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 51.2 MB |
ST7-R3.10.20.2 Harmonic Response Analysis This Webnote introduces the Natural Frequency and Harmonic Response solvers together with some basic concepts in modal analysis. This is done with reference to a simple cantilever beam model, which is harmonically excited at its free end. Ways of introducing damping to the system in Strand7 are then demonstrated, and a comparison is made with a full system transient solution, highlighting the benefits of the modal approach for this type of problem. |
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ST7-R3.20.10.1 Nonlinear Elastic and Inelastic Buckling of a Column This Webnote covers the following topics:
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ST7-R3.20.10.2 Nonlinear Analysis Basics This Webnote presents an overview of some of the basic concepts of nonlinear analysis, including iteration, load increments (or load steps), convergence and residual forces. Most nonlinear problems are solved by an iterative numerical procedure that needs to converge before the results can be accepted. Not all nonlinear problems are guaranteed to converge. However, convergence can often be improved by adjusting some of the solver parameters, depending on the model, the loads, and so on. Non-convergence can occur when attempting to solve for a physically impossible situation, or when the nonlinear solution algorithm is not sufficiently robust to solve a difficult nonlinear problem. |
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ST7-R3.20.10.3 Defining Nonlinear Static Load Increments Load in the Nonlinear Static solver is applied by defining a load increment (or load step) table. This table comprises one or more increments - these are the columns in the table. Each increment defines the total load to be applied by assigning factors to the load and freedom cases in the model - these are the rows in the table. Effectively, each increment defines a combination of load and restraint (or enforced displacement) to be applied at that step. |
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0.9 MB |
ST7-R3.20.10.4 Determining the Onset of Buckling in a Nonlinear Static Analysis Nonlinear buckling analysis involves not only identification of the point at which buckling (structural instability) may be regarded as having occurred, but also the structural behaviour leading up to the instability, and often the structural behaviour beyond the instability. In contrast to linear buckling analysis, the result is not output explicitly as a buckling load factor. Instead, the structural response needs to be interpreted, typically by inspecting a graph of applied load vs displacement or other quantity. |
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ST7-R3.20.10.9 The Nonlinear Convergence Graph This Webnote examines the nonlinear convergence graph available in the nonlinear solver window and nonlinear solver log file viewer. The graph is the visual representation of the solver convergence history, and is produced by all of the nonlinear solvers. |
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2.9 MB |
ST7-R3.40.35.3 Analysing Membrane Structures Membrane or tension structures are commonly used around the world for a variety of different applications. These typically include shading structures, tents, tarpaulins, marquees, and various other large scale architectural structures such as the Tokyo dome. These structures are highly nonlinear and rely on an internal state of pre-stress to work. |
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ST7-R3.50.20.14 Using the Nodes and Beams by Line Tool to Build Models This Webnote examines node and beam element creation using the Nodes and Beams by Line tools. Tools are available for creating nodes and beam elements on geometries such as parabolas and circular arcs, as well as on features like fillets and tangent lines. There are also tools to create construction features based on existing entities, such as finding the centre of a circular arc and extending existing lines. These tools are useful for both manual and automeshing approaches. |
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ST7-R3.50.20.4 Meshing a Pipe Elbow and Flange This Webnote outlines a procedure for creating a pipe with a 90° elbow using plate elements. This procedure could be adapted to model an elbow of any angle. It could also be adapted for use with beam or brick elements. |
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ST7-R3.50.80.16 Removing Small-Area Plates using the TEXT Tab This Webnote illustrates a method for detecting and removing plate elements with very small area. This is also applicable to brick elements with very small volume, and to beam elements with very small length. The small area elements can be a by-product of automeshing, such as when the geometry contains very small faces, or Surface Automesh parameters that are unable to accommodate the meshing of elements over small geometric features. Small elements can also be created inadvertently through manual meshing operations with tools such as Move to Absolute or Cut Elements. If these elements are too small, they can have an impact on the local stress field due to numerical round-off or ill-conditioning. Therefore, they should be removed from the mesh prior to analysis and the mesh repaired accordingly. |
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ST7-R3.57.30.14 Follower Loads for Linear Buckling and Natural Frequency Solvers Pressure loads on a surface “follow” the surface as it deforms; i.e., the direction of the resultant of the pressure follows the changing direction of the surface normal. This follower effect can lead to a reduction in buckling load and can modify natural frequencies. The linear buckling and natural frequency solvers, using the elastic and the stress stiffness matrices, do not capture this effect, and therefore the Nonlinear Static and/or Nonlinear Transient Dynamic solvers, with geometric nonlinearity, are usually required. Alternatively, the follower load option, available in the Strand7 Linear Buckling and Natural Frequency solvers, can be used to add a “load stiffness” term that depends on the geometry change to account for the follower effect. |
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0.9 MB |
ST7-1.20.10.5 Nonlinear Static Convergence A structural system can be considered nonlinear if the response is not linearly proportional to load. In reality, most systems are nonlinear, but can be considered linear within a reasonable load range. There are cases where the applied load may cause nonlinear effects. These include: Material nonlinearity (e.g. yielding, changing stiffness, creep). Geometric nonlinearity (e.g. buckling, membrane redistribution, mechanism behaviour). Boundary nonlinearity (e.g. contact, compression-only... |
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ST7-1.20.10.8 Troubleshooting Nonlinear Static Models Solutions to nonlinear FEA problems are approximate due to the iterative nature of the algorithms used to solve the problems. Before proceeding, review ST7-1.10.10.3 General Model Troubleshooting to ensure that the model is basically sound. In this example, a fictitious welded assembly, which is between two confining walls, is forced downwards by an eccentric load until lateral buckling occurs and contact is formed between the buckled member and the adjacent walls. The base of the buckling... |
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ST7-1.20.20.3 Frame Dynamic Yielding and Static Pushover A steel frame is subject to an earthquake load and also tested for pushover limits. The frame is composed of 200x200x10 mm I-beams. The coordinates of the frame (in metres) on the XY plane are shown at right. A translational mass of 2000 kg is placed at each node of the frame to represent supported mass. The two nodes at the base are fixed. The freedom case type is set as 2D Beam. The major units used in the model are: To define the nonlinear material behaviour of the beam (yielding)... |
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ST7-1.20.20.4 Transient Dynamic Analysis Time Stepping Transient analysis is analysis through time. There are four transient solvers in Strand7: Linear Transient Dynamic Nonlinear Transient Dynamic Quasi Static Transient Heat This document outlines how to determine an appropriate time step for solution accuracy for the linear and nonlinear transient dynamic solvers. The other two solvers have different requirements but are generally not as sensitive to time stepping as the dynamic solvers, which must consider structural vibration. ... |
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ST7-1.20.20.5 Modelling a Simple Double Pendulum Strand7 can model kinematic motion with the Nonlinear Transient Dynamic solver. This Webnote covers the modelling of a simple double pendulum, which can be extended to modelling more complex mechanisms. For this example, an arbitrary double pendulum is constructed. It is arranged to promote the chaotic behaviour inherent to this type of pendulum. Coordinates are indicated at right. Create a new model with Nmm units. Create three nodes with the coordinates at right using Create/Node. ... |
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ST7-1.20.20.9 Using Static Initial Conditions in Dynamic Analysis Static solutions can be used as initial conditions in dynamic analyses to model systems which are pre-loaded but initially at rest; this considers the effect of an initial state of displacement and/or stress on the dynamic response. We will analyse a simple cantilever beam which sags due to self-weight (nonlinear static solution) and is then suddenly loaded to produce a dynamic response (nonlinear transient dynamic solution). We will first set up the dynamic model without static initial conditions... |
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ST7-1.20.40.10 Modelling Nonlinear Concrete with Nonlinear Elastic Material This Webnote outlines the application of the Max Stress yield criterion for modelling nonlinear elastic concrete material. This modelling approach allows us to consider the concrete's different behaviour in compression and tension. |
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ST7-1.20.40.16 Basic Material Nonlinear Analysis This Webnote gives a brief summary of material nonlinear analysis and showcases a simple example. To start a material nonlinear analysis, a stress-strain curve is usually required. A typical stress-strain curve for low and medium carbon steels is shown below, with part of the curve exaggerated for clarity. For stresses up to the proportional limit, stress will be linearly proportional to the strain according to figure 1. If the stress exceeds the proportional limit then material nonlinear... |
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ST7-1.20.40.17 Material Nonlinearity and Yield Criteria Strand7 supports various linear, nonlinear and specialised material models suitable for modelling a range of different physical materials such as ductile metals, brittle concrete and soils. ... |
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ST7-1.20.40.2 Developing a Rubber Material Model Upon successful completion of this lesson you will be able to: Develop rubber material parameters from test data. Model nonlinear elastic rubber material in real world settings. Rubber material exhibits nonlinear stress-strain behaviour. Unlike metals, this material nonlinearity does not produce permanent strain after unloading, meaning that the behaviour is elastic in nature. Additionally, rubber exhibits near incompressibility, with Poissons ratio approaching 0.5. Strand7 provides a... |
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ST7-1.20.40.3 Plastic Beam Residual Stress The Strand7 nonlinear material beam element uses either a moment-curvature table and axial stress-strain curve (R23x and prior) or a stress-strain curve only (R241 and later). To compare equivalent beam and shell models you must choose some analogous quantities. For stress, the beam fibre stress is analogous to the plate stress in the axial direction. The two cantilevered pipes are pushed past yield and subsequently relaxed to observe the resulting residual stress. The extrapolated nodal... |
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ST7-1.20.40.5 Nonlinear Stress vs Strain Curves for Beam Elements The Strand7 beam element is the most flexible element in terms of the nonlinear material behaviour it supports. Similarly to the plate and brick elements, the beam element supports both nonlinear elastic and elastic-plastic material behaviour. Unlike the plate and brick elements, the beam element also supports elastic-plastic behaviour that is different in tension and compression (plates and bricks support different tensile/compressive behaviour only for nonlinear elastic materials). This Webnote summarises the usage of Stress vs Strain tables for beam elements. |
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ST7-1.20.40.6 Setting Up a Soil Analysis Strand7 is capable of performing common geotechnical analysis with five soil model types. Due to the nonlinear stress-strain response of the soil, the analysis generally utilises a Strand7 solver that is capable of performing Material Nonlinearity analysis (e.g. Nonlinear Static). The types of analysis that can be handled by Strand7 soil elements include Earth pressure , Short-term consolidation, Lateral earth pressure, Construction sequences . |
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ST7-1.20.50.2 Nonlinear vs Linear Buckling Analysis This Webnote examines the critical buckling load for four typical column configurations. Results from linear buckling analyses are compared with hand calculations using the familiar Euler equation in conjunction with effective length constants, which may be obtained from any text on elastic stability. Results from linear buckling analysis are then compared with those from a nonlinear buckling analysis. ... |
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ST7-1.20.50.3 Modelling a Snap-Through Buckle Buckling and post-buckling prediction is one useful applications of finite element analysis. A nonlinear buckling analysis can give a good indication of the structural response near the onset of buckling, and post-buckling if the solution can be made sufficiently stable. Snap-through buckling is one situation that exhibits stable post-buckling behaviour. This Webnote examines the prediction of snap-through buckling using Strand7. ST7-1.20.10.1 Nonlinear Elastic and Inelastic Buckling of a... |
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ST7-1.30.10.1 Nonlinear Weld Thermal Analysis Welding presents a great challenge for everyone involved, from the designer to the analyst to the manufacturer. This is because welds encompass a wide variety of nonlinear behaviours including melting, differential hardening, radiative heat transfer and large amounts of shrinkage after cooling. In this case we consider a short segment of steel web being welded to a flange. It is welded on both sides simultaneously in an attempt to avoid differential shrinkage deformation in the web. The general... |
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ST7-1.30.20.1 Nonlinear Weld Mechanical Analysis A quasi static nonlinear mechanical weld analysis is performed using thermal results and nonlinear Factor vs Temperature tables to calculate the mechanical response of a welded beam flange. This topic refers to the thermal results found in Webnote ST7-1.30.10.1 Nonlinear Weld Thermal Analysis. In this case we consider a short segment of steel web being welded to a flange. It is welded on both sides simultaneously in an attempt to avoid differential shrinkage deformation in the web. ... |
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ST7-1.30.20.3 Nonlinear Thermal Expansion Strand7 allows for the continuous variation of coefficient of thermal expansion with respect to changing temperature. The variability of the coefficient can be expressed in various ways, including thermal strain vs temperature, as the average coefficient over a range of temperatures, or as an instantaneous coefficient which must be integrated to get the total thermal strain. This Webnote outlines how to use Strand7 to model nonlinear variations of thermal expansion coefficient with respect to temperature. |
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ST7-1.40.20.2 Underwater Cable - Catenary and Forces Strand7 is equipped with cable elements which can be used to determine the catenary shape due to gravity, distributed loads and concentrated loads. This document shows an example of cable elements used to solve an underwater cable system. A 1000 m underwater cable consisting of metal chains and wire rope is shown below. Create a new SI unit model. Create a beam element joining nodes at (0,0,0) and (500,500,0). Use Tools/Split Beams with a 0.3 Split Ratio to divide the beam into two elements. ... |
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ST7-1.40.30.3 Lateral Earth Pressure and Retaining Walls Lateral earth pressure is one of the most important factors to be considered when designing retaining walls, or indeed, for designing any structure that interacts with soil. This Webnote demonstrates the application of Strand7 in the calculation of lateral earth pressure and analysis of retaining walls by using the nonlinear static solver. |
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ST7-1.40.30.4 Cable Systems Strand7 has the ability to model cable-pulley systems and catenary cables under gravity and applied loads. An example of a simplified elevated ski lift structure is demonstrated here. Create a new file and set the units to Nmm. Create a few vertical beams representing the cable support columns using Create/Element and Snap Grid or by entering node locations with Create/Node. Connect them with beam elements representing the cables. In the model shown at right, beam taper attributes... |
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ST7-1.40.35.13 Analysis of Blast Resistant Structures The design of blast resistant structure in hostile environments has previously been limited to nonlinear single degree of freedom (SDOF) approximations, which limits the analysis to point-wise design checking of individual members. This Webnote will draw on the experience of blast loading developed in UFC 3-340-02[1] and apply it to a nonlinear transient blast analysis using Strand7. The example problem, Example 2A-10 found in [1], is replicated using FEA. The resulting acceleration, velocity... |
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ST7-1.40.35.14 Modelling Nonlinear Behaviour of Steel Reinforced Concrete Steel reinforced concrete beams and columns are composite structures consisting of two very different materials. Steel has high stiffness and yield in both tension and compression whereas concrete has little strength in tension (cracks under tension). These different nonlinear material behaviours can be captured using different material models and stress-strain curves in Strand7. In the modelling sense, steel reinforced concrete beams and columns can be modelled in a variety of ways including: ... |
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ST7-1.40.35.15 Extracting Shear Wall Design Action Effects This Webnote describes a simple method for extracting the design action effects to be used for the design of shear walls. In order to provide a thorough explanation of the method, four models will be discussed: Consider the shear wall subjected to three lateral point loads shown opposite. The wall is fixed at the base, and grouped into three levels, each 4m in height. The wall is idealised as a cantilever beam and the shear forces and bending moments are calculated as shown on the following... |
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ST7-1.40.35.27 Tapered Circular Steel Towers Tapered steel towers are common due to simplicity and low cost. These towers are sometimes faceted, but often circular in cross-section. This Webnote covers the basic modelling of a tapered circular tower, comparing a plate mesh with a tapered beam element approach. The structure is a simple tower which tapers from 2 m diameter at the bottom to 1 m diameter at the top. Thickness is a constant 10 mm. The model geometry is most easily generated by drawing the axisymmetric cross-section... |
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ST7-1.40.35.36 Cable Net Analysis This Webnote describes a simple analysis of a 3D cable structure in Strand7 using the Nonlinear Static and Nonlinear Transient Dynamic solvers. All flexible members such as cables and wires in this type of structure can be modelled as Truss elements. These are axial force elements and do not provide lateral stiffness unless there is some tensile force in them. Therefore a pre-load attribute is usually applied to provide some lateral stiffness and assist solver convergence. Given the inherent... |
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ST7-1.40.35.48 Precast Slab Lifting Analysis with String Groups Precast slabs or walls are often lifted into place by crane and straps. In this analysis we model the lifting situation in which there are three pulleys arranged in a load-sharing scheme similar to a whiffle tree. Three independent cables support the panel, each with a pulley at the top. The model is a simple 2D beam model, although more complex 3D scenarios could also be modelled. The goal of this Webnote is to show how string groups work to model pulleys, and to evaluate the proposed lifting... |
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ST7-1.40.35.49 Modelling Bond Slip in Reinforced Concrete Tensile stress is generated in steel reinforcing bars via shear stress at the interface between the concrete and reinforcement. This shear stress is referred to as bond stress. If the bond stress exceeds the local shear capacity at the interface, the bar may slip relative to the concrete. This Webnote examines the implementation of a nonlinear bond stress vs slip relationship in Strand7. |
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ST7-1.40.35.5 Reinforced Concrete Slab Ductility Several methods to model reinforced concrete are discussed and compared using a typical 200 mm thick slab. The most detailed approach is to model the concrete with layers of brick elements and the reinforcing bars as beam elements embedded within. Other options include replacing the reinforcing beam elements with a smeared layer of plate mesh with equivalent cross-section area and/or replacing the concrete brick mesh with an equivalent plate mesh. |
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ST7-1.40.35.6 Modelling Post Tensioned Concrete in Strand7 Given that Strand7 is a general purpose FEA package rather than a specialised prestressed concrete (PSC) design package, users may not be aware of the potential for Strand7 to analyse PSC structures. This document outlines one method for modelling a post-tensioned one-way slab (150mm thick) and transverse band beams (400mm deep) with discrete draped bonded tendons. In addition to self-weight and prestress, the slab will be subjected to a 1 kPa superimposed dead load and a 7.5 kPa live load. ... |
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ST7-1.40.35.8 Modelling Tension-Only or Compression-Only Structural Members Many structural members and connections have different tensile and compressive behaviour. Typical structural features which are compression-only include contact and bearing situations, whilst tension-only members often include bolts, bracing, cables, ropes or chains. Nonlinear analysis is generally required to consider such members, as it is often not known beforehand which members will be in tension and which members will be in compression, particularly in complex structures. |
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ST7-1.40.70.1 Vehicle Suspension Static Stiffness An automotive suspension model is introduced and used to determine the static stiffness of the system as it responds to various operational loads. The nonlinear static solver is used to characterise the static response of the vehicle. The dynamic response of the vehicle is discussed in ST7-1.40.70.2 Vehicle Suspension Dynamic Stiffness. The provided initial model (ST7-1.40.70.1 Car Body and Suspension (0. Initial).st7) is a basic model of a car. The suspension is independent double-wishbone... |
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ST7-1.40.70.11 Analysis of a Rubber Exhaust Hanger and Grommet Exhaust systems are prone to vibration and are typically isolated from supporting structure by compliant rubberised components. Detailed models of these components are not practical in larger analyses, so it is important to estimate the stiffness to be modelled using simplified methods, such as beam elements or nodal stiffness attributes. In this analysis we investigate the stiffness of two common rubber isolator components for use in a larger model found in ST7-1.40.70.8 Tuning an Exhaust System... |
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ST7-1.40.70.22 Guard Rail Impact Analysis Guard rails must be designed to withstand impact from vehicles travelling at high speed. In this Webnote we explore modelling methods that can be used to simulate an impacting mass (820 kg) with initial velocity (100 kph) as it strikes a typical W-section guard rail at 20 degrees from parallel. A simple beam model is constructed. |
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ST7-1.40.70.23 Plate Mesh Approach to Guard Rail Impact This Webnote is a continuation of ST7-1.40.70.22 Guard Rail Impact Analysis, in which a guard rail model using beam elements was impacted. In this analysis, we convert a portion of the guard rail into plate elements in order to consider crushing of the W-beam cross-section. The Head Injury Criterion (HIC) is calculated using the acceleration time history of the impactor. As in the previous analysis, an 820 kg mass travelling at 100 kph impacts the rail at 20 degrees. |
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ST7-1.40.80.2 Meshing a Loader Bin with Reinforcing Ribs The basic surface geometry of the bin is shown at right and below. It is a tessellated welded assembly with reinforcing ribs which have not been explicitly modelled in CAD. This Webnote outlines how to add rib reinforcement features to a Strand7 model without returning to CAD, by using beam elements along lines of intended reinforcement. The geometry above is missing some definition of hoop ribs as well as ribs which run along the seams of the tesselated surfaces. Create a new model with... |
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ST7-1.50.20.12 Interfacing Different Element Types This Webnote examines the modelling considerations required to connect different element types - beams, plates, and bricks. In a mesh connecting different element types, simple element-to-element connection at the node may not transfer all load components correctly. Additional interface entities can be introduced to ensure compatibility of all degrees of freedom at the interface. |
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ST7-1.50.30.1 Wind Loads on Shell Elements Wind loads are often expressed in terms of force per unit length, and often vary with respect to height. It is quite easy to apply this sort of loading to a beam element using a distributed force, but applying equivalent wind loading to a shell element mesh takes some additional consideration. This document outlines how to apply an equivalent varying wind load to both beam and shell elements. A 1.5 m diameter tower is considered. Given a wind load of 30 kgf/m at a height of 4 m, and 100 kgf/m... |
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ST7-1.50.30.6 Using Normal Pressure to Fold a Box The plate normal pressure attribute updates the direction of applied load as the structure deforms in a geometric nonlinear analysis. This means it can be used to apply load which causes structure to fold or wrap around other structure. In this Webnote we examine the folding of a box from a flat creased aluminium plate. The load is then released and the spring-back effect is measured. The starting planform shape of the box is shown at right. The model needs to have contact elements defined... |
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ST7-1.50.40.4 Defining Contact Interfaces Contact between multiple bodies in Strand7 is achieved using contact elements, which are a type of beam element. Whenever possible, it is best to use node to node contact, which is simply a contact beam element connecting two nodes. This is generally done in situations where there is a regular mesh, or the mesh on either side of the gap is the same, facilitating extrusion of contact beam elements between them. In the model shown at right, contact has been defined between the nodes on the two... |
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ST7-1.50.40.5 Determining Appropriate Contact Stiffness Contact is modelled in Strand7 using a special type of beam element. These beam elements react load nonlinearly, and in proportion to axial compression. The stiffness of these contact elements can affect the solution results accuracy and convergence. There are many physical situations that may be modelled with various configurations of contact elements. This Webnote aims to provide a guideline of what the axial stiffness value should be. Refer to ST7-1.57.20.8 Contact Element Fundamental... |
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ST7-1.50.40.8 Sliding Contact This Webnote introduces a technique that can be used to model sliding contact with pre-strained cutoff bar elements. Examples including pedestrian step loading, sliding of an interference fit, and reeling of a cable onto a spool are presented. We will use the following example to introduce the idea: A person of mass of 70 kg walks across a simply-supported steel beam 8 m long with 1000x100x10 mm rectangular hollow section. Create a new model and choose Nmm as the unit system. Create... |
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ST7-1.50.50.18 Beam Element Orientation This Webnote discusses how beam elements are orientated in Strand7, together with methods for changing the orientation. The orientation of both Beam2 and Beam3 elements is presented. By default, Strand7 beam elements are aligned according to the principal axes of the cross section. Principal axes for an I-section, as shown in the Geometry tab of the Beam Property dialog, are illustrated at right. The orientation of the Beam2 element is fully specified by the definition of two non-coincident... |
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ST7-1.50.50.2 Beam End Releases Beam end releases are provided as a beam element attribute in Strand7. These attributes can be applied to one or both ends of a beam element. Both translations and rotations can be independently released to model a variety of joint configurations. Where no end release is applied, two beam elements that share a node are modelled as being welded together. Using end release attributes, ends of beam elements can be fixed (no end release), partially released (where a connection stiffness is specified),... |
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ST7-1.50.50.3 Tapered Beams It is common to use beams which are tapered in engineering structures. One approach for modelling a continuous tapered beam is to use a sequence of untapered beam elements of varying size as shown below. This modelling approach could take considerable time for models with many tapered beams, as the accuracy of the solution may require many stepped beams. However, to reduce modelling time and solution time, and to improve accuracy, the beam Taper attribute may be applied to beam elements.... |
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ST7-1.50.50.4 Modelling with Cables This Webnote examines different modelling approaches for cables and slender members with only axial capacity. The modelling consideration of tension-only capacity is also examined. Such cables and slender members can be modelled using Cable, Truss and Cutoff Bar type Beam elements in Strand7. |
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ST7-1.50.50.6 Using String Groups The Beam String Group attribute is used to model a continuous chain of truss type beam elements sliding through frictionless connections at nodes. The attribute ensures that a constant axial force develops in all the elements in the same string group. A common application of the attribute is to model massless cables (or strings) such as pulley systems, lifting sling cables, and pre-stressed steel tendons in reinforced concrete. This Webnote examines the Beam String Group attribute and its modelling applications. |
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ST7-1.50.70.1 Beam End Release and Node Displacement in GNL Analysis This Webnote describes the relationship between the beam end release results and nodal displacement for linear and geometric nonlinear (GNL) solution cases. The focus here is on the rotational end release attribute, but the discussion is also applicable to the translational end release attribute. The default joint condition for a beam element in Strand7 is that of a welded joint. Strand7 has two Beam End Release attributes: one is the translational end release and the other is the rotational... |
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ST7-1.50.70.12 Modelling Supporting Structure with Support Attributes Support attributes can be used to represent supporting structure which is not of interest aside from the stiffness contribution. Take for example a plate of glass resting on a rubber pad supported by a beam. Instead of modelling the beams with contact beneath the glass, a plate support attribute can be applied with an equivalent stiffness. This simplifies modelling and also allows the contouring of bearing stresses at the support points. A cross-section of a patch fitting holding two panes... |
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ST7-1.50.70.2 Beam Bending and Nodal Rotational Stiffness This Webnote illustrates the changing bending moment at the ends of beams subjected to uniformly distributed loads due to the effect of nodal restraints and joint connections. Consider a beam subjected to a uniformly distributed load as shown in the illustration. If the ends of the beam are pinned (nodes assigned zero rotational stiffness) then the bending moment at these ends is zero. If the ends of the beam are fully fixed (nodes assigned infinite rotational stiffness) then the bending... |
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ST7-1.50.70.5 Contouring Nodal Attributes Strand7 allows the automatic contouring of element attributes, but not nodal attributes. However, there is a way to contour nodal attribute values on elements by using the Online Editor, Excel and a user defined nodal contour file. A complex nodal loading is applied to the nodes of some plate elements shown at right for the purpose of demonstrating nodal attribute contours. This method applies to any other nodal attribute, and also to brick or beam elements. The following general procedure... |
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ST7-1.50.80.17 Aligning Beam Elements This Webnote examines the beam alignment tools. The beam axis system is used to define section properties, beam attributes, and beam result quantities such as force, moment, stress and strain results. The alignment of beams in a certain direction or in a consistent manner is a common modelling requirement. Strand7 provides several tools for changing the orientation of beam elements and alignment of their cross section. |
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ST7-1.55.10.1 Analytical Clutch Torque Capability Verification An automotive plate clutch is designed to slip at 400 Nm of transmitted torque. Each of the two sides of the clutch plate contributes to the transfer of torque from the engine to the transmission. The clutch plate is shown schematically at right. The plates are pressed between the flywheel and clutch spring with an axial force . The results of a Strand7 displacement controlled nonlinear static analysis are compared to the analytical solution for the critical slip torque. Given the clutch... |
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ST7-1.55.10.3 Large Displacement of a Flat Plate Strand7 offers a geometric nonlinear solver, capable of analysing structures that undergo large displacements. In this benchmark, a square plate, clamped at all four edges, is loaded by a uniform normal pressure. The nonlinear displacement and stress response is compared with a published analytical solution. The reference solution is given in National Advisory Committee for Aeronautics (NACA) Technical Note No. 847, Square Plate with Clamped Edges Under Normal Pressure Producing Large Deflections... |
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3.4 MB |
ST7-1.55.30.5 Evolution of Beam Temperature using ISO834 Fire Curve In this Webnote, the evolution of steel temperature over time is analysed based on the ISO834 fire curve, i.e. the Gas Temperature vs Time relationship as per Eurocode 3 Part 1-2. An IPE500 steel section is used for such analysis over a period of an hour and its results compared against analytical results from Eurocode 3. The temperature dependent material properties are considered. |
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0.5 MB |
ST7-1.57.10.2 Brick Element Material and Geometric Nonlinearity The stress values reported at the Gauss points in material nonlinear brick elements can exceed the corresponding values on the stress-strain curve when geometric nonlinearity is included in the analysis, even for a fully converged increment. This Webnote uses the simple example of a cylindrical bar subjected to a uniaxial load to describe the reasons for this. ... |
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0.9 MB |
ST7-1.57.10.3 Nonlinear Elastic Material Both elastoplastic and nonlinear elastic material models use stress-strain tables to define the nonlinear relationship between stress and strain in the material. However, the two material models interpret the stress-strain tables differently. The most significant difference, at least for uniaxial situations, is in the loading-unloading behaviour of the two models. |
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0.8 MB |
ST7-1.57.10.5 Elastic and Plastic Strain This Webnote gives an overview of elastic and plastic strain as reported in the Strand7 plate and brick elements for material nonlinear analysis. An elasto-plastic material with the von Mises yield criterion and isotropic hardening is used to illustrate these quantities. |
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1.2 MB |
ST7-1.57.20.12 Beam and Shell Offsets Offset attributes are a convenient way of incorporating eccentricities into a model without modifying the connectivity of the mesh. This Webnote explains how Strand7 implements offsets for beam and plate elements; comparisons are made between models with offsets and equivalent models using rigid links. The Webnote also shows how displacements in offset elements are calculated from the nodal results. The information presented applies to Strand7 Release 2.4.5 and later. Consider a node on the... |
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0.7 MB |
ST7-1.57.20.14 Connection Type Beam Element Behaviour The information in this Webnote relates to Strand7 Release 2.4.5 and later. Connection elements in Strand7 can be thought of as flexible links. This Webnote focuses only on mechanical analysis. For mechanical analysis, connection elements are defined by up to six independent stiffness values, three translational and three rotational. Unlike the beam element, there is no coupling between different degrees of freedom. The three directions 1, 2 and 3 shown on the property dialog for the connection... |
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1.7 MB |
ST7-1.57.20.15 BXS Beam Elements This Webnote examines the user-defined beam section, or BXS section, in Strand7. This functionality gives the user the ability to create detailed beam cross section shapes to include features that are not available when using the standard section shapes, such as ribs, fillets, voids, and multi-part sections of different shape and orientation. In addition to standard section shapes, Strand7 allows the assignment of a customised section (or BXS) defined by the user using a 2D plate mesh representing... |
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0.6 MB |
ST7-1.57.20.16 Comparison of the Moment Curvature and Fibre Stress Beam Nonlinear material behaviour in beams can be modelled in Strand7 using a table defining the beam's moment-curvature behaviour or a table defining the material stress-strain behaviour. These methods are illustrated and compared in this Webnote by way of examples. |
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0.6 MB |
ST7-1.57.20.17 Curved Pipe Element Stress When a beam is curved, the neutral axis shifts in towards the centre of curvature. This results in higher stress on the inner edge of the curved beam. Strand7 has a curved beam element that considers this effect, which is the pipe element with a Pipe Radius attribute applied (Attributes/Beam/Pipe/Radius). The magnitude of the shift away from the neutral axis is generally calculated from elasticity theory. |
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5.1 MB |
ST7-1.57.20.2 User Defined Beam Matrix Strand7 allows for the definition of a user defined beam element (UDB) to be used to represent a component in place of modelling the component itself. In some cases the stiffness of the component will be available from manufacturers data or in others from a detailed finite element model. This document will briefly discuss the theory behind the UDB and also give examples on how to determine what stiffness values should be used. This Webnote should be accompanied by the following models: ... |
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0.3 MB |
ST7-1.57.20.5 Virtual Overlap Virtual overlap refers to the non-physical overlap of two or more plate/shell or beam elements at a joining node. The following figure demonstrates the concept as pertaining to plate elements. The primary effect of virtual overlap is to increase the mass of the structure. This can introduce error into self-weight calculations and dynamics (natural frequencies, inertia relief analysis and transient dynamic analysis). Virtual overlap in plate elements is typically ignored, because plates... |
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0.9 MB |
ST7-1.57.20.8 Contact Element Fundamental Behaviour Contact between two bodies can be defined in Strand7 using connecting beam elements which have been assigned a Point Contact beam property. This Webnote covers the fundamental behaviour of all contact types and options. An overview of contact types and parameters is given first. Contact element behaviour is independent of the elements to which they are attached. Contact elements can be placed between any combination of element types, but must be attached to nodes or by attachment links to... |
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0.6 MB |
ST7-1.57.20.9 Beam Displacement Behaviour due to Shear Centre Offsets The Strand7 beam element captures advanced beam deflection and stiffness behaviour including influences from shear centre offsets, beam offsets and beam end releases. A non-zero shear centre offset means that a lateral force will produce an axial (torsional) rotation in the beam. Shear centre offsets are the theoretical centre of rotation of rotations induced by a lateral force. Shear centre offsets are automatically calculated by Strand7 when a beam cross section is referenced. If the shear... |
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0.7 MB |
ST7-1.57.40.1 Calculation of von Mises Stress in Circular Beam Elements This Webnote demonstrates the calculation of von Mises stress in beam elements with circular cross-section. Currently Strand7 results for general beam elements do not include von Mises stress due to approximation to torsional shear stress. For a non-circular cross-section, torsional shear stress is approximated using parametric equations. For circular cross-sections, torsional shear stress is an exact solution and hence von Mises stress can be calculated accurately. |
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0.4 MB |
ST7-1.57.40.2 Principal Stress Calculation for Beams with Circular Section Strand7 calculates the principal stresses for beams of circular cross-sections only. The stress components included in this calculation are: Fibre stress, which includes axial stress, and bending stresses in planes 1 and 2 (zz); Shear stress due to torque (xy). Shear stress in plane 1 (xz); Shear stress in plane 2 (yz). For the Pipe type element, Strand7 includes two additional stress components: Pipe radial stress (RR); Pipe hoop stress (). The principal stress... |
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2.2 MB |
ST7-1.57.40.5 Transverse Shear Stress in Plate Elements Transverse shear refers to the internal shearing force that develops on a plane perpendicular to the plate surface, due to out-of-plane loading on the plate (e.g. a plate with normal pressure). It is analogous to the shear force found in beam elements loaded in bending. A scissor cutting through paper is an extreme example of transverse shearing action on the paper. Transverse shear force is reported in units of force per width of plate element (e.g. N/mm) and produces a shear stress through... |
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0.6 MB |
ST7-1.70.100.3 Solver Restart Files This Webnote examines the options and the handling of solver restart files. Three types of solver restart files are available depending on the type of solver considered: Static Restart Files (.SRF), generated by the Nonlinear Static solver; Quasi Static Restart Files (.QRF), generated by the Quasi Static solver; and Dynamic Restart Files (.DRF), generated by the Nonlinear Transient Dynamic solver. |
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1.3 MB |
ST7-1.70.20.1 Extracting Forces and Moments from a Brick Mesh Brick elements are able to model thick structures with more accuracy than plate or beam elements. This is especially true at thick details and where parts join; beams and plates would overlap and not represent the true attachment well. However, beam and plate elements give force output which is usually easier to interpret for design purposes. This Webnote covers two approaches for extracting forces and moments from brick meshes. The simple cantilever brick mesh shown at right has a moment (1000... |
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0.6 MB |
ST7-1.70.70.1 Moment-Curvature Beam with Thermal Gradient Applied When a moment-curvature nonlinear beam is used in conjunction with an applied beam thermal gradient, validating the moment-curvature relationship requires the consideration of the stress-free thermal curvature strain. The beam used in this example is shown below. It has a point load, thermal gradient, and support applied. The support is to stabilise the solution past the point of ultimate moment by providing an alternative load path after perfectly plastic hinging occurs. The total curvature... |
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