modeling aspects in fem

8/19/2019 Modeling Aspects in FEM

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Gaurav

Indian Institute of Technology Gandhinagar

[email protected]

Short course on

Soil-Structure Interaction

Computer Applications and Material Models

19-23 January, 2015

Constitutive law

Energy

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FE formulation

Solution proceeds via minimization of energy

It is not necessary to solve full 3D problems always

Computational cost becomes an issue Need to ‘idealize’ the problem

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Typically used when one dimension is significantlylarger than the other two Strip footing

Retaining wall

Dam

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Analysis of tunnel excavations

T. Svoboda and D. Masin, Comparison of displacement field predicted by 2D and 3D finite elementmodelling of shallow NATM tunnels in clay, Geotechnik , 34(2), 115-126, 2011.

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Analysis of tunnel excavations

6T. Svoboda and D. Masin, Comparison of displacement field predicted by 2D and 3D finite elementmodelling of shallow NATM tunnels in clay, Geotechnik , 34(2), 115-126, 2011.


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Typically used when one dimension is significantlysmaller than the other two Thin plates

No out of plane loading

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Plate with a hole

σ far = 20 N/m2

E = 210 Gpa

ν = 0.25

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Typically used when there is rotational symmetryabout one axis Cylindrical geometries

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Analysis of piles

F. Tschuchnigg and H.F. Schweiger,Comparison of Deep Foundation Systemsusing 3D Finite Element Analysis EmployingDifferent Modeling Techniques, GeotechnicalEngineering Journal of the SEAGS & AGSSEA,44(3), 40-46, 2013.

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F. Tschuchnigg and H.F. Schweiger, Comparison of Deep Foundation Systems using 3D Finite Element Analysis Employing Different Modeling Techniques, Geotechnical Engineering Journal of the SEAGS & AGSSEA, 44(3), 40-46, 2013.

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L. A. Qureshi and K. Amin, Comparison of 2D & 3D Finite Element Analysis of Tunnels based on Soil-Structure Interaction using GTS, 14th International Conference on Computing in Civil and BuildingEngineering, Moscow, Russia, 2012.

Locally 2D, globally 3D

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L. A. Qureshi and K. Amin, Comparison of 2D & 3D Finite Element Analysis of Tunnels based on Soil-Structure Interaction using GTS, 14th International Conference on Computing in Civil and BuildingEngineering, Moscow, Russia, 2012.

Locally 2D, globally 3D

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Typically used when there is

symmetry about one axis Bars and beams

W.C. Mun, A. Rivai, and O. Bapokutty, Effects of Elements onLinear Elastic Stress Analysis: A Finite Element Approach, IJERT ,2(10), 561-567, 2013.

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Transition to ‘structural elements’ from ‘continuumelements’ Locally 1D, globally 2D (or 3D)

Locally, we have Beam element

Beam-column element

Bar element (also called truss element)

Globally

Use of rotation transforms Essentially: Matrix method of analysis

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local-global connection direction cosines

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local-global connection

direction cosines

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Advantages Fast analysis yet capturing the response realistically

Disadvantage No handle on modeling of ‘connections’

Workaround? Use of two-tier models

Detailed 2D or 3D model

of connection

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Steel chimney confined in RCC frame

• Chimney modeled as a shell• Frame modeled using 1D frame elements

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Bad aspect ratio/distorted elements Introduces errors

Remedy: have a ‘good’ mesh

In large deformation problems: use of updatedLagrangian formulation may help

N.-S. Lee and K.-J. Bathe, Effects of Element Distortions on thePerformance of Isoparametric Elements, Int. J. Numerical Methods inEngineering, 36, 3553-3576, 1993.

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Overlapping of elements Check: negative jacobian of coordinate transformation:

( x, y) – (r , s)

Remedy: keep checking jacobian

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Shear locking Usually happens in thin members, plane stress

idealizations

FEs introduce artificial stiffness (usually throughartificial shear stresses)

Remedy: reduced integration along one direction Causes approximations to be less exact – reduces stiffness

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Shear locking

P = 20 kN

E = 210 GPa, ν = 0.25

Exact tip deflection: u: 1.039 mm

v: 0.6615 mm

FE (2 GPs in s and r ) u: 0.9321 mm

v: 0.5935 mm

FE (2 GPs in s, 1 in r ) u: 1.038 mm

v: 0.6612 mmP

r

s

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Incompressible locking Happens when using displacement-only discretization

for 3D or 2D plane strain problems

Remedy: use of mixed-methods (Hu-Washizu,Hellinger-Reissner)/elements

Q1 element

Linear approximation of displacementat nodes

Q1/P0/V0 element

Linear approximation of displacementat nodes, Constant approximation of

pressure and volume at centroid 29

Incompressible locking Cook’s membrane

Plane strain

E = 200 GPa

ν = 0.4999

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Incompressible locking Cook’s

membrane

Plane strain

E = 200 GPa

ν = 0.4999

Q1 element ~3mm

Q1/P0/V0 element

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Modeling of discontinuities

Cracks

Cohesive interfaces

Contact problems

Cohesive elements, generalized finite element, extended

finite element

Modeling composite materials with high degree of

modulus mismatch

Causes numerical difficulties

Global error behavior

Model parameters

Validation/calibration, etc. 32


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Gaurav

Indian Institute of Technology Gandhinagar

[email protected]

modeling aspects in fem

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