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 Radius = 1.0 m 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. Radius = 1.0 m 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 Radiation problem Fluid structure interaction Electro-elasticity

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