實驗力學研究室 1 finite element model building. 實驗力學研究室 2 setting up the model...

實驗力學研究室

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Finite Element Model BuildingFinite Element Model Building


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Setting Up the Model

Should a thin-walled part be modeled with shells? Should a planar

idealization be used?

Grouping and Layering

Grouping will help organize a model into logical sections. The

various parts of an assembly model should be organized in separate

groups to assist in model building. Such organization will also

facilitate results viewing because each component can be displayed

individually.


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Resource Requirements

The time to think about memory and disk requirements is before the

modeling starts, not when it is finished. Due to the speed of today’s

systems, it is often more convenient to overmesh than to take the tim

e to be judicious. However, when you know you might be running in

to a resource crunch, you can utilize mesh control to focus the mesh

density where you need it.


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Element Selection

Modern preprocessors will default to quadrilateral elements or a

quad-dominate mesh for a shell model and triangular tetrahedrons

for a solid model. The former choice is made for accuracy, and the

latter for convenience.

Rectangular elements provide a linear strain distribution across the

edged or volume. First order triangular elements only capture a

single strain value; they are often called constant strain elements.

Therefore, you will need many more triangular elements relative to

quads to capture a high gradient. Second order element or parabolic

tetrahedrons can capture more complex local strain gradients and

provide reasonable results with proper convergence methods.


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In the case of a nonlinear solution, it might be prudent to take the

time to model in more accurate bricks for the run time savings alone.

A fair estimate is that you will need five tetrahedrons for every brick

element in a model to get the same results. Because nonlinear runs

generally tend to be more time consuming, a smaller model may

allow you to make more design iterations within the time allotted.


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Manual versus Automatic Meshing

1. If accuracy and speed were equal, few design analysts or even an

alysis specialists would dispute that automeshing is the way to g

o. The goal of FEA is not to be build a mesh but to get performa

nce data.

2. Given the power of today’s preprocessors, the need to manual m

esh a shell model should never arise. If a surface model can be d

eveloped in either a CAD system or the FEM tool, a little prepar

ation can allow you to automesh nearly the entire model.


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3. The issue of manual versus automatic arises most often in the

context of solid models. Even in solid models, a typical solid

“manual” mesh consists of revolving or extruding automatic or

semi-automatic surface meshes. The real task is in planning the

extrusions or revolutions so that the mesh matches up at the

seams between the different steps.


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The key differences between equivalent automeshed an

d manual meshed solid models are discussed below.

1. Modeling Speed

Manual meshing is very time consuming on even moderately co

mplex solid parts. Automeshing, or the other hand is the hands-d

own speed champion. However, while an automesh might get yo

u to the run button faster, the excess of elements required to achi

eve the same degree of accuracy might cause the solution to take

far longer.


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2. Solution Speed

Total modeling and solution time must be considered, which als

o means considering how many times a model must be remeshed

and how many times a particular mesh must be solved.

3. Accuracy

I. For a given mesh density, a brick will provide more accurate

answers closer to the converged solution than a second order

tetrahedral mesh.

II. A linear tet mesh should always be considered inaccurate unl

ess the time is taken in test models to confirm that the stress c

hange is gradual enough to allow linear tets to converge corre

ctly.


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III. However, properly converged second order tets can provide

the same accuracy as a linear brick mesh.

IV. One accuracy issue is the fact that many geometric simplific

ations are required to obtain a brick mesh and the simplificat

ions require to build a brick mesh cancel out any element acc

uracy issues when compared to a second order tet mesh with

little or no simplification.


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4. Convergence

While run times for the manual mesh may be faster, the time

required to modify it might be prohibitively long. The truth is

that if convergence is difficult or time consuming, most design

analysts will not invest the necessary time.

5. Perception

In any industry or specialty, you must put in a minimum amount

of work to gain credibility. If you are willing to simply accept au

tomesh results, you are not living up to your responsibility as an

FEA user.


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Manual and Automatic Mixed Meshes

If you wish to mix the two to take advantage of the best of both

worlds, you will need to break your geometry into parts. In most

cases, you will have to transition these two dissimilar meshes with

rigid links or multi-point constraints.

P-elements and H-elements

P-elements are excellent for capturing high stress gradients. For

areas of gradual stress transition or away from any area of interest,

h-elements are more efficient. H-elements can capture most stress

conditions if enough degrees of freedom are placed in the area.


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However, when the option is available, choose to use the best

element in the best location. Refer to your software’s documentation

to confirm that the option of mixing h and p elements is available

and for information on specific usage techniques.


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Meshing Beam Models

1. The best and easiest way to construct a beam model is to prepare

CAD wireframe at the neutral axis of all beams. Take the time to

split the wireframe at every joint or connection of two beams.

2. One guideline typically appearing in FEA reference is that the le

ngth of the beam should be about ten times the maximum cross-s

ectional dimension.

3. The best guideline for determining the applicability of a beam m

odel is that if it looks like beams, or if a 2D or 3D wireframe rep

resentation conveys most of the structure with little ambiguity, t

hen a beam model is probably appropriate.


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Meshing Shell Models

Building a shell model requires mid-plane surfaces in one form or

another. However, the model must be constructed with just the right

features to allow this to happen. A good technique for starting shell

models is to sketch the part first to identify the sky features required

in the model.


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Element Shape Quality

1. The ideal shape for a triangular element or face is an equilateral

triangle and the ideal shape for a quadrilateral element or face is

a square.

2. H-elements should have an aspect ratio as less than 5:1, whereas

p-elements can produce good results with an aspect ratio as high

as 20:1.


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Mapped Meshing

Mapped Meshing refers to specifying or forcing a particular mesh pa

ttern by indicating the number of nodes on all the edges of a surface

or volume. If all surfaces were perfectly rectangular, mapped meshin

g would not be as much of as issue, because most h-element meshers

will fill a rectangle with uniformly shaped elements. However, mesh

ing an irregular surface with a fixed nominal element size can yield

unpredictable results.


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Biasing a Mesh

Mesh biasing is a means of forcing smaller elements near an area of

interest, while allowing larger elements in regions with a more

gradual stress gradient.


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Transitioning Mesh Densities

The technique is to use automeshing of surfaces with the geometry b

roken into patches. A good rule of thumb for minimizing occurrence

of high aspect-ratio elements is to limit transitions to ratios of 2:1 or

less. In (a) the mesh transitions from a 0.05 nominal element size to

a 0.50 nominal element size without control of the transition. The m

esh in (b) uses a series of regions to effect the transition.


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Controlling a P-element Mesh

P-element automeshers will attempt to fill the model with the largest

elements possible, within a default or user-specified aspect ratio and

edge or face angle tolerances, for solution efficiency. However, p-el

ement solvers are not immune to element distortion. Tightening the

element creation tolerances is the simplest way to improve the gener

al mesh quality in a p-element mesh.


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Boundary ConditionsBoundary Conditions


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“Boundary conditions” is calculating the loads and constraints that

each component or system of components experiences in its working

environment.


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A Simple Example…

• The legs are rigid in compression and do not add any substantial

component to the vertical deformation.

• The legs are rigid in bending and force the chair bottom, local to

the interface, to remain perfectly horizontal.

• Any sliding of the legs on the floor due to side load components

resulting from the seat bending will be neglected; legs are bolted

to the floor or friction is sufficient to resist side loading.

• The load can be modeled as being uniformly distributed both at

the instant of its application and time thereafter.


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Types of Boundary Conditions

Boundary conditions are applied as constrains and loads.

1. Typically, loads are used to represent inputs to the system of inte

rest. These can be in the form of forces, moments, pressures, tem

peratures, or accelerations.

2. Constraints, on the other hand, are typically used as reactions to t

he applied loads. Constraints can resist translational or rotational

deformation induced by these loads.


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3. In a linear static analysis, the boundary conditions must be

assumed constant from application to final deformation of the

system. In a dynamic analysis, the boundary condition can vary

with time and, in a nonlinear analysis, the orientation and

distribution of the boundary conditions can vary as the

displacement of the structure is calculated.


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Boundary Conditions and Accuracy

1. An overly stiff model due to poorly applied constraints is typica

lly called overconstrained.

2. The second is that of an underconstrained model, which simply

has too few constraints to prevent rigid body motion.


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In many cases, redundant constraints will have no effect on the

overall behavior of the model. For example, if all nodes of a shell

element are constrained in its normal direction, constraining their

rotations about either of its parallel axes would be redundant. In

general, however, the application of redundant constraints suggests a

poorly constructed constraint scheme.

Overconstrained Models

I. Redundant Constraints

II. Excessive Constraints

Excessive constraints result both from a poor understanding of the

actual supporting structure being represented by them and

insufficient planning of the total boundary condition scheme.


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Each point should be fixed vertically, and horizontal constraints

should be selectively applied so that in-plane spatial rotation and

rigid body translation is removed without causing excessive

constraints.


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• Constraining the center point of Patch 1 in all three translational

DOFs.

• Constraining x and y translations of the center point of Patch 2.

• Constraining z and y translations of the center point of Patch 3.

• Constraining just the y translations of the center point of Patch 4.


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III. Coupled Strain Effects

Strain or material deformation in one direction is dependent on

deformation, or the freedom to deform, in other directions. This

coupled effect is governed by the Poisson’s ratio of the material and

must be considered in the application of constraints in shell, solid, or

planar models.


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Fig (a) fixes only the x DOF on the left vertical edge and the y DOF

on the bottom edge. Fig(b) has both the x and y DOFs constrained o

n all nodes of the left vertical edge. It is important to node that this v

ertical restriction on the left edge actually reduces the horizontal def

ormation by 5%.


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Understiffened Models

I. The most common underconstrained modeling errors stem from

neglecting one or more spatial degrees of freedom.

II. Insufficient Part Stiffness

Many parts are stiffened considerably by attached components, even

if they are not rigidly attached in all directions. Because loads

impart no stiffness in a linear analysis, replacing an attached

component with an equivalent load could allow the modeled part to

have much greater flexibility than it should.


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Bracketing Boundary Conditions

When the optimum or correct boundary conditions scheme is hard to

model or determine, consider bracketing the system with conditions

that take into account the various options you are considering.

Bracketing the boundary conditions of a chair analysis, using (a)

infinite friction and (b) no friction.


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Loads

1. Magnitude

2. Orientation

3. Distribution

4. Time dependence

I. Units

In defining loads, you must always verify use of a set units

consistent with the rest of your model.


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II. Load Distribution

i. Uniform

ii. Per unit length or area

iii. Interpolated, or functionally defined.

III. Load OrientationIn most cases, the orientation of an applied load will be defined by

specifying the load components in the directions of the active

coordinate system.


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IV. Nonlinear Forces

If the surface or edge on which a load is applied deforms so much

that an update to the load orientation is required, a nonlinear, large

displacement analysis is probably warranted. Another type of

nonlinear force is called a follower force. Follower forces are loads

defined with respect to local nodes or elements, not a fixed

coordinate system. As the part deforms locally, the load orientation

changes. If follower forces are required, large displacement effects

should also be solved for.


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V. Types of load

a. Forces and Moments

b. Pressure Loads

c. Acceleration Loads

d. Temperature Loads

VI. Checking Applied Loads

實驗力學研究室 1 finite element model building. 實驗力學研究室 2 setting up the model...

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