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News.St7
Strand7 Solutions in Athens 2004! Last month saw the XXVIII Olympic Games held in the birthplace of the original Games, Greece. The preparation leading up to the Games was highly scrutinised by the media, with the involvement of various Australian companies forming the basis of some of their stories. This newsletter reports on the work undertaken by one of the engineering consultancies involved in the design and analysis of the centrepiece of the Games, the main stadium, together with the vital role that Strand7 played in the analysis.
Also in this issue we focus on some details of Strand7 including Links, Points and Lines, a new section on the Strand7 API and how a thermal stress analysis can be completed efficiently.
As always, the newsletter contains a new benchmark and is packed with helpful Did You Know? items.
A highlight of the recent Olympic Games held in Greece, was the Olympic Athletic Centre of Athens Stadium, named the OAKA Stadium. This stadium was used for both the opening and closing ceremonies of the Games, as well as for numerous high-profile events such as athletics.
As part of the redevelopment of the Olympic site for the Games, a new roof structure was built over the main stadium. This roof was designed by the renowned Spanish architect and engineer Santiago Calatrava. Sinclair Knight Merz (SKM) were Engineering Consultants on the project. SKM’s brief was to engineer the entire OAKA roof structure. Working out of their London office, a team of SKM engineers from the UK, Australia and New Zealand used Strand7 to undertake this project.
Details of the Roof Structure The roof structure consists of two coverings, each spanning over 300m in length and varying in width from 60m to
100m. Each covering is supported by a curved arch structure comprising an upper arch tube and a lower arch torsion tube. The upper arch is constructed from a circular hollow section 3m in diameter with a variable wall thickness of up to 100mm. The lower arch is similar to the upper arch but is 3.6m in diameter.
The two arches on each covering are connected by a row of steel cables arranged in a vertical plane. Steel diaphragm plates are installed at every cable connection point. The
In this issue… ● Feature Article 1
● Strand7 Element Use 3
● Strand7 Functions 4
● Modelling Tip 6
● API in the Field 11
● Benchmark 13
● Announcements 15
● Training Calendar 16
● Exhibitions calendar 16
● User Profile 16
Issue 3, October 2004
2004 Athens Olympics
Newsletter for Strand7 and Straus7 users Strand7 is marketed as Straus7 in continental Europe
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main roof rafters are built into the lower arch and cantilever on both sides of the arch. An additional row of cables connected to the top arch supports the external rafters along the perimeter of the stadium, while another row of cables supports the internal rafters at approximately mid-span. Transparent cladding (polycarbonate roof tiles) are installed over the rows of purlins, perpendicular to the rafters.
Figure 1.1 - In-progress construction of arch.
Erection The entire roof structure is pin-supported at only four points. It was initially erected in two symmetrical halves at temporary locations at each side of the stadium; this allowed construction on the roof to proceed without hindering works on the main stadium.
Figure 1.2 - Aerial view showing the east side arch in position and
the west side arch ready to be moved into position.
Each half was then moved into its final position by sliding it along temporary supports where they were connected together at only two points. Finally the bases were fixed to permanent supports.
An impressive animation of this procedure can be found at www.athens2004.com/en/Videos/multigallery.
Strand7 Modelling SKM used Strand7 extensively for the modelling and analysis of the OAKA Stadium roof structure. Because of Strand7’s comprehensive suite of finite elements and sophisticated user interface, Strand7 was used not only for modelling the complex stadium roof structure but also for simulating the entire erection process.
For modelling the erection process, one of the most useful features of Strand7 was its ability to start a new analysis of
the model using the results of a previous run as the initial conditions. “Using this and other features of Strand7, we were able to simulate the stages of construction by applying new conditions and loads to a model that was already solved in a previous run,” said Ljubisa Petrovic of SKM. Another use of this feature was to establish the pre-tensions in the cables required to achieve a desired final roof shape and final levels of tension in the cables. This procedure can be easily automated using the Strand7 API.
Figure 1.3 - Strand7 model showing connection of roof girders to
lower torsion tube.
Figure 1.4 - Strand7 model showing the arrangement of cables
between the upper and lower arches.
Another extremely useful feature for SKM was Strand7’s ability to save the deflected geometry of the model and reuse it as a new and unloaded model for a subsequent run. This approach was used for calculating the preset roof geometry and to determine the initial shape that would produce the required final shape under the applied loading. As the two sections of the roof structure were to be assembled using a temporary support structure, these tools enabled SKM to establish the initial geometry such that after the complex erection procedure was completed, the entire roof deflected into the final shape as designed by the architect.
SKM engineers involved in the Strand7 simulation included Nick Ling (project manager) together with Ljubisa Petrovic (senior structural engineer, structural analyst) and Louise Harrod (structural engineer), the engineers responsible for the development of the Strand7 models and their execution. SKM may be contacted through their web address www.skmconsulting.com
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Strand7 supports seven different link types to allow the
relationship between the displacements/rotations of two nodes to be precisely specified. Among the more commonly used link types in Strand7 are the Master-Slave links and the Rigid links.
A common misconception concerning these two link types is that a Master-Slave link with all degrees of freedom linked is equivalent to a Rigid link set in Global XYZ. This article discusses the differences between these two links.
Master-Slave link Definition This link defines a master-slave relationship between two nodes. One node follows the selected displacement components of the other node (and vice versa) in the global Cartesian system or in a User Coordinate System. Any combination of DX, DY, DZ, RX, RY and RZ may be linked.
Rigid link Definition This link provides an infinitely stiff connection between two nodes.
Comparison The difference between the two links is that a Master-Slave (set in all d.o.f) links all freedoms (both translation and rotation) and therefore cannot rotate, but only translate as a rigid body. The displacements and rotations are identical and so the two nodes will translate in space such that the orientation of the displaced link remains parallel to the original orientation. A Rigid link can be thought of as an infinitely stiff beam and can rotate as a rigid body. Displacements and rotations are coupled together by considering the rigid body rotation of the link and the fact that in the direction along the axis there is no relative displacement, (i.e. the link cannot extend or shrink). As the length of the link approaches zero, the behaviour of the Master-Slave and Rigid link becomes the same. The following two examples illustrate the differences between the two link types.
Example 1 Two simple beam models are shown in Figure 2.1. The model on the left has a Master-Slave link with all degrees of freedom set. The one on the right has a Rigid link set in Global XYZ. Both models are fully restrained at the base and loaded with an identical lateral force.
Figure 2.1 – Laterally loaded beam model. Left: Master-Slave link; Right: Rigid link.
When these two models are solved using the linear static solver, the different behaviours of the two links can be clearly observed.
Figure 2.2 – Difference between Master-Slave link and Rigid link.
The Master-Slave link ensures that the global (or UCS) displacements and rotations of the linked nodes are the same. The Rigid link ensures that the relative distance and rotation between the linked nodes does not change.
Example 2 Two cantilevered beam models are shown in Figure 2.3. The model on the left has a Master-Slave link with all degrees of freedom set. The one on the right has a Rigid link set in Global XYZ. Both models are fully restrained at the base and loaded with an identical vertical force.
Figure 2.3 – Cantilever Beam Model.
Left: Master-Slave link; Right: Rigid link.
These two models are solved using the linear static solver and their response is shown in Figure 2.4.
Figure 2.4 – Response of beam under vertical loading.
From Figure 2.4, it seems that there is no difference between the two link types. From the dimensions given in Figure 2.3, we expect the moment reaction about the fixed base to be:
NmmMM
dFM
Base
Base
Base
62500625100
=×=
×=
However using the Strand7 Peek tool, a moment reaction of 50000Nmm is obtained for the Master-Slave link model. This is shown in Figure 2.5.
Master-Slave vs. Rigid Links
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Figure 2.5 – Moment reaction for Master-Slave link model.
Strand7 does not consider the length of the Master-Slave link in its calculation. For this model, the link is simply used to transfer the node restraints at the base node to the other linked node and hence the beam is considered cantilevered about its left end with a moment arm of 500mm instead of 625mm.
Using the Strand7 Peek tool again, a moment reaction of 62500Nmm is obtained for the Rigid link model as shown in Figure 2.6.
Figure 2.6 – Moment reaction for the Rigid link model.
Strand7 does consider the length of the Rigid link in its calculation and therefore the expected moment reaction is obtained.
Conclusion Hopefully the two examples shown have clearly illustrated that a Master-Slave link with all degrees of freedom set is generally not equivalent to a Rigid link set in Global XYZ.
A Master-Slave link with all degrees of freedom set is a mathematical tool and you should exercise caution when using this arrangement. If used, the length of the element should be minimised to reduce any moment-loss effects.
Master-Slave link summary:
● Transfers displacements/rotations between the linked nodes.
● The length of the link is not considered in any of the calculations.
● Particularly useful when overlaid on point contacts to ensure that they remain perpendicular to the contact surfaces (linking only the degrees of freedom required to keep the contact perpendicular).
● Also very useful in construction sequence as the state of the Master-Slave can be changed in a nonlinear run between load increments, when used in conjunction with the nonlinear restart procedure.
Rigid link summary:
● Provides an infinitely stiff connection between the linked nodes.
● The length of the link is considered in calculations.
● Particularly useful for connecting an offset lumped mass to some part of a structure.
Details of this and other theoretical issues can be found in our new Theoretical Manual.
Happy modelling!
The Points and Lines function provides an invaluable
modelling tool for mesh generation and modification. Located within Tools, Points and Lines allows the user to generate and modify a mesh by creating or moving nodes and beam elements according to the chosen geometric option.
Straight and Parabolic Lines Straight or parabolic lines consisting of nodes or a series of beams (depending on whether the Create Beams check box is set) may be generated using the Straight Line and Parabola options. These options are particularly useful for defining beams prior to extrusion or for defining nodes for the manual creation of plates and bricks.
Straight Line Parabola
Figure 3.1 displays the Parabola option. A quadratic curve is created as a series of beams between three points to define the geometry.
Figure 3.1 – Points and Lines/Parabola.
Fillets Fillets of a specified radius consisting of nodes or beam elements can be easily generated using the Three or Four Point Fillet options. Uses of the fillet options include modelling the details of welds in plate sections prior to extrusion or generating user-defined beam sections.
Three Point Fillet Four Point Fillet
Figure 3.2 shows the use of the Three Point Fillet option. A fillet is created, followed by editing the beam elements using Edit-Element to create an intersection between the fillet and straight beams.
Points and Lines
P1
P3
P2
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Figure 3.2 – Points and Lines/Three Point Fillet.
Line Extensions, Normals and Intersections Lines may be extended or trimmed or beams created tangentially to a line direction using the Line Extend option. An intersection between three or four nodes may be found using the Line Intersection tool. The Line Normal tool allows nodes or beams to be defined normal to a line in a specified plane. These tools are particularly useful for defining beams normal to a surface that will later be defined as point contact elements.
Line Extend Line Normal Line Intersection
The use of the Line Normal tool is shown in Figure 3.3. A beam normal to the blue plates is created. Using Edit/Element, the nodes of the blue plate elements are aligned with the beam, followed by smoothing of the plates using Tools/Smooth Plates.
Figure 3.3 – Points and Lines/Line Normal.
Node Averaging The Node Average tool allows nodes to be created or relocated to a midpoint between two nodes in terms of the specified coordinate system. The Cartesian Node Average tool produces a node at an averaged position according to a
Cartesian coordinate system. The UCS Node Average tool produces an averaged node position according to the selected UCS.
Cartesian Node Average UCS Node Average
Figure 3.4 illustrates the use of the UCS Node Average option. A node is aligned such that the coordinates are an average of the selected corner nodes according to a cylindrical UCS. The positioning of the node allows a Quad8 element to be correctly defined using Create/Element, with the repositioned node defined as a mid-side node of the element, still lying on the correct radius.
Figure 3.4 – Points and Lines/UCS Node Average.
Circles and Ellipses Circles and ellipses consisting of nodes or a series of beams may be defined using the Two Point Circle, Three Point Circle, Ellipse and Variable Radius Curve. The Two Point Circle and Three Point Circle tools allow the definition of a partial or full circle. The centre of a circle may be located using the Find Circle Centre tool. The Ellipse and Variable Radius Curve options allow a partial or full ellipse to be defined.
Two Point
Circle Three Point
Circle Find Circle
Centre Ellipse Variable
Radius Curve
Figure 3.5 uses the Find Circle Centre tool with the Create Beams option set. By selecting three points on the circle, a node defining the circle centre and three beam elements are created. Using the Entity Inspector (Shift), the circle radius may be determined from the beam length. This is particularly useful for QA purposes.
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Figure 3.5 – Points and Lines/Find Circle Centre.
Circle Intersections and Tangents The intersections and tangents of circles may be determined using the Two Circles Intersect, Circle Line Intersect, Circle Line Fillet, Two Circle Fillet, Two Circle Tangents and One Circle Tangent tools. The Two Circles Intersect and Circle Line Intersect tools allow the intersections between circles and lines to be determined in the form of nodes or beams. Fillets may be created between circles and lines using the Circle Line Fillet and Two Circle Fillet tools. The Two Circle Tangents and One Circle Tangent tools may be used to create nodes or beams tangent to the circles.
Two Circles
Intersect Circle Line Intersect Circle Line Fillet
Two Circle Fillet Two Circle
Tangents One Circle Tangent
Figure 3.6 shows the Circle Line Fillet tool. A fillet is created by selecting the circle centre, two points lying on the straight line and defining the circle and fillet radii. The circle and straight line beams were joined to the fillets using the Edit-Element option.
Figure 3.6 – Points and Lines/Circle Line Fillet.
A comprehensive description of each geometric option is available within the Strand7 Online Help
It is well known that a variety of thermal factors can
greatly affect the structural behaviour of a body or component. With service temperatures having an influence on material properties as well as leading to load considerations in the form of thermal expansion or shrinkage, it is important to take these thermal effects into account when performing a finite element stress analysis.
In this issue, we will look at a number of features available in Strand7 that allow users to progress from a thermal analysis to stress analysis in a few simple steps. Also discussed is the manner in which the Strand7 structural solvers use applied temperature load case data and Strand7 heat results.
1. Using Heat Results in the Strand7 Structural Solvers Strand7 is equipped with solvers that are able to analyse a variety of heat transfer problems including steady-state heat problems - where the equilibrium temperature distribution at infinite time is calculated, and transient heat problems - where the temperature distribution is calculated as a function of time.
Both the steady-state and transient temperatures calculated from the heat solvers can be used as the input temperatures in a thermal stress analysis.
For example consider the model shown in Figure 4.1. Here, a composite material is embedded in a high-thermal conductivity material maintained at 400 oC. The upper surface is exposed to a convection environment at 30 oC with convection coefficient h = 25 W/m2 oC.
Did you know?
Subdivide only Normal Beams When a model contains both normal beams and other line elements, e.g. trusses and springs, you may not want to subdivide the truss/spring elements when the beams are subdivided as it could lead to singularities. Preferences within Strand7 can be changed so that when all beams in a model are selected, only those that are normal beams are subdivided. Choose Tools/Options. Under Subdivide set Subdivide only Normal Beams.
Modelling Tip – Thermal Stress Analysis
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Figure 4.1 – Thermal stress analysis example.
After specifying the model’s boundary conditions and material properties, either of the heat solvers can be used to determine the temperature distribution through the structure:
Figure 4.2 – Steady state heat solution for the equilibrium
temperature field.
The contour plot in Figure 4.2 shows that the temperature at Point A is approximately 242oC. The transient heat solution reinforces these results with the evolution of the temperature at Point A to its steady state value after 100 minutes of 242 oC shown in Figure 4.3.
Figure 4.3 – Transient heat solution for the variation in
temperature with time.
To use the nodal temperatures calculated by the heat solvers in a structural analysis, with the model open choose Attribute/Node and select Temperature. Then in the dialog box, shown in Figure 4.4, click Import:
Figure 4.4 – Node temperature attribute dialog box.
If the results from a steady-state heat solution are required, make sure the *.sha file is selected for importing. The nodal temperature results from the steady-state heat solution will then be applied to all the nodes in the model as a temperature attribute for the currently active load case.
If, instead, the results from the transient heat solve are required for importing, ensure that the .tha file type is selected in the Import files of type drop down list. Following this, you may choose to either import the temperatures from a single time step or from all the saved time steps from the transient heat analysis.
Choosing the temperature distribution from one specific time step, as shown in Figure 4.5, will import nodal temperatures, for that time step, into the current active load case.
Figure 4.5 - Importing nodal temperatures from a specific step of
the transient heat results file.
Alternatively, selecting to import all the saved steps in the transient heat solution results in the nodal temperatures from each of the time steps being allocated to different load cases. The dialog is shown in Figure 4.6.
Figure 4.6 - Importing nodal temperatures from all steps of the
transient heat results file.
Note: If the model does not contain enough load cases to assign all of the steps, new load cases are automatically created during the import.
400oC
Tamb = 30 oC h = 25 W/m2 oC
400oC 400oC
Outer Composite material: k = 0.3 W/m oC ρ = 2000 kg/m3 C = 800 J/kg oC
Inner Composite material: k = 2.0 W/m oC ρ = 2800 kg/m3 C = 900 J/kg oC
Point A
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Once the temperature results have been imported back into the Strand7 model, as load case dependent nodal temperature attributes, the finite element model needs to be set up for a structural analysis. This includes all the usual considerations of defining the correct structural material
properties (i.e. Young’s modulus E, Poisson’s ratio v etc.), applying restraints and specifying the thermal expansion coefficient for each property set (note that these are aspects of the structural analysis and are not necessary for the initial steady-state or transient heat analysis).
The thermal strains εo resulting from the applied node temperature attributes are calculated from the following equation:
( )refo TT −=αε
where α is the coefficient of thermal expansion, T is the temperature of the body and TR is the reference (or strain-free) temperature.
It is therefore also important to properly specify the correct reference temperatures for the model. This is found under Global/
Load and Freedom Cases and is load case dependent. The manner in which the different Strand7 solvers determine and use this reference temperature is discussed in more detail later.
For the embedded composite material model, shown in Figure 4.1, the thermal stress results obtained from the Strand7 linear static solver based on the steady-state temperature field are shown in Figure 4.7.
Figure 4.7 – Thermal stress field based on steady state
temperatures.
It can be seen that the highest value of approximately 62MPa for the maximum principal stress is predicted at point B.
If it is necessary to determine the development of the thermal stresses with time, the transient heat results obtained earlier can be used in conjunction with the nonlinear transient dynamic solver. Choose Solver/Nonlinear Transient Dynamic to bring up the solver dialog box. Then click Temperature. This will bring up the dialog box shown in Figure 4.8, where the user has the option to input nodal temperatures via load case data or by choosing the results of a transient heat solution.
In the current case study the nodal temperature input is from the Transient Heat File. The time steps for the transient dynamic analysis can be the same or different to those of the transient heat analysis. If they are different, then Strand7 will interpolate the transient heat steps to determine the values to use in the stress analysis.
Figure 4.8 – Temperature input for the nonlinear transient
dynamic solver via transient heat file.
Once the reference temperature has been specified, the variation of the thermal stress can be calculated by the Strand7 nonlinear transient dynamic solver. The results obtained for point B are shown in Figure 4.9:
Figure 4.9 – Nonlinear transient solution for variation of stress
with time.
It can be seen that the thermal stress at point B relaxes with time to its steady-state value of 62 MPa.
Note: With this method the Reference Temperature specified in each load case is ignored. Instead it is enforced in the dialog shown in Figure 4.8 since there could be multiple load cases with different values of Reference Temperature.
2. Modelling material properties that change with temperature. Material properties such as Young’s modulus and the thermal expansion coefficient can be a function of material temperature. In Strand7, such dependency is described through the use of a Factor vs. Temperature table (choose Tables/ Factor vs. Temperature to define these).
Did you know? Brick Cutting Plane Animations Viewing internal stresses in a brick can often be difficult and so the cutting plane option is used to view the stresses through a slice. You can then create an animation in the usual manner, (Results/Create Animation), which will create an animation of results for this slice. But what about if you want to see this slice progress through the brick structure for a single load step? Choose to create an animation and set Move Cutting Plane. When animated the slice will progress through the structure for that load step, between the extremities of the model.
Point B
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As an example, if the stiffness (Young’s Modulus) of a material decreases as the temperature increases, the table shown in Figure 4.10 could be used.
A nominal value of Young’s Modulus is defined via the Structural tab in the Element Property dialog box and the table of Factor vs. Temperature type is assigned to the property via the Tables tab (see Figure 4.11 and Figure 4.12).
At a given temperature the Young’s Modulus is calculated by multiplying the nominal value by the table factor. In other words, the table defines the ratio between the nominal value of modulus and the value of a specific temperature. It is not a table of Modulus as a function of temperature.
Figure 4.10 – Factor vs. Temperature Table for Young’s Modulus.
Figure 4.11 – Specifying nominal value EO via structural tab.
Figure 4.12 – Assigning Factor vs. Temperature Tables to
properties.
3. How each Strand7 solver uses the applied load case temperature data. Due to the fundamental differences in their underlying theories, the manner in which load case temperature data is used varies quite markedly between each of the Strand7 solvers. Table 4.1 details how the static and transient dynamic solvers make use of load case temperature data.
Further to the details given in Table 4.1, it is important to be aware of the treatment of applied temperature load case data by the other Strand7 solvers (not listed in Table 4.1). For example, while the linear buckling solver does not support temperature dependence options directly, any temperature dependence used in the initial conditions file (either from a linear or nonlinear static analysis) will be effectively used in the buckling analysis.
Did you know? Auto-Assign restraints
When creating a rigid link array there is no need to go through the process of creating rigid links one at a time. Instead you can make use of the auto-assign tool in Strand7. Select all the nodes you wish to be connected via rigid links then choose Tools/Auto Assign/Restraints. Select Rigid Connections as the Type and click Apply. This will connect all the nodes via rigid links to an automatically generated master node, which will lie at the average of the selected nodes. Alternatively you can select your own master node for the rigid links to radiate from.
This tool is particularly useful for models that have bolted connections or areas where a point load is to be applied over an area.
EO
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Solver Temp. Dependent Material Properties Thermal Loads Reference Temperature Linear Static In the solver dialog box, the user can
specify any one load case which contains nodal temperatures (Tmat) to be used to calculate temperature dependent material parameters (eg. E0 and α0). This means that all load cases use the same value of E.
For each load case (l), the thermal loading or strain is determined from:
( ) ( )refllmatl TTTf −= )(00 ααε [1]
Each load case uses its own temperature distribution to determine the temperature loading Tl.
Each load case (l) uses its own
reference temperature )( reflT
specified in Global/Load and Freedom cases data.
Nonlinear Static
At each load step a temperature distribution is calculated using the load factors lλ and temperature distribution Tl of included load cases according to: 1. A combined temperature change is derived from the linear combination of temperature change in all of the included thermal load cases:
( )∑=
−=∆NLC
l
reflll TTT
1λ [2]
2. The combined temperature value is defined as the combined temperature change plus the reference temperature:
refcomb TTT +∆= [3]
The temperature loading1 is determined from the temperature change calculated in equation [2] and based on the material parameters evaluated at the actual combined temperatures given by equation [3].
Each load case (l) uses its own
reference temperature )( reflT
specified in Global/Load and Freedom cases data to determine the combined temperature change using equation [2]. However, the reference temperature used in equation [3] to determine the combined temperature value is the smallest reference temperature of the included thermal load cases2:
( )reflNLCl
ref TTK,2,1
min=
= [4]
where NLC is the number of included
thermal load cases, and reflT is the
reference temperature for load case l.
Linear Transient Dynamic
In the solver dialog box, the user can specify a load case that contains nodal temperatures (Tmat) to be used to calculate temperature dependent material parameters. All material models are assumed to be linear and material parameter values will remain unchanged during the solution. The temperature distribution at t = 0 will be used to determine temperature dependent material parameters.
The combined temperature change at a time instance t, is calculated as:
( ) ∑=
−=∆NLC
l
reflll TtTtftT
1)()()( [5]
where fl represents the Factor vs. Time table assigned to load case l evaluated at time t.
Each load case (l) uses its own
reference temperature )( reflT
specified in Global/Load and Freedom cases data to determine the combined temperature change using equation [5].
Nonlinear Transient Dynamic Note the two options for defining the material temperatures: 1 - Transient Heat File or 2 - Load Case Data
1 - Transient Heat File: material parameters are determined based on the temperatures at any time t from the transient heat results.
2 - Load Case Data: The material temperature distribution at a time instance t is calculated by first determining the combined temperature change ∆T from all included load cases l using equation [5]. The current combined material temperatures Tcomb are then calculated from equation [3] and used to calculate temperature dependent material parameters.
1 - Transient Heat File: the temperatures used to determine the thermal loads1 at any time t are obtained directly from the transient heat results.
2 - Load Case Data: The temperature loading1 is determined from the combined temperature change calculated in equation [5] and based on the material parameters evaluated at the combined temperature values given by equation [3].
1 - Transient Heat File: the reference temperature is specified directly by the user.
2 - Load Case Data: Each load case (l) uses its own reference temperature
)( reflT specified in Global/Load and
Freedom cases data to determine the combined temperature change using equation [5]. However, the reference temperature used in equation [3] to determine the combined temperature value is the smallest reference temperature of included thermal load cases2 (i.e. determined using equation [4] ).
Table 4.1 – Details for the use of applied load case temperature data by the static and transient dynamic solvers.
1 – If the thermal strain ε calculation includes the effects of temperature dependence of the thermal expansion coefficient, the following integral is used dTTf )(0 ααε ∫= ,
where α0 is the nominal expansion coefficient and fα represents the Factor vs. Temperature table 2 – When the reference temperatures of different load cases are not the same, a warning message is written to the log file.
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Similarly, if an initial condition is used for a natural frequency analysis, the temperature dependence in the initial file (either from a linear or nonlinear static analysis) is effectively used. Otherwise (i.e. if an initial condition is not used), the temperature distribution in any load case may be selected to determine temperature dependent material parameters in the same way as the linear static solver.
While the harmonic response and spectral response solvers do not directly consider material temperature dependence these effects can be included via the results of a previous natural frequency analysis
Various material parameters required for the heat solvers (such as conductivity, convection coefficients and radiation coefficients) can also be temperature dependent - their treatment follows the description given in Section 2. In nonlinear steady heat analysis, the solver iterates on temperature, continually updating material parameters based on the temperature at the current iteration until convergence is achieved. For transient heat analysis, the material parameters are updated, according to the temperature distribution at the commencement of the time step based on the matrix update option selected in the solver dialog.
4. Discussion When planning a quasi-coupled thermal stress analysis in Strand7, it is important to remember that the mesh requirements for obtaining accurate stress results might
differ to those required for calculating the temperature distribution. In the heat solvers, temperature is the fundamental quantity that is calculated at the nodes. Therefore, depending on the nature of the problem, a relatively coarse mesh might suffice for determining an accurate temperature distribution. However, when undertaking the stress analysis, a much more refined mesh may be needed to properly determine the resulting thermal strain and stress fields.
Also, when performing a thermal stress analysis in Strand7 it is very important to be aware of how Strand7 uses different applied load case temperature data (see Section 2), setting the appropriate solver dialog box accordingly. As in any analysis, check the log file for any warnings before post-processing
The Strand7 API was released mid 2003 and received a
major update earlier this year with Strand7 Release 2.3 incorporating over 100 new API functions.
A relatively unknown feature of Strand7 is the ability to contour a model according to a user defined text file. The text file has to conform to a specific format that is described in detail in the Strand7 Online Help (for nodal contours the text file consists of simply a title followed by a list of node number – contour value pairs). Creating these text files for big models can be a repetitive and tedious task, a task perfectly suited for the Strand7 API.
With the power of the Strand7 API, user defined contour files can be created with ease. This article shows you how to produce your own user defined contour file.
Introduction A simple fatigue analysis will be carried out on a structural component undergoing cyclic loading. The material S-N curve is shown in Figure 5.1.
Figure 5.1 – Typical S-N Curve.
Two contour files will be produced – endurance stress and fatigue life – and contoured within the Strand7 graphical environment.
The Model The component is fixed at the base as shown in Figure 5.2. Two load cases, unequal in magnitude, representing the
Did you know? Ctrl-Click Retrieve
Have you ever found yourself wanting to assign a restraint to a node similar to an adjacent node, or perhaps assign a common value of normal pressure to a brick face?
Within Strand7 is a simple procedure that can retrieve this information, ready for it to be assigned elsewhere. Open the required attribute dialog and then ctrl-click the node or element. The dialog will be automatically filled out with all the attribute values of the clicked entity, which can then be applied to other elements. For example, open the node restraint dialog and ctrl-click a node with translational restraints. The node restraint dialog box will change to set the translational X, Y and Z boxes. This procedure can be used for all element attributes.
User Defined Contour Files
Ctrl-Click
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limits of the operating cycle are specified – a compressive load case and a tensile load case.
Figure 5.2 – The model with the tensile load case active.
Initial Processing A linear load case combination, to derive the principal stress range, is specified in Strand7 as shown in Figure 5.3.
Figure 5.3 – Linear Load Case Combinations dialog.
The two load cases are combined according to their fundamental stress components – that is, XX, YY, ZZ, XY, YZ and ZX – to create the combination load case. For this analysis, the principal stresses from the combination load case are used to predict fatigue life.
The Coding
The code used to calculate the endurance stress and fatigue life has been written with Microsoft Excel VBA XP. This VBA code is available for News.St7 readers to download and run on their own computer from our website www.strand7.com/News.st7.htm.
The pseudo code is:
- Initialise the Strand7 API. - Open the Strand7 model. - Run the Linear Static solver. - Open the Linear Static results and generate the
linear load case combination. - Extract the principal stresses and evaluate the
alternating stress at each node for each plate. Where Salternating = (σ11 - σ22) / 2
- Extract the principal stresses and evaluate the mean stress at each node for each plate. Where Smean = (σ11 + σ22) / 2
- Find the averaged alternating and mean stresses at each node.
- Use the ultimate material strength and the Goodman equation:
−
=
ultimate
mean
galternatinendurance
SS
SS
1
to evaluate the endurance stress at each node.
- Use the endurance stress and find the corresponding fatigue life at each node from the S-N curve.
- Export two Strand7 Node point contour text files: - endurance stress.txt - fatigue life.txt
Contour with User Defined Text Files The two exported text files can be used to contour the model within Strand7.
- Choose View/Entity Display - Under Contour Type select User Defined (file) as
shown in Figure 5.4.
Figure 5.4 – Entity Display.
- Select the endurance stress.txt file. Ensure that for Files of type, Plate Node Contour File (*.txt) is selected as shown in Figure 5.5. Click Open.
Figure 5.5 – Selecting endurance stress.txt file.
The model will now be contoured according to endurance stress as shown in Figure 5.6.
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Figure 5.6 – Endurance Stress contour.
Similarly, the fatigue life contour can be displayed as shown in Figure 5.7.
Figure 5.7 – Fatigue life contour.
Conclusion This article has shown that with the Strand7 API, users can create their own User Defined results, which can be subsequently contoured within Strand7
In this edition we will look at a benchmark problem
dealing with seismic analysis.
There are three common methods accepted by design codes around the world for performing seismic analysis of structural systems. These are:
● Equivalent Static Analysis
● Spectral Analysis
● Transient Dynamic Analysis
The equivalent static analysis is a straightforward method to evaluate horizontal force distributions in simple structures. This method has been common practice in the past and remains a good, quick tool for sizing members in a conceptual design. Spectral and transient dynamic analyses are more accurate methods of analysis and, these days, much more straightforward with the tools available in Strand7. Throughout this discussion we implicitly refer to clauses of AS1170.4 – 1993.
1. Equivalent Static For seismic analysis, the dynamic load due to the earthquake can be described as quasi-static and the structural response then can be determined by running a linear static analysis.
The implementation in Strand7 is a general one, which therefore makes it applicable to virtually any national design code (e.g. AS1170.4 – Australian Standard, Minimum design loads on Structures, Part 4: Earthquake loads).
An equivalent static analysis can be applied to buildings with the following attributes:
● Structural regularity (plan and elevation)
● First Natural Period smaller than 2.0 seconds.
Within Strand7 a seismic load case can be created and solved by entering the appropriate values from design codes.
2. Spectral This analysis is a more general approach and allows a much larger number of structural configurations to be dealt with. However, a few assumptions are still needed:
● Linear material and geometry
● Small structural damping
Did you know? Run Time Improvements
There are a few tips that you should keep in mind when trying to improve the run time of your Strand7 solve. Firstly store your temporary files locally, not across a network. Choose File/Preferences, to change the location of your temp directory. Also if it is a very large model try saving the results files to your local drive while solving, reducing the time taken to write across the network. However while all this will show some small performance improvements in solve time, for large improvements, the Sparse Solver should be top of the agenda.
Benchmark
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● Spectral results are based on a natural frequency analysis. These frequencies are linear and undamped.
3. Transient This analysis is the most realistic as it considers the structure subject to a time acceleration history. The previous hypothesis regarding linear behaviour and small damping are no longer required. You can also consider material and geometric nonlinearities. Since the model is solved at every time step the complete solution time can be an important consideration.
Benchmark Example The model (Figure 6.1) used is a simple concrete four-storey building. Its dimensions are 12m x 6m with a floor height of 3m.
Figure 6.1 – Four-storey building model.
An appropriate earthquake time history and response spectrum has been chosen such that the results given by
each method are directly comparable.
The reference acceleration time history chosen is a modified Athens Earthquake shown in Figure 6.2.
Figure 6.2 – Modified Athens earthquake history.
This acceleration time history can be converted to a response spectrum using Strand7’s inbuilt Convert to
Response Spectrum tool in the table dialog. An AS1170.4 response spectrum curve is also used for the comparison (an appropriate acceleration coefficient for Athens has been chosen as part of the factors, see Table 6.1, to allow for direct comparison between the two curves). These are given in Figure 6.3.
Figure 6.3 – Response Spectrum.
For this example the following parameters have been chosen from AS1170.4
Site Factor (S) 1.25
Importance Factor (I) 1.00
Acceleration Coefficient (a) 0.30
Structural Response Factor (Rf) 4.00
Table 6.1 – AS 1170.4 Factors.
The natural frequencies of the building are:
Mode 1: 0.659 Hz
Mode 2: 0.745 Hz
These first two natural frequencies are free of torsional effects and together they have a total mass participation greater than 90%. Hence in this case all three approaches can be applied.
Did you know? Strand7 Viewer
If you have clients that don’t have a copy of Strand7 and you want to be able to display your Strand7 model and results to them in their office the Strand7 Viewer can be used. You can download a free copy of the Strand7 Viewer from our website www.strand7.com. This allows you to interrogate a model file and results in the same way as you would in the full version of Strand7.
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Equivalent Static Analysis Create a new seismic load case in the Global/Load and Freedom Case dialog. The direction of the earthquake is in the X direction (horizontal).
The parameters required are based on the following:
GV β=
where,
V = base shear.
β = a factor, which may be related to the importance of the structure, the site factor, etc.
G = total gravity load = ag (MT).
where,
ag = the acceleration of gravity.
MT = ( )QM ψα + = the effective mass of the structure, which is a combination of the structural (M) and the non-structural (Q) masses.
α and ψ = non-dimensional combination factors, which are usually greater than zero and never negative.
And finally,
k = an exponent related to the period of the structure
h0 = the vertical coordinate of the base.
For more details on exactly how these factors are applied in an analysis see the Strand7 Online Help.
Spectral Analysis (Calculated Spectrum) Click Direction Vectors in the Spectral Response Solver dialog. Select the calculated response spectrum table. This table in is units of m/s2 and so a factor of 1 is applied in the X direction. Damping was included at 5% when the curve was created so damping should be set to None in the solver dialog.
Spectral Analysis (AS1170.4 Response Spectrum) For the Direction Vectors in the Spectral Solver dialog for this case select the AS1170.4 response spectrum curve. This curve is in units of g’s so the factor needs to include gravity. The code also requires the value to be factored according to the following:
fRIasmFactor ×= 2/81.9
Apply 5% Rayleigh Damping.
In this example a factor of 0.736 is assigned in the X direction.
Linear Transient Click Base Acceleration in the Linear Transient solver dialog and select the time history table that has already been created for the building. The table is in units of m/s2 so a factor of 1.0 should be applied in the X direction. 5% Rayleigh damping should be applied.
Results Figures 6.4 and 6.5 illustrate the results for the different approaches.
Figure 6.5 – Comparison of Max DX.
Figure 6.6 – Comparison of Bending Moment.
Conclusion
As the Calculated spectrum is derived directly from the time response graph we expect these results to be virtually identical to the linear transient results. This is shown in figures 6.5 and 6.6. The Australian Code spectrum includes design factors, i.e. site and importance factors, and will therefore give a more conservative result. The equivalent static analysis is more conservative again.
Exclusively to readers of News.St7: You can download this benchmark model from the News.St7 readers’ page of our website:www.strand7.com/news.st7.htm
We are pleased to announce the release of the Strand7
Theoretical Manual.
This manual will provide users with the theory beyond the Strand7 interface.
Already some supported users have discovered the benefits of this manual having been sent small sections as part of their support query.
Please contact us for more details on how to obtain a copy of this manual
Announcements - Theoretical Manual
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Training Training Calendar
In the last issue of News.st7 we discussed the availability of tailored
training courses. Following on from this we have recently completed a very successful training course in South Africa. For a week in early September a number of engineers from a variety of fields took part in an intensive Strand7 course, ranging from introductory lessons to the more advanced nonlinear and dynamics fields. Thanks to course organiser (and Strand7 distributor in South Africa) Allyson Lawless and Hatch South Africa for providing the training venue. To find out the thoughts of the course attendees, visit www.strand7.com/SATraining.htm.
If you are interested in tailored onsite training courses then please contact us for more information.
In October we are running our full series of courses ranging from Introductory through to Structural Analysis held in our offices in Sydney. These are the final courses for this year. But our calendar for next year’s courses will be released soon.
You can find full details of the content of the courses, prices and booking form at: www.strand7.com/training.htm
Recently Strand7 exhibited at the China International Steel
Construction Expo/Conference with great success. We were delighted with the opportunity to meet all those who attended. We plan to exhibit at the following upcoming conferences:
15-17 December 2004
2004 FHWA Steel Bridge Conference
San Antonio, Texas, USA
10-12 January 2005
Pacific Design and Manufacturing Show
Anaheim, California, USA
If you get the chance then we would be delighted to meet you and discuss Strand7 with you. You will have the opportunity to meet representatives from Strand7 and from our US distributor.
We will be keeping you updated on the latest developments in future editions of News.St7
Strand7 Head Office G+D Computing Pty Ltd Suite 1, Level 7 541 Kent Street Sydney NSW 2000 AUSTRALIA
Tel +61 2 9264 2977 Fax +61 2 9264 2066 Website: www.strand7.com Email: [email protected]
Strand7 User Profile Peter Seid APS Plastics Pty Ltd
Q - How would you describe your business? Plastics Designers and Engineers.
Q - What types of jobs do you use Strand7 for? Anything plastic basically. This includes new inventions and concepts in the industrial and automotive industries, consumer goods, medical devices, etc. Recent projects have included theatre seats, car grills, a pull-along cooler and syringe.
Q - How does Strand7 help you in what you design and analyse? It helps to identify a new product’s weaknesses and enables us to iterate to a satisfactory design.
Q - What features of Strand7 do you find most useful? The automesher has reduced modelling time as well as the sparse solver. The animation of results with amplified deflections also helps visualise behaviour. Also ranging the stress levels helps to identify “hot-spots” above the materials yield limit leading to mesh refinement or redesigning. Contact Details Unit 41/756 Burwood Highway Ferntree Gully 3156 VIC Australia 03 9752 2144 www.apsplastics.com.au [email protected]
Exhibitions
200412-15 October Introducing Strand7 19-20 October Nonlinear Analysis 21-22 October Dynamic Analysis 26-27 October Structural Engineering 28 October Automeshing with Strand7 29 October Heat Transfer Analysis
