Cone with a Parabolic Cap: Online Calculator

Cone with a parabolic cap

This calculator allows calculating pressure p, displacement (elastic deformation) w, average pressure p_0 and resultant force F_N for the case of indentation of elastic half-space by a rigid cone with a parabolic cap. In this case, the intender is rigid and of conical shape. The substrate is elastic, the geometric parameters d – rigid body displacement, a – radius of the contact, \theta – inclination angle of the cone, b – radius of the parabolic cap, and material parameters E^*=E/(1-\nu^2) are the inputs (see the figure and definitions below).

Equations were taken from [1].


Poisson’s ratio \nu dimensionless,
Young’s modulus of elasticity E, [Pa],
Equivalent elastic constant  E^* = \left( \frac{1-\nu^2}{E} \right)^{-1}, [Pa],
Normal load F, [N]


[1] Valentin L. Popov, Hanbook of Contact Mechnics, Exact Solutions of Axisymmetric Contact Problems, pg. 35


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