# Clamped Circular plate

HYFEM
A MATLAB/FORTRAN BASED MULTI-PHYSICS SOFTWARE
Current Capabilities
Linear Structural Analysis
Static Analysis
Modal Analysis
Transient Analysis
Linear Acoustic Analysis
Linear Static
Analysis
Harmonic
Analysis
HYBRID ELEMENTS
Displacement and stress are Interpolated
separately.
Why Use them ?
Can simulate thin geometries as well as
geometries with high curvature.
Ability to simulate almost incompressible
material without undergoing locking.
Gives accurate results with the coarse
mesh.
Pinched Hemi-sphere problem, conventional
elements undergo severe membrane locking,
while hybrid elements do not.
CLAMPED CIRCULAR PLATE
Thickness= 0.01 m
Fixed at the outer surface.
Problem: Find the natural frequencies and evaluate the mode shapes.
Difficulty : High radius to thickness ratio (100) makes FEM elements
susceptible to shear locking.
ERROR WITH ANALYTICAL
27 NODE ELEMENTS
Coarse mesh
N r  8, N  32, N z  2
Fine mesh
N r  16, N  64, N z  4
Coarse hybrid mesh gives same order of accuracy as fine mesh
conventional elements.
Coarse hybrid mesh takes 7 sec while fine conventional mesh takes 85
sec.
ERROR WITH ANALYTICAL
8 NODE ELEMENTS
Coarse mesh
N r  8, N  32, N z  2
Fine mesh
N r  16, N  64, N z  4
For first natural frequency conventional 8 node results has error of 270%
with fine mesh, while with hybrid elements it is around 2%.
Fine hybrid 8 node mesh results are comparable to coarse conventional
27 node element.
(Note: 8 node fine mesh and 27 node coarse mesh has same degree of freedoms.)
TRANSIENT PROBLEM
p  2 sin(500t )
It is an axisymmetric problem.
On a Circular clamped plate a sinusoidal pressure
is applied.
Thickness= 0.01 m
We need to find the deflection at center point.
Difficulty : High radius to thickness ratio (100) makes FEM elements
susceptible to shear locking.
ERROR WITH ANALYTICAL
4 NODE ELEMENTS
b4 : Conventional Element
a4 : Hybrid Element
Initial transient effects are accurately captured by the hybrid elements.
Hybrid elements with the coarsest mesh give better result compared to
finest mesh convectional elements.
ERROR WITH ANALYTICAL
9 NODE ELEMENTS
b4 : Conventional Element
a4 : Hybrid Element
Initial transient effects are accurately captured by the hybrid elements.
Hybrid elements with the coarse mesh gives accurate results.
HARMONIC ACOUSTIC
Pressure distribution of an oscillating sphere
(only quarter of sphere is displayed)
For exterior acoustic an ‘outward wave favoring’ FEM is implemented.
Near and far field response are accurately calculated.
Superiority of the element is more prominent at higher frequency.
COMING SOON ..
Fluid Flow
Structural Analysis
Non-linear Analysis
Incompressible fluid flow
Non-linear Dynamics
Acoustic Analysis
Multi- Physics
Transient Analysis
Acoustic structure interaction
Electromagnetics
Scattering problem
Fluid structure interaction
Electro-elasticity