Linear Static Analysis
When loads are applied to a body, the body deforms and the effect of
loads is transmitted throughout the body. The external loads induce internal
forces and reactions to render the body into a state of equilibrium.
Linear Static analysis calculates displacements, strains, stresses,
and reaction forces under the effect of applied loads.
Linear static analysis makes the following assumptions:
All loads are applied slowly and gradually until they reach their full
magnitudes. After reaching their full magnitudes, loads remain constant
(time-invariant). This assumption allows us to neglect inertial and damping
forces due to negligibly small accelerations and velocities. Time-variant
loads that induce considerable inertial and/or damping forces may warrant
dynamic analysis. Dynamic loads change with time and in many cases induce
considerable inertial and damping forces that cannot be neglected.
It is important to verify the static assumption
since a dynamic load may generate stresses up to 1/(2x)
times the stresses generated by static loads with the same magnitude,
where x is the viscous damping ratio. For a lightly
damped structure with 5% damping, the dynamic stresses will be 10 times
larger than the static stresses. The worst case scenario occurs at resonance.
Please refer to the section of Dynamic
You can use static analysis to calculate the
structural response of bodies spinning with constant velocities or travelling
with constant accelerations since the generated loads do not change with
Use linear or nonlinear dynamic studies to
calculate the structural response due to dynamic loads. Dynamic loads
include oscillatory loads, impacts, collisions, and random loads.
The relationship between loads and induced responses is linear. For example,
if you double the loads, the response of the model (displacements, strains,
and stresses), will also double. You can make the linearity assumption
all materials in the model comply with Hooke’s
law, that is stress is directly proportional to strain.
the induced displacements are small enough
to ignore the change in stiffness caused by loading.
boundary conditions do not vary during the
application of loads. Loads must be constant in magnitude, direction,
and distribution. They should not change while the model is deforming.