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Abaqus Analysis User’s Manual Abaqus Version 6.10 ID: Printed on: Abaqus Analysis User’s Manual Volume V Abaqus Version 6.10 ID: Printed on: Legal Notices CAUTION: This documentation is intended for qualifi ed users who will exercise sound engineering judgment and expertise in the use of the Abaqus Software. The Abaqus Software is inherently complex, and the examples and procedures in this documentation are not intended to be exhaustive or to apply to any particular situation. Users are cautioned to satisfy themselves as to the accuracy and results of their analyses. Dassault Systmes and its subsidiaries, including Dassault Systmes Simulia Corp., shall not be responsible for the accuracy or usefulness of any analysis performed using the Abaqus Software or the procedures, examples, or explanations in this documentation. Dassault Systmes and its subsidiaries shall not be responsible for the consequences of any errors or omissions that may appear in this documentation. The Abaqus Software is available only under license from Dassault Systmes or its subsidiary and may be used or reproduced only in accordance with the terms of such license. This documentation is subject to the terms and conditions of either the software license agreement signed by the parties, or, absent such an agreement, the then current software license agreement to which the documentation relates. This documentation and the software described in this documentation are subject to change without prior notice. No part of this documentation may be reproduced or distributed in any form without prior written permission of Dassault Systmes or its subsidiary. The Abaqus Software is a product of Dassault Systmes Simulia Corp., Providence, RI, USA. Dassault Systmes, 2010 Abaqus, the 3DS logo, SIMULIA, CATIA, and Unifi ed FEA are trademarks or registered trademarks of Dassault Systmes or its subsidiaries in the United States and/or other countries. Other company, product, and service names may be trademarks or service marks of their respective owners.For additional information concerningtrademarks,copyrights,andlicenses,seetheLegalNoticesintheAbaqus6.10ReleaseNotesandthenoticesat: Abaqus Version 6.10 ID: Printed on: Locations SIMULIA Worldwide HeadquartersRising Sun Mills, 166 Valley Street, Providence, RI 02909–2499, Tel: +1 401 276 4400, Fax: +1 401 276 4408, simulia.support@ SIMULIA European HeadquartersGaetano Martinolaan 95, P. O. 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China, Tel: +8621 3856 8000, .support@ Czech the default variation depends on the procedure chosen, as shown in “Procedures: overview,” Section 6.1.1. In Abaqus/Standard the variation of many prescribed conditions can be defi ned in user subroutines. In this case the magnitude of the variable can vary in any way with position and time. The magnitude variation for prescribing and removing conditions must be specifi ed in the subroutine (see “User subroutines and utilities,” Section 15.1”). In Abaqus/Explicit if no amplitude is referenced from the boundary condition or loading defi nition, the total value will be applied instantaneously at the start of the step and will remain constant throughout the step (a “step” variation), although Abaqus/Explicit does not admit jumps in displacement (see “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 30.3.1). If no amplitude is referenced from a predefi ned fi eld defi nition, the total magnitude will vary linearly over the step from the value at the end of the previous step (or from zero at the start of the analysis) to the magnitude given (a “ramp” variation). When boundary conditions are removed (see “Boundary conditions in Abaqus/Standard and Abaqus/Explicit,” Section 30.3.1), the boundary condition (displacement or rotation constraint in stress/displacement analysis) is converted to an applied conjugate fl ux (force or moment in stress/displacement analysis) at the beginning of the step. This fl ux magnitude is set to zero with a “step” or “ramp” variation depending on the procedure chosen, as discussed in “Procedures: overview,” Section 6.1.1. Similarly, when loads and predefi ned fi elds are removed, the load is set to zero and the predefi ned fi eld is set to its initial value. In Abaqus/CFD if no amplitude is referenced from the boundary or loading condition, the total value is applied instantaneously at the start of the step and remains constant throughout the step. Abaqus/CFD does admit jumps in the velocity, temperature, etc. from the end value of the previous step to the magnitude given in the current step. However, jumps in velocity boundary conditions may result in a divergence-free projection that adjusts the initial velocities to be consistent with the prescribed boundary conditions in order to defi ne a well-posed incompressible fl ow problem. Applying boundary conditions and loads in a local coordinate system You can defi ne a local coordinate system at a node as described in “Transformed coordinate systems,” Section 2.1.5. Then, all input data for concentrated force and moment loading and for displacement and rotation boundary conditions are given in the local system. Loads and predefined fields available for various procedures Table 30.1.1–1 Available loads and predefi ned fi elds. Loads and predefined fieldsProcedures Added mass (concentrated and distributed) Abaqus/Aqua eigenfrequency extraction analysis (“Natural frequency extraction,” Section 6.3.5) 30.1.1–2 Abaqus Version 6.10 ID: Printed on: PRESCRIBED CONDITIONS Loads and predefined fieldsProcedures Procedures based on eigenmodes: “Transient modal dynamic analysis,” Section 6.3.7 “Mode-based steady-state dynamic analysis,” Section6.3.8 “Response spectrum analysis,” Section 6.3.10 Base motion “Random response analysis,” Section 6.3.11 Boundary condition with a nonzero prescribed boundary All procedures except those based on eigenmodes Connector motion Connector load All relevant procedures except modal extraction, buckling, those based on eigenmodes, and direct steady-state dynamics Cross-correlation property“Random response analysis,” Section 6.3.11 Current density (concentrated and distributed) “Coupled thermal-electrical analysis,” Section 6.7.2 Electric charge (concentrated and distributed) “Piezoelectric analysis,” Section 6.7.3 Equivalent pressure stress“Mass diffusion analysis,” Section 6.9.1 Film coeffi cient and associated sink temperature All procedures involving temperature degrees of freedom Fluid fl ux Analysis involving hydrostatic fl uid elements Fluid mass fl ow rateAnalysis involving convective heat transfer elements Flux (concentrated and distributed)All procedures involving temperature degrees of freedom “Mass diffusion analysis,” Section 6.9.1 Force and moment (concentrated and distributed) All procedures with displacement degrees of freedom except response spectrum Incident wave loadingDirect-integration dynamic analysis (“Implicit dynamic analysis using direct integration,” Section 6.3.2) involving solid and/or fl uid elements undergoing shock loading Predefi ned fi eld variableAll procedures except those based on eigenmodes Seepage coeffi cient and associated sink pore pressure Distributed seepage fl ow “Coupled pore fl uid diffusion and stress analysis,” Section 6.8.1 30.1.1–3 Abaqus Version 6.10 ID: Printed on: PRESCRIBED CONDITIONS Loads and predefined fieldsProcedures Substructure loadAll procedures involving the use of substructures Temperature as a predefi ned fi eldAll procedures except adiabatic analysis, mode-based procedures, and procedures involving temperature degrees of freedom With the exception of concentrated added mass and distributed added mass, no loads can be applied in eigenfrequency extraction analysis. 30.1.1–4 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES 30.1.2AMPLITUDE CURVES Products:Abaqus/StandardAbaqus/ExplicitAbaqus/CFDAbaqus/CAE References • “Prescribed conditions: overview,” Section 30.1.1 •*AMPLITUDE • Chapter 55, “The Amplitude toolset,” of the Abaqus/CAE User’s Manual Overview An amplitude curve: • allows arbitrary time (or frequency) variations of load, displacement, and other prescribed variables to be given throughout a step (using step time) or throughout the analysis (using total time); • can be defi ned as a mathematical function (such as a sinusoidal variation), as a series of values at points in time (such as a digitized acceleration-time record from an earthquake), as a user-customized defi nition via user subroutines, or, in Abaqus/Standard, as values calculated based on a solution-dependent variable (such as the maximum creep strain rate in a superplastic forming problem); and • can be referred to by name by any number of boundary conditions, loads, and predefi ned fi elds. Amplitude curves By default, the values of loads, boundary conditions, and predefi ned fi elds either change linearly with time throughoutthestep(rampfunction)ortheyare appliedimmediatelyandremainconstantthroughout the step (step function)—see “Procedures: overview,” Section 6.1.1. Many problems require a more elaborate defi nition, however. For example, different amplitude curves can be used to specify time variations for different loadings. One common example is the combination of thermal and mechanical load transients: usually the temperatures and mechanical loads have different time variations during the step. Different amplitude curves can be used to specify each of these time variations. Other examples include dynamic analysis under earthquake loading, where an amplitude curve can be used to specify the variation of acceleration with time, and underwater shock analysis, where an amplitude curve is used to specify the incident pressure profi le. Amplitudes are defi nedas modeldata (i.e., theyare not stepdependent). Eachamplitude curve must be named; this name is then referred to from the load, boundary condition, or predefi ned fi eld defi nition (see “Prescribed conditions: overview,” Section 30.1.1). Input File Usage: *AMPLITUDE, NAME=name Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Name:name 30.1.2–1 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES Defining the time period Each amplitude curve is a function of time or, for the steady-state dynamics procedure, a function of frequency (see “Direct-solution steady-state dynamic analysis,” Section 6.3.4, and “Mode-based steady- state dynamic analysis,” Section 6.3.8). Amplitudes defi ned as functions of time can be given in terms of step time (default) or in terms of total time. These time measures are defi ned in “Conventions,” Section 1.2.2. Input File Usage:Use one of the following options: *AMPLITUDE, NAME=name, TIME=STEP TIME (default) *AMPLITUDE, NAME=name, TIME=TOTAL TIME Abaqus/CAE Usage:Load or Interaction module:Create Amplitude: any type:Time span: Step timeorTotal time Continuation of an amplitude reference in subsequent steps Ifaboundarycondition,load,orpredefi nedfi eldreferstoanamplitudecurveandtheprescribedcondition is not redefi ned in subsequent steps, the following rules apply: • If the associated amplitude was given in terms of total time, the prescribed condition continues to follow the amplitude defi nition. • If no associated amplitude was given or if the amplitude was given in terms of step time, the prescribed condition remains constant at the magnitude associated with the end of the previous step. Specifying relative or absolute data You can choose between specifying relative or absolute magnitudes for an amplitude curve. Relative data By default, you give the amplitude magnitude as a multiple (fraction) of the reference magnitude given in the prescribed condition defi nition. This method is especially useful when the same variation applies to different load types. Input File Usage: *AMPLITUDE, NAME=name, VALUE=RELATIVE Abaqus/CAE Usage:Amplitude magnitudes are always relative in Abaqus/CAE. Absolute data Alternatively, you can give absolute magnitudes directly. When this method is used, the values given in the prescribed condition defi nitions will be ignored. Absolute amplitude values should generally not be used to defi ne temperatures or predefi ned fi eld variables for nodes attached to beam or shell elements as values at the reference surface together with the gradient or gradients across the section (default cross-section defi nition; see “Using a beam section integrated during the analysis to defi ne the section behavior,” Section 26.3.6, and “Using a shell section 30.1.2–2 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES integrated during the analysis to defi ne the section behavior,” Section 26.6.5). Because the values given intemperaturefi eldsandpredefi nedfi eldsareignored, theabsoluteamplitude valuewillbeusedtodefi ne both the temperature and the gradient and fi eld and gradient, respectively. Input File Usage: *AMPLITUDE, NAME=name, VALUE=ABSOLUTE Abaqus/CAE Usage:Absolute amplitude magnitudes are not supported in Abaqus/CAE. Defining the amplitude data The variation of an amplitude with time can be specifi ed in several ways. The variation of an amplitude with frequency can be given only in tabular or equally spaced form. Defining tabular data Choose the tabular defi nition method (default) to defi ne the amplitude curve as a table of values at convenient points on the time scale. Abaqus interpolates linearly between these values, as needed. By default in Abaqus/Standard, if the time derivatives of the function must be computed, some smoothing is applied at the time points where the time derivatives are discontinuous. In contrast, in Abaqus/Explicit no default smoothing is applied (other than the inherent smoothing associated with a fi nite time increment). You can modify the default smoothing values (smoothing is discussed in more detail below, under the heading “Using an amplitude defi nition with boundary conditions”); alternatively, a smooth step amplitude curve can be defi ned (see “Defi ning smooth step data” below). Iftheamplitudevariesrapidly—aswiththegroundaccelerationinanearthquake, forexample—you mustensurethatthetimeincrementusedintheanalysisissmallenoughtopickuptheamplitudevariation accurately since Abaqus will sample the amplitude defi nition only at the times corresponding to the increments being used. If the analysis time in a step is less than the earliest time for which data exist in the table, Abaqus applies the earliest value in the table for all step times less than the earliest tabulated time. Similarly, if the analysis continues for step times past the last time for which data are defi ned in the table, the last value in the table is applied for all subsequent time. Several examples of tabular input are shown in Figure 30.1.2–1. Input File Usage: *AMPLITUDE, NAME=name, DEFINITION=TABULAR Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Tabular Defining equally spaced data Choose the equally spaced defi nition method to give a list of amplitude values at fi xed time intervals beginning at a specifi ed value of time. Abaqus interpolates linearly between each time interval. You must specify the fi xed time (or frequency) interval at which the amplitude data will be given,. You can also specify the time (or lowest frequency) at which the fi rst amplitude is given,; the default is =0.0. If the analysis time in a step is less than the earliest time for which data exist in the table, Abaqus applies the earliest value in the table for all step times less than the earliest tabulated time. Similarly, 30.1.2–3 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES 1.0 1.0 0.0 1.0 1.0 0.0 1.00.0 Relative load magnitude Relative load magnitude Relative load magnitude Time period a. Uniformly increasing load b. Uniformly decreasing load c. Variable load 1.0 Amplitude Table: Time Relative load 1.0 0.0 1.0 0.0 1.0 0.01.0 0.0 0.0 0.4 0.6 0.8 1.0 0.0 1.2 0.5 0.5 0.0 Time period Time period Figure 30.1.2–1 Tabular amplitude defi nition examples. if the analysis continues for step times past the last time for which data are defi ned in the table, the last value in the table is applied for all subsequent time. Input File Usage: *AMPLITUDE, NAME=name, DEFINITION=EQUALLY SPACED, FIXED INTERVAL=, BEGIN= Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Equally spaced:Fixed interval: The time (or lowest frequency) at which the fi rst amplitude is given,, is indicated in the fi rst table cell. 30.1.2–4 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES Defining periodic data Choose the periodic defi nition method to defi ne the amplitude, a, as a Fourier series: for for where, N,,,, and, , are user-defi ned constants. An example of this form of input is shown in Figure 30.1.2–2. Input File Usage: *AMPLITUDE, NAME=name, DEFINITION=PERIODIC Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Periodic p p = 0.2s a = A0 + Σ [An cos nω(t−t0) + Bn sin nω(t−t0)] for t ≥ t0 a = A0 for t t0 a = A0 A0= 1.0, A = 2.0, ω1 = 10π, ω2 = 20π, t0 = .2 with Time( x 10-1) a for t ≤ t0 Figure 30.1.2–3 Modulated amplitude defi nition example. 30.1.2–6 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES Defining exponential decay Choose the exponential decay defi nition method to defi ne the amplitude, a, as for for where, A,, and are user-defi ned constants. An example of this form of input is shown in Figure 30.1.2–4. Input File Usage: *AMPLITUDE, NAME=name, DEFINITION=DECAY Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Decay 0 1 2 3 4 102345678910 5 Time a ( x 10-1) a = A0 + A exp [−(t−t0)/td] for t ≥ t0 a = A0 for t < t0 A0 = 0.0, A = 5.0, t0 = 0.2, td = 0.2 with Figure 30.1.2–4 Exponential decay amplitude defi nition example. 30.1.2–7 Abaqus Version 6.10 ID: Printed on: AMPLITUDE CURVES Defining smooth step data Abaqus/Standard and Abaqus/Explicit can calculate amplitudes based on smooth step data. Choose the smooth step defi nition method to defi ne the amplitude, a, between two consecutive data points andas for where. The above function is such thatat,at, and the fi rst and second derivatives of a are zero atand . This defi nition is intended to ramp up or down smoothly from one amplitude value to another. The amplitude, a, is defi ned such that for for whereand are the fi rst and last data points, respectively. Examples of this form of input are shown in Figure 30.1.2–5 and Figure 30.1.2–6. This defi nition cannot be used to interpolate smoothly between a set of data points; i.e., this defi nition cannot be used to do curve fi tting. Input File Usage: *AMPLITUDE, NAME=name, DEFINITION=SMOOTH STEP Abaqus/CAE Usage:Load or Interaction module:Create Amplitude:Smooth step Defining a solution-dependent amplitude for superplastic forming analysis Abaqus/Standard can calculate amplitude values based on a solution-dependent variable. Choose the solution-dependent defi nition method to create a solution-dependent amplitude c

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