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ST7-1.20 Nonlinear

ST7-1.20.10 Nonlinear / Statics

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ST7-1.20.10.1 Nonlinear Elastic and Inelastic Buckling of a Column
This Webnote will cover the following topics: Comparison of a linear buckling analysis with a nonlinear buckling and post-buckling analysis. Comparison of the nonlinear buckling results between the original model and a model containing geometric imperfections corresponding to the initial linear buckling analysis. The effects of material nonlinearity in a post-buckling analysis.  A comparison is to be made of the buckling and post-buckling behaviour of a column subject to axial compression....

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ST7-1.20.10.2 Nonlinear Analysis Basics
This Webnote presents a simple overview of some of the basic concepts of nonlinear analysis: iteration, load increments, convergence and residual forces. Most nonlinear problems are solved by an iterative numerical procedure, which needs to converge before results can be interpreted or assessed. For problems with significant nonlinearity, the load is usually applied progressively instead of all at once. Alternatively, the automatic load stepping option can be used (set in the Solver Defaults)....

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ST7-1.20.10.3 Defining Nonlinear Static Load Increments
Each solver type has different requirements concerning the application of load. Open the nonlinear static solver with Solvers/Nonlinear Static. Click the Load Increments button.  The load increments dialog will appear blank as shown at right.  Click the Add button a few times. Note that the Include column is critical. If any load or freedom cases are to be excluded from the analysis you can deselect the Include option for that row. For a load case row this is equivalent to setting...

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ST7-1.20.10.4 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.

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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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ST7-1.20.10.9 The Nonlinear Convergence Graph
This Webnote examines the nonlinear convergence graph available in the nonlinear solver window. The graph is the visual representation of the solver convergence history, and is available in the nonlinear solvers.
ST7-1.20.20 Nonlinear / Dynamics

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ST7-1.20.20.1 Modelling the Impact of a Mass on a Plate
This document outlines the procedures required to model the impact of a mass with an initial velocity impacting on a plate. The initial example model is a flat plate 1 m ( 1 m. A mass of 500 kg is located 0.3 m above the surface. It is travelling at 20 m/s. The deflections and stresses of the plate are required during and after impact. Here the flat plate is modelled using plate/shell elements; point contact elements are used to connect the mass to the plates.

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ST7-1.20.20.2 Modelling the Impact of a Mass on a Tube
This document outlines the steps required to model dynamic impact of a mass with a metallic tube. The modelling is only concerned with the behaviour of the impacted structure, and as such the mass is modelled as a rigid body. The critical region of the model is shown on the right. The mass of the impactor is modelled using the translational mass nodal attribute. Zero Gap point contact elements are used to simulate contact between the impactor and the structure. To create a cluster of contacts...

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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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ST7-1.20.20.6 Using the Equation Editor to Define Factor vs Time Tables
This Webnote examines the definition of Factor vs Time tables using the Equation Editor. The Equation Editor is a powerful tool when creating time histories based on equations. It offers the flexibility of defining tables in segments, using multiple equations in sequence.

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ST7-1.20.20.7 Cable Sag and Natural Frequency
This Webnote presents a parametric study of the relationship between the natural frequency of a cable and its degree of sag. As a cable is tensioned, generally the natural frequency will increase. Due to variability in cable installation tension (as well as thermal expansion), it is important to understand the range of natural frequencies produced for a given range of tension. A steel cable of 240 m in length with a diameter of 80 mm is pinned on both ends but is held axially with a 20 kN/mm stiffness...

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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...
ST7-1.20.40 Nonlinear / Material

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ST7-1.20.40.1 Scaling Elastic Modulus and Yield Strength with Temperature
Many structural simulations involve parts which have a temperature variation. If the changes in temperature are great enough, the mechanical properties of the material will change. Examples include structures subjected to fire, welding, hydration of concrete, power generation systems and high temperature engine components. Strand7 allows for the modification of several material parameters with temperature: Modulus, Yield Strength, Coefficient of Thermal Expansion, Thermal Capacitance and Thermal...

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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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ST7-1.20.40.4 Varying Modulus with Time and Temperature Elastic and Plastic
The modulus of elasticity can be modified with respect to time and/or temperature by applying a Factor vs Time (or vs Temperature) table in the material property Tables tab. These two options give quite different results based on both the changing load and the changing modulus. With the Elastic option, the Factor vs Time (or vs Temperature) table associated with the modulus establishes the total displacement for the total load at a particular instant. In a constant loading situation, displacements...

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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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ST7-1.20.40.8 Strand7 Soil Models
Strand7 offers five different soil material models for 2D plane strain, axisymmetric and 3D analysis: Linear Elastic Soil Mohr-Coulomb Soil Drucker-Prager Soil Duncan-Chang Soil Modified Cam-Clay Soil All of the soil models consider the effects of fluid content (e.g. water), void ratio, and in-situ stress. Soil models require a range of parameters to characterise their behaviour; this is illustrated in the following sections. The Linear Elastic Soil model is an isotropic soil material...

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ST7-1.20.40.9 Fluid Level in Soil Models
Soil in a natural state contains voids between grains that are filled by air and fluid such as water. The fluid can greatly affect the in-situ stress state of the soil by adding mass and pressure to the soil strata. Trapped fluid in soil can also influence the stress in the soil skeleton under external loads by sharing a portion of the loads with the soil skeleton. Depending on the fluid content, the soil can be approximated with one of two limit situations: saturated or unsaturated. ...

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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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ST7-1.20.40.12 CEB-FIP MC 90 Concrete Creep and Shrinkage
The basic creep and shrinkage formulation in the CEB-FIP Model Code 90 utilises the hyperbolic law. This formulation can be directly entered into Strand7 using the Concrete Creep and Shrinkage Hyperbolic Law creep option. This document illustrates the process of extracting the required factors from the CEB-FIP Model Code 90 for concrete creep and shrinkage and entering them into Strand7. In this section the calculation procedure for the concrete material parameters is examined. where ...

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ST7-1.20.40.13 ACI-209 Concrete Creep and Shrinkage
The basic creep and shrinkage formulation in ACI-209 utilises the hyperbolic law. This formulation can be entered directly into Strand7 using the Concrete Creep and Shrinkage Hyperbolic Law creep option. This Webnote illustrates the process of extracting the required factors from ACI-209 for concrete creep and shrinkage and entering them into Strand7. In this section the calculation procedure for the concrete material parameters is examined. The second material parameter considered is the...

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ST7-1.20.40.14 AS 3600-2009 Concrete Creep and Shrinkage
This Webnote illustrates the process of extracting the required factors from AS3600-2009 for concrete creep and shrinkage effects and entering them into Strand7. The basic creep formulation in AS3600-2009 utilises the hyperbolic law. In this section the calculation procedure of concrete material parameters is examined. The next material parameter considered is the density of the concrete, . The third material parameter considered is the elastic modulus of the concrete at any time, Ecj. = 1.5 0.043 ...

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ST7-1.20.40.15 AASHTO Concrete Creep and Shrinkage
This Webnote illustrates the process of extracting the required factors from the AASHTO LRFD Design Specifications (AASHTO LRFD) for concrete creep and shrinkage and entering them into Strand7. The basic creep and shrinkage formulation in AASHTO LRFD Bridge Design Specifications utilises the hyperbolic law with time-dependent factors. This formulation can be directly entered into Strand7 using the Concrete Creep and Shrinkage User Defined option. Article 5.4.2.3.1 of AASHTO LRFD Bridge...

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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. ...
ST7-1.20.50 Nonlinear / Geometry

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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...
ST7-1.20.60 Nonlinear / Construction Sequence

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ST7-1.20.60.1 Construction Sequence Analysis
Strand7 allows the modelling of construction sequence scenarios with sophisticated construction sequence tools. These tools have been designed to allow the user to easily model a staged construction such as a multi-storey building, a cable stay bridge, a staged excavation, a tunnel, an in-ground water tank, etc.  For many structures it is important to understand how the structure will behave during its construction. The entire construction, excavation or deconstruction process can be simulated...

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ST7-1.20.60.2 Soil In-Situ Stress in Construction Sequence Analysis
Construction sequence analysis involving soil requires the consideration of the soil in-situ stress state in each of the defined analysis stages. When adding soil in a subsequent stage of a staged analysis (i.e. soil that is not present in the initial stage), the in-situ stress distribution of the added soil needs to be pre-computed. One minor consideration that may affect the results interpretation when adding soil is that existing soil can displace during the construction stage, before the new...

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ST7-1.20.60.3 Applying Pre Strain Attributes in Construction Sequence Analysis
This Webnote explores the handling of the element pre strain attribute in construction sequence (staged) analysis. In a staged analysis, the dimensions of an element at the beginning of a stage may be different to the as modelled mesh dimensions. The "initial" dimension depends on the Morph setting in the element's birth stage and the morphed element dimensions, which in turn affect the amount of contraction or expansion resulting from a pre strain attribute.
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