Computer Aided Engineering (CAE) FEA Case Study: Structural Analysis Types
A linear static approximation of nonlinear dynamic problem 
This is actually a very complex analsysis because to solve the problem technically correctly, it calls for all dynamic analsysis types, non linear properties and it's a complex system - the bump/impact is reacted by a tyre, wheel, suspension and ultimately the car's chassis. Each of these components/assemblies have their own material properties and coefficients. Also, many physical phenomeon are happening with this impact event:
Dynamic transient response and impulse
Impact is a transient response dynamic analysis - load varying with the function of time, hence this anlaysis type will yield the forced response of the system, i.e tyre, wheel, suspension and chassis (if modeled) to a varying load/time function. Sharp impacts produce impluse effects - that it as amplication of load due to the short time peroid in which it is applied. The impact event would have to recorded via the empirical testing using accelerarometers on a car wheel. This would give the load/time event required.
Dynamic frequency response and natural frequencies
Since the car will also be moving at 'a' speed, the wheel is also rotating at a given frequency. The impact into the tyre could produce an axial and radial osciallitory motion which will be damped by the material properties of the tyre. Tyres are very complex composite parts - with stiffer sidewalls and of course air pressure supporting the enitre internal structure. This osciliatory motion could induce resonance effects into the wheel which is totally dependent on the frequency of the wheels rotation (car speed), the magnitude of impact (and impulse effects) and the natural frequencies (real eigen values) of the wheel. This is frequency response dynamic analysis. If resonance is induced, then an amplification of load will be observed.
Nonlinear properties
The tyre is highly non-linear, being a sophisticated compotsite part with anisotropic characteritics. All three nonlinear characteristics - material, geometric and boundary conditions could influence the results. The only way to proove this, is to model the 'correct' tyre properties and run the simulation. A complete and complex FE study could be made just on the tyre alone!