24. Chapter 24 - Main Steps in Fea _a4

8/11/2019 24. Chapter 24 - Main Steps in Fea _a4

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Chapter 24 Introduction to Computer Codes Procedures___________________________

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CHAPTER 4

INTRODUCTION TO COMPUTER CODES PROCEDURES

The computer code architecture follows the main steps of performing a

Finite Element Analysis. Usually, each computer code has three main

components (or routines): the preprocessor (corresponding to the

preprocessing phase), the processoror solver(corresponding to solving or

solution phase) and thepostprocessor(corresponding to the postprocessing

phase). In a condensed form, a typical FEA consists in the following steps:

building the model, applying the loads, obtaining the solution and

withdrawing the results (the term loads has in this context a general

meaning, due to various types of analyses that can be performed).

24.1 THE PREPROCESSING

The preprocessing is the stage dedicated to the virtual model building. Due

to the complexity of data that should be delivered, usually this is the most

time consuming phase of the analysis (at least from the users involvement

point of view).

Before building the virtual model, the FEA user should already have in

mind the final result, in terms of the desired complexity of the model,

acceptable simplified geometry, loads and modeling hypothesis, etc. It is a

matter of experience and engineering judgment to create an adequate model

of the real physical system, in order to be able to draw out the results with

an appropriate refinement and also, to keep the model as simple as possible.

In order to create the virtual model database using the FEA computer code,

the following tasks should be accomplished:

- to choose the appropriate element types that will be used in the model;

- to assign the material properties;

- to define the domain and to provide the associated real constants;

- to apply the boundary conditions;

-

to apply the loads *;- to save the database in a database file.

*The term load may have different meanings, as it was shown before


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______________________Basics of the Finite Element Method Applied in Civil Engineering

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24.1.1 Element types

When building the model, the main information that should be delivered as

entry data concerns the geometry of the model and the material properties.

According to the geometry of the model and its physical behavior, the user

chooses the appropriate elements out of the element library. Each

commercial computer code has a collection of elements usually called

element library, some of them for general modeling purpose and others for

special use. Some elements (as 2D and 3D solids) have a complete defined

geometry by their nodes position, while other types of elements need an

associated set of real constantsin order to be completely defined: the cross

section of truss or beam elements, the thickness of shell elements, the initial

gap for contact elements, diameter and thickness for pipe elements, and soon. The element type is also chosen according to the physical phenomenon

and the desired solution in terms of the characteristic shape functions and

degrees of freedom: linear, quadratic, etc. Special purpose elements as

contact elements have more available options: point to point, point to

surface, surface to surface and also more behavior options: rigid contact,

elastic contact, sliding contact, etc.

In the same model one or more element types can be used. For each element

type, if the case, the specific real constants should be assigned according to

real dimensions of the members. When using different classesof elements

in the same model (elements connected to each other having different

number of degrees of freedom per node) a special attention should be paidto boundary conditions or displacement compatibility.

A very important rule is to define from the beginning the physical units for

data entry and results withdrawal. Although for usual materials the

commercial computer codes have assigned values for common material

properties by default, the user should be careful when using those values. A

coherent system of units concerning dimensions and material properties is

of utmost importance, especially for dynamic analyses.

24.1.2 Material properties

Material properties are assigned to elements according to the distribution of

various materials in the model. Usually each material has a user defined

identification number (ID), to which all the assigned properties are referred


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to. Depending on the analysis type, material properties can be constantvalues only (thermal conductivity, Young modulus, etc), or variable

properties associated to nonlinear physical phenomena (a stress strain

relationship, time or load step dependency, temperature-dependent

properties, etc). According to the ID, the delivered material properties are

organized in the computer code database in the material properties table.

24.1.3 Defining the domain - modeling approaches

Usually, the preprocessing routine of a FEA computer code enables the user

to use two different methods when generating the model:solid modelingand

direct generation. Withsolid modelingthe geometry of the model is defined

using simple shape primitives (lines, areas or volumes) which are subjectedto Boolean operations (merge, addition, subtraction, extrusion, etc). After

controlling, by specific commands, the desired size and shape of the

elements, the computer code generates the nodes and elements

automatically. By contrary, with the direct generation, the user defines

every node prescribing its location (in a Cartesian or cylindrical coordinate

system) and then the elements are defined by node connections. Even in this

case some generation procedures are available.

The solid modeling is more appropriate for large and complex models,

especially 3D volumes, for witch nodes and elements generation procedures

are cumbersome. A major advantage is the relative low number of entry data

required (comparing with node coordinates tables or node connection tableswhen defining elements). Solid modeling allows geometric operations with

primitives that are not possible with nodes and elements. For some

computer codes, it is the only way to use the design optimizationfeatures or

adaptive meshing. Also, geometry modifications of the model are easy to

perform. However, solid modeling has sometimes disadvantages regarding

the computing time or even it can fail under certain circumstances when

generating the mesh. There is no possible control on nodes coordinates,

except some specific location properties (such as belonging to a line, an

area, or to an interval of coordinates).

However, the automatic mesh generation is subjected to some geometrical

conditions. To types of meshes are available: the mapped mesh and the free

mesh, the difference being represented in figure 24.1. The free mesh option

is always possible, accepting a complete or local element degeneration


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(hexahedral bricks in the 3D space or quadrilateral solids in the 2D spaceinto triangular prisms, pyramids or triangular solids, respectively). For

mapped meshes, the geometry of the model should provide opposite faces

(in 3D) or lines (in 2D) with similar shape and dimensions. In order to take

advantage as much as possible of mapped meshes, different regions

(volumes or areas) of the model should be meshed separately. An example

is shown in figure 24.2. The 3D model is made by assembling three

different volumes, with two common contact areas. Supposing a prescribed

element size for the whole model, a different number of line divisions occur

for volumes V1and V3. Each one of these volumes, fulfilling the geometric

requirements, is meshed automatically using the mapped mesh option. As

consequence, to connect the already defined meshes, a free mesh option will

be chosen for volume V2.

Fig. 24.1 Solid modeling mapped and free meshing

Thedirect generationis appropriate for small and/or regular models, wherethe geometry allows node definition by coordinates and also the use of

generation procedures. Nodes and elements generation is usually based on

Solid model (volume) to be meshed

into 3D solid finite elements

a. Mapped mesh b. Free mesh


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repetitive copying of existing patterns of nodes and elements, or onsymmetry reflection. The most important advantage of the method is due to

the complete control over nodes and elements numbering and also over the

position of each node in the mesh. However, the direct generation is more

time consuming in the data preparing phase and cannot be used in model

optimization procedures. Also, the mesh modification is more difficult.

Fig. 24.2 Advantage of regular volumes for mapped meshes. The free mesh is usedfor the transition regions.

Furthermore, high performance FEA computer codes enable the alternative

to create solid models by means of various CAD (Computer AssistedDesign) systems and to import them in appropriate file formats (

.iges; .sat;

3D solid made of 3 volumes

V3

V2

V1

Mapped meshes of volumes V1and V3 Free mesh of volume V2

Separate volumes


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etc). The imported items are automatically transformed into lines, areas andsolids, on which usual meshing procedures are applied.

Whatever the chosen modeling method, before going on with the following

step, the nodes of the model should be defined. In a FE model, the boundary

conditions (constrains) and the loads can be applied only at nodes. Even

though, using the solid modeling method, the computer code usually allows

boundary conditions assigned to geometrical features such as areas, lines or

key points. This is only a user facility. In the background, dedicated

subroutines are doing the transfer to the associated nodes. The same remark

is available for distributed loads on lines, areas or even on element faces.

The distributed loads (i.e. an applied pressure) are transferred to nodes as

resultant concentrated forces after a simple evaluation, according to theelements face area or length. A similar automatic procedure is used for

body load assessment (i.e. own weight or inertia loads).

24.1.4 The boundary conditions

The assigned boundary conditions should be in accordance with the

expected (or desired) behavior of the model. The first important rule when

defining boundary conditions is to provide at least the required number of

constrains in order to avoid singularity of the master equation system

matrix. For a structural or mechanical FEA that means to suppress rigid

body motion, i.e. the boundary conditions should provide the statically

determination of the solid; in a thermal field analysis, at least two differenttemperatures should be assigned, and so on.

Boundary conditions can be applied on each node separately or on sets of

nodesafter an appropriate node selection. In structural or mechanical FEA,

boundary conditions are the suppressed or prescribed displacements*. The

number of suppressed (or prescribed) degrees of freedom is chosen

according to the desired behavior of the model and with the element types in

the mesh. After accomplishing static determination, it is not necessary to

suppress all available nodal DOF of a peculiar element. To model a hinge at

one end of a beam (which has fixed support capabilities due to the quadratic

shape function) only the displacement components should be suppressed,

the rotations resting free. One can achieve different behaviors of the model

on each direction by using the appropriate boundary conditions.

*In this context these are generalized displacements: displacements and rotations


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In both cases, to create on purpose a structural discontinuity the appropriatesolution is to define sets of coincident nodes and to couple the desired

degrees of freedom. The coincident nodes are nodes with a different ID

(number in the database) but with the same coordinates. In the first example

two coincident nodes are necessary, one assigned to the left-hand side

member (beam element e7) and one to the right-hand side member (beam

element e8). In the second example, actually two coincident planes should

be defined. Each of them is the sum of the solid elements faces which are

mutually sliding. Thus, all nodes defining the sliding planes should be

coincident pairs.

Fig. 24.4 Frictionless sliding by coupling the uxDOF of coincident nodes

The coupling of degrees of freedom is a peculiar type of boundary

condition. To achieve a hinge behavior in the frame example (a 2D-space

problem) both displacement degrees of freedom uxand uyof the coincident

nodes should be coupled regardless the orientation of the coordinate system.For the frictionless working joint example (a 3D problem) the coupling

direction of nodal displacement should be normal to the sliding plane.

xy y

z z

Sliding plane mesh with pairs of

coincident nodes

Relative displacement capabilities

of sliding parts


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Consequently, an appropriate coordinate system should be defined beforeassigning the coupling direction.

Briefly, coupled nodes will have the same displacements but only along the

selected directions out of all available degrees of freedom. There is no limit

for the number of coincident nodes that can be coupled together

simultaneously (i.e. a 3D hinge connecting nbeams).

In case of analyses dedicated to field problems, as thermal conduction (heat

transfer) or seepage phenomena, the boundary conditions should be

expressed in two different ways. Firstly, as prescribed nodal values of the

independent parameters, which are the known temperatures or the known

water head levels, respectively (nodal values). Secondly, as contourproperties regarding the flow direction along the boundaries. In this

context, the meaning of the flow term is heat flux qin thermal conduction

problems or water particles velocity v in the seepage phenomena. In both

cases, the boundary condition should force the flow line to be tangent to

the selected boundary or contour. Hence, the physical interpretation of the

constrain in a thermal field problem is that the boundary is a perfect

insulated limit (through which no heat transfer is possible), while in a

seepage problem the boundary is a watertight limit.

Other boundary conditions for field problems are heat flow rates and

convection.

24.1.5 Applying the loads

Without detailing the procedures of applying loads (the topic will be

discussed later) only few introductory remarks are necessary. First of all, the

most usual meaning of the load term refers to forces applied on a body or

structure within a structural analysis. This interpretation is true but

incomplete. It was stated before that for a finite element model, mechanical

loads can be applied only in nodes, as concentrated forces. Each loaded

node has assigned force components along one or few directions of the

coordinate system, in order to define the total magnitude and orientation of

the force. Usually, the finite element model is also subjected to other loads,

such as body loads or inertia, surface loads (pressures) and thermal effects

due to constrained displacements. In these circumstances, the previous

assertion remains valid, but the computer code has special subroutines


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which facilitate the transformation of those loads into nodal forces. Usingsolid modeling, the user may also assign pressures on lines or areas, which

are automatically transferred to nodes and elements. When using direct

generation, a constant or variable pressure can also be applied on sets of

selected element faces.

Sometimes, the boundary conditions (as prescribed, not null displacements),

are replacing explicit loads in a structural analysis. When a structural model

is not subjected to external forces and pressures, its own weight or

temperature variation, but exhibits local prescribed displacements, the

solution still leads to a deformed shape of the structure, stress and strain

fields, reaction forces, etc.

Moreover, in most thermal field or seepage analyses, loads are only the

boundary conditions.

Another important remark refers to the analysis step (or moment) when

loads are defined. For a so-called static or steady-state analysis, where loads

are constant, applied simultaneously and instantaneously, the loads can be

assigned in the preprocessing phase, being saved in the models database.

By contrary, when the loading conditions are changing during the analysis

due to load or time stepping, the solution phase has more then one step and

the loads are redefined (or modified) during the subsequent phases.

24.2 THE SOLUTION

In the beginning of the solution phase of the analysis, the user has to assign

the appropriate solution options and settings. The computer code options

refer to the following topics:

- the analysis type (static, modal, transient, etc);

- the method to be applied for solving the master equation system,

according to the models characteristics, the acceptable computing time

and the available computer memory;

- the method to be applied when solving a nonlinear problem, i.e. type of

the Newton - Raphson algorithm;

- the load (or time) step definition and the appropriate changes between

load steps;


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- the convergence norm (or acceptable error) and the maximum number ofequilibrium iterations within a load step.

Once the computer code settings are chosen and the load steps defined (by

interactive commands or using batch files) the solution process may be

started. The results of the solution phase, as nodal DOF values (primary

unknowns) and the derived values (the element solution) are saved in the

results database file. The computing time and the memory requirements

depend on the complexity of the model, number of load steps, computer

performances, etc. Although the solution process is running in the

background, generally the computer code has an output window (or file)

where live information are printed regarding the evolution of the analysis,

as well as warning or error messages.

24.2.1 Load stepping and equilibrium iterations

During a FEA the structure (or the domain) can be subjected to various

loading conditions. The simplest way to apply loads is common to a linear,

static or steady-state analysis, where the loads are applied all at once and at

full intensity. The solution is in this case a single stepsolution, leading to a

unique set of results (displacements, stress field, temperature field, etc).

Loads, constraints and material properties are unique and constant, while the

characteristic matrices and vectors are calculated only once during the

solution phase.

Sometimes, the interest is focused on the response of the structure when

subjected to loads with various configurations and/or values. Each load

configuration applied on the finite element model becomes a load step. To

perform a FEA with several load steps, the solution phase is repeated for

each load configuration. If all other characteristics of the model remain

constant, only the load vector changes. Consequently, a different set of

results will be stored in the results database for each load step.

In static analyses, the load steps solutions are very useful to emphasize the

influence of various loads applied on a linear-elastic structure (only in this

case the principle of effects superposition is available): own weight,

concentrated loads, distributed loads, prescribed displacement, etc. Each

load is assigned to a load step and the solution phase is repeated for all the

defined load steps. Afterwards, the results are analyzed separately or, they


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are combined in the postprocessing phase, using algebraic operations and/orweighting coefficients.

Load steps can be used to specify a transient load history graph. Usually the

time parameter is connected to load stepping, even in static analyses, to

achieve the same computer code representation as for transient or time

history analyses. Because time always increases monotonically, it has also

the advantage of being a consistent counter in all cases.

Sometimes, loads should be applied gradually in order to obtain an accurate

and convergent solution. It is the case of nonlinear static or transient

analyses, when the material properties are changing according to the stress

level. If necessary, each load step can be further divided into sub-steps. Theloads can vary over a load step in asteppedor rampedmanner. A different

solution is calculated and saved in the results database file for each step or

sub-step. In nonlinear solutions, inside each load step or sub-step

subsequent solutions are calculated, called equilibrium iterations.

24.2.2 Solution method options

When starting the solution phase, the computer code accomplishes the

following tasks:

- calculates the elements characteristic matrices;

- calculates the load vector;- solves the global algebraic equation system;

- calculates the elements results.

For each load (or time) step (or sub-step), some or all of the previous tasks

are repeated, depending on the chosen non-linear solution options and on

the changes encountered when proceeding from one load step to another.

Several methods of solving the global equation system are available: the

frontal solution, the sparse direct solution, the Jacobi Conjugate Gradient

solution, etc. Each method has its own advantages, being suitable for a

specific type of analysis. The frontal solution and the sparse direct solution

methods are direct elimination solvers while the Jacobi Conjugate Gradient

solution and other similar methods are iterative solvers.


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The frontal solution method, after calculating the elements matrices, createsa complete triangularized matrix by eliminating, element by element, the

DOF which can be expressed in terms of other degrees of freedom. Then,

the nodal DOF solution is calculated by back substitution. The element

solution is calculated using the individual element matrices. In this method

the complete global matrix is not assembled. A specific characteristic of the

frontal solver method is the wave front, which is the instantaneous number

of DOF in the solver triangularization process. Being directly bounded to

node or element numbering, the wave front magnitude affects the computing

time and memory requirements.

The sparse direct solver is based on direct elimination of equations from the

global equation system. Consequently, using this method, the globalstiffness matrix is calculated.

The iterating solution methods, after calculating the element matrices,

assemble the global stiffness matrix. Then the solution is found by iterating

to convergence starting with some initially assigned values.

24.2.3 Solution failures

The solution process may stop before finalizing the computations. The main

cause generating a solution failure is the equation system singularity. The

singularity means an indeterminate or non-unique solution, because of a

negative or zero equation pivot. There are other reasons for solution failures,too. Usually, the solution process stops due to the following modeling

errors:

- insufficient number of constraints;

- nonlinear elements behavior (due to material properties or large

deflections);

- unconstrained joints due to elements relative position.

The solution process also stops when reaching the maximum default or

prescribed number of iterations without attaining convergence.


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24.3 THE POSTPROCESSING

Postprocessing represents the third phase of a FEA. In a general acceptance

the postprocessing represents all the available procedures that can be

followed in order to review the results of the solution phase. These results

are saved in the so-called results database file, which itself is organized

according to the analysis option: load (or time) steps, primary and derivative

results, etc. In terms of physical parameters, the results database contains

numerical values of the calculated DOF (primary unknowns of the

problem), as nodal displacements, nodal temperatures or nodal water head

values, or derivative parameters, as stress, heat flow or seepage velocity.

The importance of the postprocessing phase is due to the fact that it enablesthe user to know how the boundary conditions and the applied loads affect

the finite elements model, how the mesh refinement responds to the

expected results, how suitable the load steps were chosen, etc.

The numerical values stored in the results database should be analyzed, used

in the design process or even delivered as final results. According to the

computer code performances, the results can be reviewed as:

- lists of numerical values;

- graphical representations in raster or vector mode, showing the

distribution of various parameters over the model (contour plots or

diagrams);- graphs of parameters evolution over load (time) steps or along a

specified direction across the model;

- animated pictures.

Usually, all these reviewing methods are available on screen and can be

saved as formatted text, graphics or animation files. Printing or plotting

facilities are also available.

It should be emphasized that the postprocessing doesnt means only the use

of a set of tools for results representation. It also means to apply computer

code subroutines in order to combine or to compare different load case

results. The only condition for combining load cases in order to define new

ones is to obtain the results on the same finite element model and to fulfill

the physical requirements (the requirements for effect superposition). A


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typical example is that of a structural linear-elastic FEA with a few numberof load cases (each one representing a load step). The database file stores the

results for all the performed load steps. Afterwards, according to the load

combination hypotheses, these values can be subjected to algebraic

operations (with or without the use of weighting coefficients). The result of

each combination becomes a new load case that can be represented in the

before mentioned fashions.

A civil engineering frame structure is subjected to gravity

(permanent load), wind and earthquake. Accepting for each

load an equivalent static distribution and the material

behavior in linear-elastic state, each load can be applied

separately. The results database file will contain threesets of results (primary and derived variables as nodal

displacements, stress components, etc.), actually the load

cases LC1, LC2and LC3, which are independent one to each

other. During postprocessing, new load cases can be

defined, by summation of the permanent load effects to each

of the other two.

LC4= a1LC1+ a2LC2 (permanent load + wind load)

LC5= a1LC1+ a3L C3 (permanent load + earthquake load)

LC6= a4LC1+ a5L C2+ a6L C3

(permanent load + wind load +

earthquake load)

The weighting (or safety) coefficients aiare usually given

by specific design codes.

24.3.1Lists of numerical values

The lists of numerical values are organized in tabular form according to the

users selected items. Some variables, as displacement, temperature or

reaction forces, are associated to nodes while derived parameters, as stress

or heat flux, are characterizing the elements. However, such derived

parameters can also be listed in nodes, using weighted average values. A

nodal stress value can be calculated as the mean value of stresses evaluatedin the elements converging in that node, weighted by the elements length,

surface or volume.


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The tabular data are saved in normal text (ASCII) format, to provide easyediting and exporting to another computer code environment (

.xls files,

.dbffiles, etc). Two examples are presented in tables 24.1 and 24.2.

Table 24.2. List of nodal reaction forces and bending moments

PRINT F REACTION SOLUTIONS PER NODE

LOAD STEP= 1 SUBSTEP= 1

TIME= 1.0000 LOAD CASE= 0

NODE FX FY MZ

1 680.34 27994. 0.19794E+06

14 -1942.5 60697. 0.48114E+0627 -2396.5 60536. 0.54242E+06

40 -4341.3 30772. 0.75514E+06

--------------------------------------

TOTAL VALUES

VALUE -8000.0 0.18000E+06 0.19766E+07

24.3.2 Contour plots and diagrams

A contour plot is the graphical representation of a single parameter

distribution over the finite element model (or over a selected region). It is

probably the most suggestive way to review the results. In such arepresentation the nodal or element results are sorted in ascending order.

Then, they are drawn as isolines in the vector mode representation, or as

graduate colored areas in the raster moderepresentation. Each isoline is the

path of a constant value of the represented parameter and each colored area

corresponds to a predefined interval of the parameters value. Either the

isoline positions or the extent of colored areas are computed by

interpolation. Labels and colors are assigned to each line or interval, while

the correspondence to the numerical values is made by an attached legend.

The number of contours used in the representation may be the computer

codes default value or a user defined one. The number of contours is

usually associated to the available output resolution (on screen or atprinting) and to the desired refinement of the results presentation. The

contour values can be uniformly distributed by default between their


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extremes (in this case, it is called an equal intervalplot) or, they can be userdefined contour values (a non-uniform plot distribution).

Non uniform contours can sometimes be more appropriate for the

representation, emphasizing gradients or extreme values. Anyway, the same

results database can lead to various graphical representations according to

the users option. In the following figures two contour plot examples are

shown, in raster and vector mode representations. Figures 24.5.aand 24.5.b

are based on the same results database file*.

Fig. 24.5 Contour plots the distribution of horizontal displacement (cm)

b. Vector mode

a. Raster mode

* The model is dedicated to a deep excavation analysis; the excavation is

performed under the protection of molded walls and an internal bracing system.


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Another group of results is made of line-shape element features, used instructural analyses, such as the axial force, the shear force, the bending

moment, the torsion moment and their corresponding stress values. These

features, as element results database components, are appropriate for

diagram representations. Consequently, the computer code facilities should

contain the diagrams representation option. An example of results obtained

on a 2D frame structure is presented in figure 24.6.

Fig. 24.6 Diagram representations on a frame structure model


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A very useful graphical representation is the deformed shape of thestructure. Without any associated numerical values, the deformed shape

drawing is the most intuitive way to compare the expected structural

behavior with the analysis results. The deformation scale used in the

graphical representation is set by default in order to render evident the

displacement tendency, regardless its value (usually the maximum

displacement equals a fixed ratio of the maximum dimension of the model).

The drawn deformed shape can overlap the undeformed (initial) shape of the

structure. An example, concerning the previous frame structure is shown in

figure 24.7.

Fig. 24.7 Deformed shape of the frame structure

The same graphical subroutine is used for representing the vibration modes

(vibration shapes) calculated via a modal analysis. Each vibration mode

corresponds to a load step result. The vibration shape is in this case the

result of normalized displacements corresponding to the natural frequency.The first vibration modes determined using the 3D finite element model of

the main block of a buttress dam, by performing a modal analysis, are

represented in figure 24.8.

24.3.3 Graphs

Two types of graphs are available during postprocessing. The first one

applies to multiple load steps analyses or to transient analyses. This

graphical representation shows the results evolution over load steps or time,

using all load step results in the database. Whatever the interesting

parameter is (the displacement, the stress, the temperature or any other

primary or derived unknown), the graph represents its evolution at asinglespecified item of the model (node or element). With a convenient scaling, a

few parameters can be represented in the same graph.


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Fig. 24.8 First vibration modes of a buttress dam (single block 3D model)

The second type of graph is based on the results of a single load step

analysis or a selected load step out of a multiple load step database. Such a

graph shows the evolution of one or few selected parameters along a

predefined geometrical path. Usually, the path is defined by node location or

by the coordinates of the path vertexes. As an example, the vertical,

horizontal and shear stress distributions, along a path defined by a straight

line connecting two nodes, are shown in figure 24.9. The stress values arecalculated during a static analysis, used for calibrating the finite element

model. The nodes are selected as midpoints of the upstream and

1stvibration mode 2ndvibration mode

3rdvibration mode 4th

vibration mode


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downstream faces of the dam block, close to the foundation line, at theelevation represented in the figure.

Fig. 24.9 Graph of stress distribution along the defined path

The same computer code subroutines can be used to review the nonlinear

material property relationships or to examine the correlation between any

two items concerning the analysis.

Node 2623 Node 234

[KPa]


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24.3.4 Animation pictures

The powerful computer codes dedicated to FEA are usually outfitted with a

postprocessing subroutine for animating any type of display. Animation is a

very intuitive tool for interpreting the numerical results. The basic procedure

is to capture a sequence of images, frame by frame, and to save them as a

video file ( .avi, .mpeg or another file format). Such files are then

reviewed by loading them in any computer code view-player. The number

of frames between the extreme positions of the structure (and consequently

the smoothness of movement) should be correlated to the computer graphics

performances.

The deformed shape of the structure corresponding to a static analysis andthe natural vibration shapes of each expanded vibration mode are unlabeled

animations (without assigned numerical values). Contour plots can be

attached to the animated deformed shapes in order to reveal the evolution of

displacements, stresses or other parameters.

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24. Chapter 24 - Main Steps in Fea _a4