buletinul institutului politehnic din iaşi - Universitatea Tehnică ...

222 Petronela Paraschiv and Ciprian Paraschiv
i) static shaping, when the system is in equilibrium, stable or unstable,
without move;
ii) cinematic shaping, when only the system movement is regarded,
without taking into consideration the mechanical load (force and force
moments) that produce the movement;
iii) dynamic shaping, when the system movement is analysed taking into
consideration all forces and moments that determine the movement.
The analytical shaping generally behaves the following stages: physical
or structural shaping, mathematical shaping, pysical or structural shaping
supposes the formulation of a “physical model”, which behaviour is supposed to
approximate as well as possible the one of the real system. The physical model
resembles the real system concerning the basic characteristics, but it is simpler
and therefore more approachable to the analysis. Therefore, the component
elements of a biomechanical system can be shaped through solid bodies, rigid or
elastic, bows, buffers etc., while the mutual action of two bodies can be drawn
through concentrated forces, concentrated couples, distributed loads etc.
(Budescu & Iacob, 2005).
In many cases, the dynamic response of the biomechanical structures can
be represented through a model with `concentrated parameters`, composed from
masses, bows and buffers.
The approximations done to the formulation of the physical models refer
to: neglecting the secondary effects; neglecting some interactions with the
environment; replacing the characteristics `distributed` through similar
“concentrated” parameters; linearization of cause – effect relations between
physical variables; neglecting the time variation of some parameters.
Along the improvement of the model and of defining more precisely the
problem analysed, one will give up part of these approximations.
Mathematical shaping supposes the elaboration of a `mathematical
model` that will represent the physical model, respectively the writing of the
estate equations (cinematic, static, dynamic) of the physical system
(Memislogu, 2003).
Passing from the physical model to the mathematical model is realised
through successive stages:
i) choosing variables that describe the estate of the system at a given
moment;
ii) establishing the estate equations (for instance, equilibrium, static or
dynamic equations) for the analysed system;
iii) establishing the compatibility equations, which express the link
between the moves of interconnected subsystems;
iv) writing the physical laws, meaning the constitutive relationships for
each component element of the system (Burnstein & Wright, 1994).