max'
for maximum pressure.
| Parameters: |
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|---|---|
| Returns: | p_hertz – The Hertzian contact pressure in the contact. |
| Return type: | scalar |
reff(r_x_1, r_y_1, r_x_2, r_y_2)[source]¶Calculate the effective radii for two bodies according to Hertzian contact theory. It is assumed that the two major axis of each body (x- and y-axis) are perpendicular to each other and that the x and y axes of both bodies are aligned.
| Parameters: |
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| Returns: |
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