Mechanical-Nonlin 13.0 App2A Element Technology

8/12/2019 Mechanical-Nonlin 13.0 App2A Element Technology

1/57

Customer Training Material

Appendix 2A

Element Technology

Structural Nonlinearities

A2A-1ANSYS, Inc. Proprietary

2010 ANSYS, Inc. All rights reserved.Release 13.0

December 2010


2/57

ANSYS Mechanical Element Technology

Customer Training MaterialOverview

This is an optional lecture intended for users who want to obtain a

better understanding of element technology options used in

s ruc ura non near s mu a ons.

With the variety of technologies available in many elements,

choosing the best element formulation option to solve problems

most efficiently can be challenging.

Fortunately, WB Mechanical will automatically activate the best

options based on the analysis challenges present in the model.



December 2010


3/57


Customer Training Material Overview

However, the analyst of nonlinear problems still has decisions to

make. For example, since large nonlinear models can be very

c a eng ng an compu a ona y expens ve, s some mes

advantageous to drop element mid-side nodes.

Advantages to lower order elements:

Runtime Efficiency

Computational Stability

Disadvantage to lower order elements:

Shear Locking with conventional,

displacement based formulations in

en ng om na e pro ems. To address this challenge, WB-

Mechanical automatically enhances the



December 2010

technology.


4/57


5/57



In addition, material incompressibility can also present problems with

conventional formulations. In anticipation of this challenge, WB-

.

Solution output reports when Mixed u-P is activated.

Solution out ut also re orts its effects on conver ence



December 2010


6/57



The general recommendation is to accept the automatic formulation

settings when they are activated.

It is however im ortant to understand them:

What triggers these changes to element formulation? What are the effects on convergence patterns and results?

With these questions in mind, the following topics will be covered:

A. Conventional Displacement Formulation.

C. Selective Reduced Integration (B-bar)

D. Uniform Reduced Integration (URI)

. F. Simplified Enhanced Strain (SES)

G. Mixed u-P Formulation



December 2010

.


7/57


Customer Training MaterialA. Conventional Displ. Formulation

For any element, DOF solution uis solved at nodes

Stresses and strains are calculated at

inte ration oints. The are derived from

DOF. For example, we can determine

strains from displacements via:,

uB =

Where B is called the strain-displacement matrixu

en we pos -process resu s, s ress s ra n va ues a

integration points are extrapolated or copied to nodal

locations

The image on the right shows a 4-node quad element

with 2x2 integration, integration points shown in red.



December 2010


8/57


Customer Training Material Conventional Displ. Formulation

Integration points for conventional displacement-based elements

follow Gauss quadrature rules and are the same order as the element.

This is called full integration.

Element Type Full Integration Order

8 Node Quad 3x3

8 Node Hex 2x2x2

20 Node Hex 3x3x31

In other words, full integration means that the numerical integration

rule is accurate for all components of strain energy for geometrically

.



December 2010

1 Note that ANSYS uses a 14pt integration scheme, which is also considered full

integration


9/57


Customer Training Material... Conventional Displ. Formulation

Fully integrated, lower-order conventional displacement elements are

susceptible to shear and volumetric locking, so they are rarely, if

ever, used.

Fully integrated, higher-order conventional displacement elementsare also prone to volumetric locking.



December 2010


10/57


Customer Training MaterialB. Shear and Volumetric Locking

There are two problems with conventional displacement-based

elements: shear locking and volumetric locking:

Shear Lockingresults in bending behavior being too stiff(parasitic

shear stresses). This is a property of the geometry, when thinmembers are subject to bending.

Volumetric Lockingresults in overly stiffresponse. This is a

property of the material, when the Poissons ratio is near or equal

to 0.5.



December 2010


11/57


Customer Training Material... Shear Locking

Fully integrated lower order elements exhibit overstiffness in

bending problems. This formulation includes shear strains in

, .

Below are element shear strain plots in MAPDL. Both beams are identicalin geometry, material properties, boundary conditions and loading.

Higher Order Elements

produce correct results

Lower Order Elements with

conventional, fully integrated,



December 2010

bending produces shear locking


12/57


Customer Training Material... Shear Locking

Recall, for a beam in pure bending the shear strain is zero.

y

M M x

Correct Response:

Pure bending deformation for

a differential volume, plane

Shear Locking:

Fully integrated lower order

element deformation, top and

sections remain plane, topand bottom edges become

arcs, xy = 0.bottom edges remain straight,right angles are not preserved,xy is non zero.



December 2010


13/57


Customer Training Material... Volumetric Locking

Volumetric locking occurs in fully integrated elements when the

material behavior is nearly or fully incompressible (Poissons ratio

approaches or equals 0.5).

The incompressibility can occur from a hyperelastic material or plasticflow (discussed later).

,

element to have an overstiffness for deformations that should not

cause any volume change.

.

Volumetric locking can occur for various stress states, including

plane strain, axisymmetric, and 3-D stress.

For plane stress problems, volumetric locking does not occur becauseout-of-plane strains are used to satisfy incompressibility condition.



December 2010


14/57


Customer Training Material... Example of Volumetric Locking

Contours of hydrostatic pressure results in conventional elements

are shown below (ANSYS Results Plot (NL,HPRES)).



December 2010


15/57



We can separate stress into volumetric (-p) and deviatoric (s)components:

sI += p

p -p

3 p 3 -

= +

Stress State

(Where: = 2 = 3) Hydrostatic stress (p) causingvolume change only Deviatoric stress (s) causingangular distortion only2 3 2 -p 3



December 2010


16/57



The hydrostatic pressure (p) is defined as the product of the bulkmodulus (K) and volumetric strain (vol):

volKp =

zyx ++=3

( )K

=

213

( )zyxvol

++=

21



December 2010

zyxE


17/57



From the equations on the previous slide, if Poissons ratio is near

or equal to 0.5, we can see that:

Volumetric strain volwill be near or equal to zero This is called nearlyor fully incompressible material behavior

Nearly or fully incompressible materials present numerical

difficulties, and they also exhibit overly stiff behavior.

From a computational standpoint, nearly incompressible and fully

incompressible problems are treated differently.



December 2010


18/57


Customer Training Material... Example of Volumetric Locking

Example of Volumetric Locking in Thick-Walled Cylinder with

Conventional displacement based elements

As incompressibility,

locking develops,

resulting in unacceptable



December 2010

%18 Error in

displacement calculation


19/57


Customer Training Material... Element Control

The 18x series of structural elements that WB-Mechanical usesoffers up to five different technologies to address potentialproblems with shear and volumetric locking: B-Bar, URI, ES, SES,

.

ogy

rder

s rder

s cking

) essible

ty,sticity)

essible

asticity)

Element

Technol

Lower-O

Element

Higher-

Element

ShearL

(Bendin

Nearly-

Incompr

(Plastici

Hyperel

Fully-

Incompr

(Hyperel

B-Bar Y - N Y N

Enhanced Strain Y - Y Y NSim lified Enhanced Strain Y - Y N N

Higher-order 18x elements (PLANE183, SOLID186-187) use URI by default.

URI Y Y Y Y N

Mixed U-P Y Y N Y Y

.

Lower-order 18x elements (PLANE182, SOLID185) use ES by default, except whenhyperelastic material is assigned..

B-Bar, ES, and SES are not applicable to higher-order elements.

Mixed u-P technolo is inde endent of the others so ma or ma not be activated



December 2010

in conjunction with B-Bar or URI.


20/57


Customer Training Material Element Control

The element technology is defined by a particular key option

(KEYOPT):

KEYOPTS are switches, used to turn various element options on or off.

KEYOPTS have many applications. Controlling element technology is just

one use.

For example, PLANE182 element uses KEYOPT(1) to define which

ec no ogy s use an o con ro m xe u- ormu a on



December 2010

Refer to the Elements Reference Manual for more details on each of the

18x element types and their respective key options.


21/57



The syntax for the KEYOPT command is as follows:

KEYOPT, ITYPE, KNUM, VALUE

Where ITYPEis the Element t e number

KNUMis the number of the KEYOPT

VALUEis the value of this KEYOPT

Example, if element type#1 is PLANE182, enhanced strain can beactivated with the following command:

KEYOPT 1 1 2

Key Option Number (for element technology)

Key Option Value (for enhanced strain)

Element Type Number



December 2010

Refer to the ANSYS Commands Manual for more details


22/57


Customer Training MaterialFormulations

The next few sections present details on each of the formulations

used in WB-Mechanical 18X Structural elements

C. Selective Reduced Integration (B-bar)D. Uniform Reduced Integration (URI)

.

F. Simplified Enhanced Strain (SES)

G. Mixed u-P Formulation

-.



December 2010


23/57


Customer Training MaterialC. The B-Bar Method

The B-bar method (a.k.a., selective reduced integration, constant

dilatational elements, constant pressure approach) uses an

.

Recall that the stress state can be separated in hydrostatic (p) anddeviatoric (s) terms.

sI

K

p

=

+=

es G

vo

2

=

=

In the above equation, vol is volumetric strain and e is deviatoric strain.

Kis the bulk modulus and Gis the shear modulus.

vo



December 2010


24/57


Customer Training Material... The B-Bar Method

Strains are related to displacements via the following:

BBBdv

+=

B

B v

v= VdV

uB

BBBdv

=

+=

When evaluating B, however, we will use two different integration

orders for volumetric and deviatoric components.

Bv is evaluated with one integration point(reduced integration)



December 2010

On the other hand, Bd is evaluated with 2x2

integration points (full integration)


25/57


Customer Training Material... The B-Bar Method

As shown on the previous slide, the volumetric and deviatoric

components of B are not evaluated at the same order of integration.

Only the volumetric component Bvhas reduced integration. That is

why this method is called selective reduced integration or constant

pressure approach. It is also known as the B-bar methodbecause Bis averaged on the volumetric term.

uB = The fact that the volumetric term Bvhas reduced integration allows it

to be softer since it is not fully integrated. This allows for solution

of nearly incompressible behavior and overcomes volumetric

oc ng. However, because the deviatoric term Bdremains the same, parasitic

shear strains still exist, so this formulation is still susceptible to



December 2010

shear locking.


26/57


Customer Training MaterialD. Uniform Reduced Integration

Uniform Reduced Integration (URI) uses an integration rule one orderlower than needed for numerically exact integration

Element Type Ful l Integration

Order1

Reduced Integration

Order4 Node Quad 2x2 1x1

8 Node Hex 2x2x2 1x1x1

20 Node Hex 3x3x3 2x2x2

,and deviatoric terms have reduced integration.

This formulation leads to a more element flexibility which helpseliminate shear and volumetric locking.

Reduced integration of volumetric terms allows solution of nearlyincompressible problems.

Reduced integration of deviatoric terms prevents shear locking in bending



December 2010

.

1 This is full integration as noted in literature, not necessarily related to 18x elements implementation


27/57


Customer Training Material... Uniform Reduced Integration

Unfortunately, the reduced integration of deviatoric terms causes

modes of deformation which have zero strain energy, called zero

modes of deformation which lead to physically unrealistic behavior.

In the lower order element with one integration point shown below,

point does not capture any strain energy in the element.

By default, Mechanical, will not use the URI option in the lower order



December 2010

PLANE182 and SOLID185 elements.


28/57



URI elements have many nice benefits:

Can be used in nearly incompressible problems to overcome volumetric

lockin

Can be used in bending problems without worrying about shear locking No additional DOF are required, and, in fact, less CPU time is required for

e emen ca cu a ons. e s zes e.g., .esav are re uce . s prov es

efficient solutions, especially for nonlinear problems.



December 2010


29/57



On the other hand, a user needs to consider a few things when using

URI:

Lower-order URI elements are susceptible to hourglassing, hence URI is

not the set automatically by Simulation.

Lower-order URI elements may be too flexible, especially in bending-

dominated problems, so a iner mesh may be required such that

displacements are not over-predicted

Both lower- and higher-order URI elements have an integration rulew c s one or er ower t an u ntegrat on. s means stresses are

evaluated at 1 point for lower-order elements and 2x2 or 2x2x2 for

higher-order elements. Hence, more elements may be required to

ca ture stress radients.

URI cannot be used alone in fully incompressible analyses. For fully-

incompressible situation, URI can be used with Mixed u-P (discussed

later



December 2010


30/57


Customer Training MaterialE. Enhanced Strain Formulation

Enhanced Strain Formulation (a.k.a. Incompatible Modes, Assumed

Strain) adds internal degrees of freedom to lower-order quad/hex

elements. The displacement gradient tensor is modified with these

extra enhanced terms, hence the name Enhanced Strain.

Enhanced Strain elements are useful when shear or volumetric locking

are encountered (e.g., bending dominated problems or nearly

incompressible material behavior).

,

quad or hex shape:

PLANE182 when KEYOPT(1)=2

SOLID185 when KEYOPT(2)=2



December 2010


31/57


Customer Training Material... Enhanced Strain Formulation

This formulation is only applicable for lower-order elements in

quad or hex shape.

emen per orms es w en near y rec angu ar; on e o er an ,

they do not perform well when trapezoidal. This is a limitation of theEnhanced Strain technology.

- .

Shape PLANE182 PLANE183 SOLID185 SOLID187 SOLID186

Rectangular 1.004 1.001 1.005 1.000 1.002

Axial Mode: 1st Natural Frequency Ratio

rapezo . . . . .

Trapezoid (30) 1.004 1.001 1.005 1.000 1.002

Trapezoid (45) 1.005 1.001 1.006 1.000 1.002

Parallelogram (15) 1.004 1.001 1.005 1.000 1.002

Parallelogram (30) 1.004 1.001 1.005 1.000 1.002

Parallelogram (45) 1.004 1.001 1.005 1.000 1.002

Bending Mode: 1st Natural Frequency Ratio

Shape PLANE182 PLANE183 SOLID185 SOLID187 SOLID186

Rectangular 1.010 0.999 1.010 1.004 0.999

Trapezoid (15) 1.567 1.000 1.596 1.005 1.000

Trapezoid (30) 1.973 1.003 2.009 1.008 1.003

Trapezoid (45) 2.207 1.012 2.245 1.020 1.012

Parallelogram (15) 1.040 0.999 1.042 1.005 0.999



December 2010

. . . . .

Parallelogram (45) 1.119 0.999 1.126 1.020 0.999


32/57



Example of Volumetric Locking in Thick-Walled Cylinder

Ri=3,Ro=9

SOLID185 with enhanced strain

SOLID45 with extra shape

Pure elastic material (E=1000)

Different Poissons ratios (nu=0.0, 0.25, 0.3, 0.49, 0.499,0.4999)

Linear analysis



December 2010

S S


33/57



Example of Volumetric Locking in Thick-Walled Cylinder

Results from older Element 45 Results from Element 185

%18 Error in %1.6 Error in



December 2010

ANSYS M h i l El t T h l


34/57



Enhanced Strain Formulation was designed for bending and nearly

incompressible applications in mind

Enhanced Strain alone cannot be used for full incom ressible anal ses

but it can be used in conjunction with Mixed u-P (discussed later) for

those situations.

It is enerall not recommend for use with Mixed u-P when bulk

compression is the dominant behavior. In this case B-Bar with Mixed u-P

is considered more effective.

computationally expensive

The extra internal DOF mentioned on the previous slides are condensed

,

*.esav file) associated with it.

Quad PLANE182 and hex SOLID185 use Enhanced Strain



December 2010

The Enhanced Strain terms will have little benefit in bending if the

element is distorted, especially if trapezoidal.

ANSYS Mechanical Element Technolog


35/57



Additional notes on Enhanced Strain Formulation:

By default, the Enhanced Strain Formulation is used for quad or hex

sha e onl . In de enerate form, the Enhanced Strain formulation is not

used, and degenerate shape functions are automatically used instead,

which provides greater robustness for nonlinear solutions.

With the ETCONTROL,,OFF command, re ular sha e functions includin

use of Enhanced Strain formulation) can be used in degenerate form,

although this is not recommended.

Despite the above points, in general, degenerate lower-order elementsshould not be used at all except as fillers in unimportant regions since 3-

node triangles and 4-node tetrahedra are constant strain elements.



December 2010



36/57


Customer Training MaterialF. Simplified Enhanced Strain

Simplified Enhanced Strain (a.k.a. Extra Displacement Shapes,

Bubble Functions) can be thought of as a subset of Enhanced Strain,

discussed earlier.

Simplified Enhanced Strain has additional internal degrees of freedom for

lower-order quad/hex elements to prevent shear locking only. The extrainternal DOF to treat volumetric locking are not present.

Although the internal DOF are meant to augment the shape functions to

provide more flexibility (as discussed in Section E), this also results in

softening of the element, so volumetric locking is also sometimesa ev a e n rec y o some egree.

However, if material incompressibility is a concern, the user should not

use Simplified Enhanced Strain, as it does not address volumetric

oc ng rec y.



December 2010



37/57


Customer Training Material... Simplified Enhanced Strain

There are two 18x elements which can use Simplified Enhanced

Strain, when in quad or hex form:

PLANE182 when KEYOPT(1)=3

SOLID185 when KEYOPT(2)=3

Similar to Enhanced Strain, Simplified Enhanced Strain terms will havelittle benefit in bending if the element is distorted, especially if

rapezo a .

For 2D elements (PLANE182), 4 internal DOF are added whereas for, n erna are presen . ese n erna are

condensed out at the element level.



December 2010



38/57


Customer Training Material... Simplified Enhanced Strain

Simplified Enhanced Strain can be used in situations where shear

locking may be present, but volumetric locking is not an issue

It is a subset of Enhanced Strain, so it may be slightly more efficient

in situations where volumetric locking is not a concern

Simplified Enhanced Strain can be used with Mixed u-P formulation

for nearly- or fully-incompressible situations.

In these cases, there will be no difference in the use of Simplified

Enhanced Strain or regular Enhanced Strain in conjunction withMixed u-P

As noted in Section E, Enhanced Strain does not use extra internal

DOF for volumetric terms if used in conjunction with Mixed u-P.

Hence, Enhanced Strain and Simplified Enhanced Strain will be the

same if Mixed u-P formulation is also activated.



December 2010



39/57


Customer Training MaterialG. Mixed u-P Formulation

Mixed u-P formulation is used to treat volumetric locking by solving

hydrostatic pressure (or volumetric strain) as an additional DOF.

hydrostatic pressure (or volumetric strain) DOF.

There are three different Mixed u-P formulations that can be used for

Nearly-incompressible elasto-plastic materials (Mixed u-P I)

Fully-incompressible hyperelastic materials (Mixed u-P II)

Nearly-incompressible hyperelastic materials (Mixed u-J)

Only Mixed u-P II is activated automatically in WB-Mechanical when

-

plane stress states. This section will focus on Mixed u-P II only.

Users can refer to the ANSYS documentation for more details on the

- -



December 2010

.

the nearly incompressible cases as necessary using a command

object.



40/57


Customer Training Material... Mixed u-P Formulation

When Mixed u-P is activated, hydrostatic pressure is treated as an

independent DOF which is solved for. The matrix equation is:

=

00F

Pu

KKK uPuu

Note: Because the material is fully incompressible, [Kpp

]=0,

Because the Lagrange Multipliers (internal DOF P) are kept in the

assembled stiffness matrix, direct solvers mustbe used with this

ormu a on. era ve so vers suc as canno an e e

resulting ill-conditioned matrices.



December 2010



41/57

gy


For hyperelasticity, the volume ratio (J) is defined as:

V=

where V and Vo are the updated and original volumes of the element,

oV

.

To maintain incompressible behavior, a volumetric compatibilityconstraintmust be satisfied

For fully-incompressible hyperelastic materials, no volume change

should occur.

e use o , e vo ume c ange can e quan e

For fully-incompressible case, J should be equal to 1. In other words, the

final and original volumes should be the same (no volume change)



December 2010



42/57

gy


The discussion on the previous slide emphasized the fact that the

volume ratio Jshould be constant (J=1), which is true for fully

incompressible materials:

This leads to the following volumetric compatibility equation:

01 =J

J1Vtol

V

JV



December 2010



43/57


The default value of Vtol is 1e-5. The Solution Information Branch will

record when this condition is not satisified.

If the model fails to converge because the Mixed u-P volumetric

,

this tolerance.

Note: Loosening this tolerance has the effect of allowing some small

a last resort after other solution convergence options (i.e. increasing thenumber of substeps) have been tried.



December 2010



44/57

Customer Training Material... Volumetric Tolerance

WB-Mechanical users do not have direct access to the tolerance on

volumetric compatibility constraints, but it can be changed via

Command Objects.

Manuall activatin Mixed u-P is necessar in order for

subsequent solc,,,vtol to be accepted

Solution Information Branch will record this change



December 2010



45/57

Customer Training Material... Considerations for Mixed u-P

For a fully incompressible problem, no unique solution may exist if all

boundary nodes have prescribed displacements. This is due to the

fact that hydrostatic pressure (internal DOF) is independent of

deformation. Hydrostatic pressure needs to be determined by a

force/pressure boundary condition. Without this, the hydrostaticpressure cannot be calculated i.e., there is no unique solution. For

,

applied boundary condition will remedy this situation.

When the number of pressure DOF (Np) is greater than the number of

active (unconstrained) displacement DOF (Nd), this is an over-

constrained model which results in lockin . Ideall the ratio of

Nd/Np should be 2/1 for 2D problems or 3/1 for 3D problems. Over-constrained models can be overcome by mesh refinement, especially

in areas without displacement constraints.



December 2010



46/57

Customer Training Material... Considerations for Mixed u-P

WB-Mechanical provides an extensive library of element technologyusing Mixed u-P formulation for nearly and fully incompressible

materials.

Mixed u-P, by itself, addresses the issue of volumetric locking

For fully-incompressible hyperelastic materials, WB-Mechanical mustuse

- .

For nearly-incompressible elasto-plastic material, WB-Mechanical will not

turn on mixed u-P automatically.

Mixed u-P Formulation can be combined with B-bar, URI, Enhanced

Strain, or Simplified Enhanced Strain Formulations in nearly

incompressible applications using command objects.



December 2010



47/57

Customer Training MaterialH. Solid-Shell Formulation

A special Solid-Shell Element is available to model thin to

moderately-thick shells in 3D form.

This is a 3D 8-node hex element with translational DOF

This element has 7 internal DOF, similar to Enhanced Strain but

decoupled in bending direction. Assumed strain method also used for

- .

These 7 internal DOF are condensed out at the element level

This formulation is available in the SOLSH190 element

There are some situations where use of either shell or regular solid

elements may not be desirable (next slide), so the SOLSH190 element

provides a good solution in these cases



December 2010



48/57

Customer Training Material Solid-Shell Formulation

Considerations for Shells:

Nonlinear MPC required for

connectin shells to solids for lar e-

Considerations for Solids:

The error in the kinematic

approximation with linear 3D solid

deflection analyses

Currently supported by 17x

elements becomes apparent in

bending dominant problems as

thickness decreases

bonded contact

DOF not continuous at interface

Higher-order 3D solid elements

do not have this problem

Treatment of variable thickness is

complicated

,

as Enhanced Strain, are not

sufficient to remedy this numerical

Currently, AI*Environment

5.0/5.1 supports variable

thickness midsurface extraction

when thickness/ length ratio is very

small



December 2010

Limited application to thick shells


S lid Sh ll F l ti


49/57


Although a 8-node hex element, SOLSH190 element coordinate

system not defined solely by ESYS but by nodal connectivity

- .

Use of VEORIENT (prior to meshing) or EORIENT (aftermeshing) is required to redefine z-axis. Element x- and y-

The nodal connectivity shown on the right of I-J-K-L

forms the bottom face.The top face is formed by M-N-O-P.

The element z-axis is then defined as the

normal of the mid lane shown in li ht blue

Prism form of SOLSH190 is stiff in bending,

so it should only be used as filler elements.



December 2010



50/57


SOLSH190 has 2x2x2 integration points

Unlike SHELL elements, SZ is not automatically zero.-

SHELL181 has user-defined section integration pointsthrough-plane (section definition) and either 1 or 2x2integration points in-plane. SOLSH190 currently has afixed number of integration points. This is an important

consideration for nonlinear materials since more thanone element through the thickness may be required (seeexample below, 2 elements thru thickness)



December 2010


E l f S lid Sh ll El t


51/57

Customer Training Material Example of Solid-Shell Element

Simple example of buckling of arch

shown on right

Comparison of SHELL181,

SOLID185 (Simplified Enhanced

Strain), and SOLSH190 For thin structures, SOLSH190

3rd mode thick

SOLID185 requires additional

elements along edge

For thick structures, SOLSH190

. - . - . - . .

SHELL181 1 10 3.7496 3750 3.74E +06 3.09E+09 1.64E+10

20 3.4509 3451 3.44E +06 2.89E+09 1.57E+10

50 3.3743 3374 3.37E +06 2.84E+09 1.55E+10

SOLID185 1 10 3533.8000 39403 4.31E+06 3.55E+09 2.23E+10

20 50.9320 4096 3.48E +06 3.23E+09 2.07E+10

matches SOLID185. . . .

3 10 3534.0000 39403 4.31E+06 3.49E+09 2.13E+10

20 50.8300 4096 3.48E +06 3.18E+09 1.99E+10

50 3.6230 3386 3.38E+06 3.10E+09 1.96E+10

5 10 3533.8000 39403 4.31E+06 3.45E+09 2.04E+10

20 50.9040 4096 3.48E +06 3.14E+09 1.91E+10

. . . .

SOLSH190 1 10 3.7232 3722 3.72E+06 3.40E+09 2.23E+10

20 3.4530 3445 3.44E+06 3.17E+09 2.07E+10

50 3.3751 3373 3.37E+06 3.11E+09 2.04E+10

3 10 3.6055 3722 3.72E+06 3.37E+09 2.13E+10

20 3.4384 3445 3.44E+06 3.15E+09 1.99E+10

+ + +



December 2010

. . . .

5 10 3.4980 3722 3.72E+06 3.33E+09 2.04E+10

20 3.4201 3445 3.44E+06 3.12E+09 1.91E+10

50 3.2714 3373 3.37E+06 3.06E+09 1.88E+10



52/57


As stated earlier, the Solver Output reports the element technologybeing activated based on the element order chosen by user and thematerial association.

Elastic material or

metal plasticity withhigher order elements

2D Plane Stress/Strain

Metal Plasticity with

2D Plain Strain

Elastic material with

Fully incompressible

lower order elements

Simplified Enhanced Strain



December 2010

higher or lower order

elements B-Bar with Mixed u-P


El t C t l


53/57


Users do have the option to turn Element Control off, thereby: Accepting the default technology

Receiving only suggestions in the Solution output with no changes.

The exception to this is Mixed u-P which must be turned on for fullyincompressible materials.

Refer also to ETCONTROL in Commands Manual



December 2010



54/57


With Element Control set to Manual, users can manually

toggle between Full and Reduced Integration Schemes

This switch only applies to higher order elements.

It is sometimes helpful to force full integration when only one

element exists across the thickness of a part. Doing this helps

prevent hour-glassing.



December 2010


El t C t l


55/57


Users can also override the default key option settings by executingthe following KEYOPT command within a command object under the

part branch. Recall:

KEYOPT, ITYPE, KNUM, VALUE

Where ITYPEis the Element type number

VALUEis the value of this KEYOPT

xamp e, e emen ype s , en ance s ra n can e

activated with the following command:

KEYOPT,1,1,2

Key Option Number (for element technology)



December 2010

Element Type Number


Summary


56/57

Customer Training MaterialSummary

In summary, there are many different technologies forcontinuum elements to alleviate shearand volumetric locking

Unfortunatel , there is no silver bullet in circumventin mesh

locking, but Mechanical provides a wealth of element formulations,

so that users can balance accuracy, robustness, and efficiency insolving a wide range of nonlinear problems.

Lower-order elements can use B-Bar, URI, Enhanced Strain, or

Simplified Enhanced Strain. Moreover, Mixed u-P may be used in

conjunction with any of these formulations.

Higher-order elements usually use URI only (except for SOLID186,

which can also use full integration). Mixed u-P may be toggled on or

off, depending on the problem.

Mechanical will automatically set the best formulation option based

on the material properties and element order, although having an

understanding of the pros and cons of each formulation can be very



December 2010

.

The general recommendation is too accept these defaults


References for Further Reading


57/57

Customer Training MaterialReferences for Further Reading

Some useful references on numerical theory:1. Non-Linear Finite Element Analysis of Solids and Structures Vol.1 and 2,

M.A. Crisfield, John Wiley & Sons, 1996 & 1997.

2. Nonlinear Continuum Mechanics for Finite Element Analysis, Bonet and

Wood, Cambridge University Press, 1997.3. Introduction to the Mechanics of a Continuous Medium, Malvern,

- , .



December 2010

Documents

Mechanical-Nonlin 13.0 App2A Element Technology