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ABAQUS Theory Manual

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ABAQUS Theory Manual 0-1 ADAMS is a registered United States trademark of Mechanical Dynamics, Inc. ADAMS/Flex and ADAMS/View are trademarks of Mechanical Dynamics, Inc. CATIA is a registered trademark of Dassault Systémes. C-MOLD is a registered trademark of Advanced CAE Technology, Inc., doing business as C-MOLD. Compaq Alpha is registered in the U.S. Patent and Trademark Office. FE-SAFE is a trademark of Safe Technology, Ltd. Fujitsu, UXP, and VPP are registered trademarks of Fujitsu Limit
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  ABAQUS Theory ManualABAQUS Theory Manual 0-1  ADAMS is a registered United States trademark of Mechanical Dynamics, Inc.ADAMS/Flex and ADAMS/View are trademarks of Mechanical Dynamics, Inc.CATIA is a registered trademark of Dassault Systémes.C-MOLD is a registered trademark of Advanced CAE Technology, Inc., doing business as C-MOLD.Compaq Alpha is registered in the U.S. Patent and Trademark Office.FE-SAFE is a trademark of Safe Technology, Ltd.Fujitsu, UXP, and VPP are registered trademarks of Fujitsu Limited.Hewlett-Packard, HP-GL, and HP-GL/2 are registered trademarks of Hewlett-Packard Co.Hitachi is a registered trademark of Hitachi, Ltd.IBM RS/6000 is a trademark of IBM.Intel is a registered trademark of the Intel Corporation. NEC is a trademark of the NEC Corporation.PostScript is a registered trademark of Adobe Systems, Inc.Silicon Graphics is a registered trademark of Silicon Graphics, Inc.SUN is a registered trademark of Sun Microsystems, Inc. TEX is a trademark of the American Mathematical Society.UNIX and Motif are registered trademarks and X Window System is a trademark of The Open Groupin the U.S. and other countries.Windows NT is a registered trademark of the Microsoft Corporation.ABAQUS/CAE incorporates portions of the ACIS software by SPATIAL TECHNOLOGY INC. ACISis a registered trademark of SPATIAL TECHNOLOGY INC.This release of ABAQUS on Windows NT includes the diff program obtained from the Free SoftwareFoundation. You may freely distribute the diff program and/or modify it under the terms of the GNULibrary General Public License as published by the Free Software Foundation, Inc., 59 Temple Place,Suite 330, Boston, MA 02111-1307 USA.This release of ABAQUS/CAE includes lp_solve, a simplex-based code for linear and integer  programming problems by Michel Berkelaar of Eindhoven University of Technology, Eindhoven, the Netherlands.Python, copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands. AllRights Reserved. Permission to use, copy, modify, and distribute the Python software and itsdocumentation for any purpose and without fee is hereby granted, provided that the above copyrightnotice appear in all copies and that both that copyright notice and this permission notice appear insupporting documentation, and that the names of Stichting Mathematisch Centrum or CWI or ADAMS is a registered United States trademark of Mechanical Dynamics, Inc.ADAMS/Flex and ADAMS/View are trademarks of Mechanical Dynamics, Inc.CATIA is a registered trademark of Dassault Systémes.C-MOLD is a registered trademark of Advanced CAE Technology, Inc., doing business as C-MOLD.Compaq Alpha is registered in the U.S. Patent and Trademark Office.FE-SAFE is a trademark of Safe Technology, Ltd.Fujitsu, UXP, and VPP are registered trademarks of Fujitsu Limited.Hewlett-Packard, HP-GL, and HP-GL/2 are registered trademarks of Hewlett-Packard Co.Hitachi is a registered trademark of Hitachi, Ltd.IBM RS/6000 is a trademark of IBM.Intel is a registered trademark of the Intel Corporation. NEC is a trademark of the NEC Corporation.PostScript is a registered trademark of Adobe Systems, Inc.Silicon Graphics is a registered trademark of Silicon Graphics, Inc.SUN is a registered trademark of Sun Microsystems, Inc. TEX is a trademark of the American Mathematical Society.UNIX and Motif are registered trademarks and X Window System is a trademark of The Open Groupin the U.S. and other countries.Windows NT is a registered trademark of the Microsoft Corporation.ABAQUS/CAE incorporates portions of the ACIS software by SPATIAL TECHNOLOGY INC. ACISis a registered trademark of SPATIAL TECHNOLOGY INC.This release of ABAQUS on Windows NT includes the diff program obtained from the Free SoftwareFoundation. You may freely distribute the diff program and/or modify it under the terms of the GNULibrary General Public License as published by the Free Software Foundation, Inc., 59 Temple Place,Suite 330, Boston, MA 02111-1307 USA.This release of ABAQUS/CAE includes lp_solve, a simplex-based code for linear and integer  programming problems by Michel Berkelaar of Eindhoven University of Technology, Eindhoven, the Netherlands.Python, copyright 1991-1995 by Stichting Mathematisch Centrum, Amsterdam, The Netherlands. AllRights Reserved. Permission to use, copy, modify, and distribute the Python software and itsdocumentation for any purpose and without fee is hereby granted, provided that the above copyrightnotice appear in all copies and that both that copyright notice and this permission notice appear insupporting documentation, and that the names of Stichting Mathematisch Centrum or CWI or  0-2  Corporation for National Research Initiatives or CNRI not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission.All other brand or product names are trademarks or registered trademarks of their respectivecompanies or organizations.Corporation for National Research Initiatives or CNRI not be used in advertising or publicity pertaining to distribution of the software without specific, written prior permission.All other brand or product names are trademarks or registered trademarks of their respectivecompanies or organizations. 0-3  General conversion factors (to five significant digits)QuantityU.S. unitSI equivalent Length1 in0.025400 m1 ft0.30480 m1 mile1609.3 mArea1 in 2 0.64516 ´ 10 -3 m 2 1 ft 2 0.092903 m 2 1 acre4046.9 m 2 Volume1 in 3 0.016387 ´ 10 -3 m 3 1 ft 3 0.028317 m 3 1 US gallon3.7854 ´ 10 -3 m 3 Conversion factors for stress analysisQuantityU.S. unitSI equivalent Density1 slug/ft 3 = 1 lbf s 2 /ft 4 515.38 kg/m 3 1 lbf s 2 /in 4 10.687 ´ 10 6 kg/m 3 Energy1 ft lbf1.3558 J (N m)Force1 lbf 4.4482 N (kg m/s 2 )Mass1 slug = 1 lbf s 2 /ft14.594 kg (N s 2 /m)1 lbf s 2 /in175.13 kgPower1 ft lbf/s1.3558 W (N m/s)Pressure, Stress1 psi (lbf/in 2 )6894.8 Pa (N/m 2 ) Conversion factors for heat transfer analysisQuantityU.S. unitSI equivalent Conductivity1 Btu/ft hr °F1.7307 W/m °C1 Btu/in hr °F20.769 W/m °CDensity1 lbm/in 3 27680. kg/m 3 Energy1 Btu1055.1 JHeat flux density1 Btu/in 2 hr454.26 W/m 2 Power1 Btu/hr0.29307 WSpecific heat1 Btu/lbm °F4186.8 J/kg °CTemperature1 °F5/9 °CTemp °F9/5 ´ Temp °C + 32°9/5 ´ Temp °K - 459.67° Important constantsConstantU.S. unitSI unit Absolute zero-459.67 °F-273.15 °CAcceleration of gravity32.174 ft/s 2 9.8066 m/s 2 Atmospheric pressure14.694 psi0.10132 ´ 10 6 PaStefan-Boltzmannconstant0.1714 ´ 10 -8 Btu/hr ft 2 °R  4 5.669 ´ 10 -8 W/m 2 °K  4 where °R = °F + 459.67where °K = °C + 273.15 Approximate properties of mild steel at room temperatureQuantityU.S. unitSI unit Conductivity28.9 Btu/ft hr °F50 W/m °C2.4 Btu/in hr °FDensity15.13 slug/ft 3 (lbf s 2 /ft 4 )7800 kg/m 3 0.730 ´ 10 -3 lbf s 2 /in 4 General conversion factors (to five significant digits)QuantityU.S. unitSI equivalent Length1 in0.025400 m1 ft0.30480 m1 mile1609.3 mArea1 in 2 0.64516 ´ 10 -3 m 2 1 ft 2 0.092903 m 2 1 acre4046.9 m 2 Volume1 in 3 0.016387 ´ 10 -3 m 3 1 ft 3 0.028317 m 3 1 US gallon3.7854 ´ 10 -3 m 3 Conversion factors for stress analysis   QuantityU.S. unitSI equivalent Density1 slug/ft 3 = 1 lbf s 2 /ft 4 515.38 kg/m 3 1 lbf s 2 /in 4 10.687 ´ 10 6 kg/m 3 Energy1 ft lbf1.3558 J (N m)Force1 lbf 4.4482 N (kg m/s 2 )Mass1 slug = 1 lbf s 2 /ft14.594 kg (N s 2 /m)1 lbf s 2 /in175.13 kgPower1 ft lbf/s1.3558 W (N m/s)Pressure, Stress1 psi (lbf/in 2 )6894.8 Pa (N/m 2 ) Conversion factors for heat transfer analysisQuantityU.S. unitSI equivalent Conductivity1 Btu/ft hr °F1.7307 W/m °C1 Btu/in hr °F20.769 W/m °CDensity1 lbm/in 3 27680. kg/m 3 Energy1 Btu1055.1 JHeat flux density1 Btu/in 2 hr454.26 W/m 2 Power1 Btu/hr0.29307 WSpecific heat1 Btu/lbm °F4186.8 J/kg °CTemperature1 °F5/9 °CTemp °F9/5 ´ Temp °C + 32°9/5 ´ Temp °K - 459.67° Important constantsConstantU.S. unitSI unit Absolute zero-459.67 °F-273.15 °CAcceleration of gravity32.174 ft/s 2 9.8066 m/s 2 Atmospheric pressure14.694 psi0.10132 ´ 10 6 PaStefan-Boltzmannconstant0.1714 ´ 10 -8 Btu/hr ft 2 °R  4 5.669 ´ 10 -8 W/m 2 °K  4 where °R = °F + 459.67where °K = °C + 273.15 Approximate properties of mild steel at room temperatureQuantityU.S. unitSI unit Conductivity28.9 Btu/ft hr °F50 W/m °C2.4 Btu/in hr °FDensity15.13 slug/ft 3 (lbf s 2 /ft 4 )7800 kg/m 3 0.730 ´ 10 -3 lbf s 2 /in 4 0-4
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